Method for measuring three-dimensional profile of inner surface of yixing teapot based on optical measurement

Abstract

The present application relates to the field of three-dimensional optical precision measurement, and discloses a three-dimensional profile measurement method for the inner cavity surface of a purple sand pot based on optical measurement. The method constructs a multi-band spectral light source system, projects a light beam to the inner cavity surface according to a preset sequence of incident angles, and synchronously collects multi-spectral interference fringe images and ambient light noise data. According to the correlation between image distortion and light noise, a surface phase shift atlas is generated, and the measurement area and the occluded area are divided based on phase continuity. Phase unwrapping and geometric calculation are performed on the complete area to generate an initial three-dimensional point cloud, the boundary information of the occluded area is fused to complete hole speculation and surface extension, and a preliminary three-dimensional profile model is constructed. The model is registered with a standard theoretical model to generate a surface profile deviation field and output a process analysis report. The present application realizes accurate identification of the occluded area of a complex inner cavity through phase topology analysis, and uses spatial analysis of the deviation field to enable the measurement result to directly guide production process improvement.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional optical precision measurement technology, specifically a method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement. Background Technology

[0002] Currently, structured light or laser scanning techniques are commonly used for 3D measurement of complex internal curved surfaces such as those found in Yixing teapots. These techniques reconstruct the 3D shape by projecting gratings or light stripes onto the object's surface and capturing its deformation images using a camera. However, in the complex structures of teapots, such as deep cavities and steep inner walls, the measurement beam is easily obstructed by the structure itself, resulting in large areas of shadow and missing phase information in the acquired striped images. Existing methods typically rely on the image's grayscale gradient or edge information to identify these obstructed areas. However, under conditions of weak surface texture and uneven reflection, such image feature-based identification methods are prone to failure, leading to inaccurate region segmentation and directly affecting the integrity of subsequent 3D reconstruction.

[0003] Conventional 3D measurement processes culminate in obtaining point cloud data or triangular mesh models of an object's surface. The measurement results are primarily used for dimensional verification or reverse modeling. This approach makes the measurement process relatively independent of subsequent manufacturing processes. Measurement reports typically only provide discrete dimensional errors or overall deviations, failing to clearly present the specific spatial distribution patterns of these deviations. Process engineers struggle to intuitively and quickly understand the morphology and location of product defects from massive amounts of point cloud data or simple error statistics, thus hindering the formation of direct and effective quantitative guidance for subsequent processes such as mold repair and molding. Summary of the Invention

[0004] The purpose of this invention is to provide a method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides a method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement, the method comprising:

[0006] A multi-band spectral light source system was constructed to project beams of specific wavelengths onto the inner surface of the target purple clay teapot at a preset incident angle sequence, thereby obtaining a multi-band interference fringe image formed by reflection from the inner surface, and simultaneously recording the real-time ambient light noise data corresponding to each incident angle.

[0007] Based on the correlation between the morphological distortion of the interference fringe image and the real-time ambient light noise data, a surface phase shift map is generated. Based on the phase continuity of different regions in the surface phase shift map, the complete measurement area and the occlusion area of ​​the inner cavity surface are identified and divided.

[0008] A pixel-by-pixel phase unwrapping operation is performed on the complete measurement area, and the wrapped phase is mapped to an absolute phase distribution field. Based on the geometric constraint relationship between the absolute phase distribution field and the known projection beam parameters, the initial three-dimensional point cloud data set of the inner cavity surface is generated point by point.

[0009] By fusing the boundary geometry information of the occluded area, hole inference and surface smoothing extension processing are performed on the initial 3D point cloud data set to form a complete preliminary 3D contour model.

[0010] The preliminary three-dimensional contour model is spatially registered with the theoretical three-dimensional model of the inner cavity of a standard Zisha teapot. The residual distribution of the registered preliminary three-dimensional contour model and the theoretical three-dimensional model in each spatial dimension is calculated to generate a surface contour deviation field. Based on the numerical characteristics and spatial distribution pattern of the surface contour deviation field, a measurement and analysis report is output to guide subsequent processes.

[0011] Preferably, the construction of the multi-band spectral light source system, which projects beams of specific wavelengths onto the inner surface of the target purple clay teapot at a preset incident angle sequence, includes:

[0012] Multiple solid-state light sources with independently modulated intensity and wavelength are configured to form a ring light source array, the axis of which coincides with the central axis of the mouth of the Zisha teapot;

[0013] Set up a beam combination containing at least three different center wavelengths, where each center wavelength corresponds to an independent measurement spectrum;

[0014] A set of incident angle sequences is predefined for each measurement spectral band, the incident angle sequences containing multiple discrete angle values ​​from grazing incidence to near normal incidence;

[0015] The control light source array works sequentially according to the order of the measurement spectrum segments. Within each measurement spectrum segment, the projection angle is switched sequentially according to its corresponding incident angle sequence.

[0016] Each time a beam is projected, a high-speed image sensor is synchronously triggered to capture an image of the reflected light field on the surface of the cavity at that moment;

[0017] Record the precise beam parameters corresponding to each image capture, including the current effective wavelength, the current incident angle, and the current beam intensity.

[0018] Preferably, the step of acquiring a multi-band interference fringe image formed by reflection from the inner cavity surface and simultaneously recording real-time ambient light noise data corresponding to each incident angle includes:

[0019] The raw image stream is received from the high-speed image sensor and classified and stored according to the measurement spectrum segment identifier and incident angle identifier in the beam parameters;

[0020] Background subtraction is performed on each classified image. The subtracted background is the environmental background image acquired without an active projection beam.

[0021] Extract the alternating bright and dark stripe pattern from the image after background subtraction, and define the alternating bright and dark stripe pattern as the interference fringe image formed under the current projection conditions;

[0022] Within each exposure time window for acquiring interference fringe images, ambient light intensity data is continuously sampled using an independent ambient light sensor;

[0023] Calculate the average value and fluctuation variance of the ambient light intensity data within the exposure time window, and record the average value and fluctuation variance together as the real-time ambient light noise data corresponding to this interference fringe image;

[0024] An index mapping relationship is established between the interference fringe image and its beam parameters and real-time ambient light noise data to form a multi-spectral interference image database with environmental labels.

[0025] Preferably, the step of generating a surface phase shift map based on the correlation between the morphological distortion degree of the interference fringe image and the real-time ambient light noise data includes:

[0026] For each interference fringe image in the multi-band interference image database, calculate its fringe contrast and fringe spatial frequency;

[0027] The calculated fringe contrast is compared with the illumination fluctuation variance in the corresponding real-time ambient light noise data. If the fluctuation variance exceeds a preset threshold, the grayscale value of the interference fringe image is corrected by variance-based weighted filtering.

[0028] A two-dimensional Fourier transform is performed on the corrected interference fringe image to extract the fundamental frequency components characterizing the surface height variation in the spatial frequency domain.

[0029] The fundamental frequency components are reconstructed into a complex amplitude image containing phase information through inverse Fourier transform.

[0030] The phase angle is extracted from the complex amplitude image to obtain a wrapped phase map, where each pixel value of the wrapped phase map represents the relative phase located in the interval from negative π to positive π.

[0031] The wrap-around phase maps obtained from all measurement spectral segments and all incident angles are weighted and fused according to their corresponding beam parameters to generate a comprehensive, highly redundant surface phase shift map. The phase value of each location point in the surface phase shift map is constrained by multiple independent measurement results.

[0032] Preferably, the step of identifying and delineating the complete measurement area and the occlusion area of ​​the inner cavity surface based on the phase continuity of different regions in the surface phase shift map includes:

[0033] Phase gradient calculations are performed on the surface phase shift map to obtain the phase change rate of each pixel in the row and column directions;

[0034] Set a phase continuity decision threshold, traverse the surface phase shift map, and mark the connected pixel regions whose phase change rate is less than the decision threshold in both the row and column directions as high confidence regions;

[0035] Pixels whose phase change rate in the row or column direction is greater than the decision threshold are marked as phase change points;

[0036] Using the phase abrupt change point as the boundary, the closed region enclosed by it, which has a gentle internal phase change but cannot be connected to the high confidence region, is marked as a potential occlusion region.

[0037] Analyze the phase value distribution pattern of potential occlusion areas. If the phase distribution shows irregular jumps or constant characteristics, it is finally confirmed as an occlusion area.

[0038] All regions in the surface phase shift map, except for the occluded regions, are uniformly defined as the complete measurement region, and binary mask images are generated for the complete measurement region and the occluded region respectively.

[0039] Preferably, the step of performing pixel-by-pixel phase unwrapping operation on the complete measurement region to map the wrapped phase into an absolute phase distribution field includes:

[0040] Load the binary mask image generated for the complete measurement area, and process only the pixels with true mask values;

[0041] Starting from a seed pixel within the complete measurement region of the surface phase shift map, the phase value of the seed pixel is set as the absolute phase zero.

[0042] A flood-fill algorithm is used to propagate phase unwrapping from the seed point to the surrounding neighboring pixels; during the propagation process, the wrapping phase difference between the current pixel and its neighboring pixels is calculated.

[0043] If the absolute value of the phase difference exceeds π, then add or subtract an integer multiple of 2π to the absolute phase of the adjacent pixel, so that the absolute value of the absolute phase difference between the current pixel and the adjacent pixel is less than or equal to π.

[0044] The number of integer multiples of two π added to or subtracted from each pixel is recorded; this number is called the phase transition order.

[0045] After traversing all pixels within the complete measurement area, two result data fields are generated: one is the absolute phase distribution field composed of the absolute phase values ​​of each pixel, and the other is the order distribution field composed of the phase transition orders of each pixel.

[0046] Preferably, the step of generating an initial three-dimensional point cloud data set of the inner cavity surface by solving point by point based on the geometric constraint relationship between the absolute phase distribution field and the known projection beam parameters includes:

[0047] A mapping model is established from the image pixel coordinate system to the object space coordinate system of the inner cavity of the Zisha teapot. The mapping model includes the intrinsic parameters of the image sensor, the extrinsic parameters of the multi-band spectral light source system, and the beam projection geometry.

[0048] For each pixel in the absolute phase distribution field, based on its absolute phase value, combined with the wavelength and incident angle in the beam parameters used to generate the phase value, the total optical path difference from the light source to the inner cavity surface point corresponding to the current pixel and then to the sensor is calculated.

[0049] Based on the principle of triangulation and the total optical path difference, the three-dimensional spatial coordinates of the inner cavity surface point corresponding to the current pixel point relative to the optical center of the sensor are calculated.

[0050] Simultaneously, the phase transition order corresponding to the current pixel is used to perform a consistency check on the calculated three-dimensional spatial coordinates. If the order difference of the neighboring points contradicts the calculated depth change trend, the local phase recalculation process is initiated.

[0051] The three-dimensional spatial coordinates, surface normal vector estimates, and reflectivity information from the original interference fringe image corresponding to all the verified pixels are combined to form the initial three-dimensional point cloud data set of the inner cavity surface.

[0052] The initial 3D point cloud dataset has missing data at spatial locations corresponding to the occluded areas.

[0053] Preferably, the fusion of the boundary geometry information of the occluded region is used to perform hole inference and surface smoothing extension processing on the initial 3D point cloud data set to form a complete preliminary 3D contour model, including:

[0054] Extract the boundary pixel coordinates of all occluded regions from the binary mask image of the occluded regions;

[0055] The boundary pixel coordinates of the occluded area are back-projected into three-dimensional space, and the corresponding boundary three-dimensional points are found in the initial three-dimensional point cloud data set.

[0056] Analyze the normal curvature and torsion of the three-dimensional points along the tangent of the boundary of the occluded region, and use the principles of differential geometry to predict the possible orientation of the surface within the occluded region.

[0057] Based on the inferred surface orientation, the minimum curvature change is used as a constraint to construct the Poisson surface reconstruction equation;

[0058] Solve the Poisson surface reconstruction equation to generate a triangular mesh surface that can smoothly connect the known 3D point cloud around the occluded region;

[0059] The triangular mesh surface is seamlessly stitched and fused with the initial three-dimensional point cloud data set to obtain a triangular mesh model with a continuous surface and no holes. The triangular mesh model is defined as a complete preliminary three-dimensional contour model.

[0060] Preferably, the step of spatially registering the preliminary three-dimensional contour model with the theoretical three-dimensional model of the standard purple clay teapot's inner cavity includes:

[0061] Key feature geometric elements are extracted from the theoretical three-dimensional model of the inner cavity of a standard Zisha teapot. These key feature geometric elements include the ridge line at the junction of the spout and the body, the maximum circumference of the inner wall of the teapot, and the center point of the bottom of the teapot.

[0062] The corresponding feature geometric elements are extracted from the actual measured positions of the preliminary 3D contour model through geometric fitting.

[0063] The iterative nearest point algorithm is used to calculate the optimal spatial rigid body transformation parameters with the goal of minimizing the overall distance between the actual measured feature geometric elements and the theoretical feature geometric elements. The spatial rigid body transformation parameters include three translations and three rotations.

[0064] Using the calculated optimal spatial rigid body transformation parameters, the complete preliminary three-dimensional contour model is rotated and translated as a whole to align its spatial orientation with the theoretical three-dimensional model of the standard purple clay teapot's inner cavity.

[0065] Calculate the root mean square error between corresponding points of the feature geometric elements of the two models after registration. If the root mean square error is less than the tolerance value, the registration is considered successful, and the final registration transformation matrix is ​​recorded.

[0066] Preferably, the residual distribution of the pre-registered three-dimensional contour model and the theoretical three-dimensional model in each spatial dimension generates a surface contour deviation field, including:

[0067] On the surface of the theoretical 3D model, a dense set of sampling points is generated according to a predetermined spatial sampling density;

[0068] For each sampling point on the surface of the theoretical 3D model, find the nearest point on the registered preliminary 3D contour model and calculate the signed distance between them. The sign of the signed distance indicates whether the measured surface is outside or inside the theoretical surface.

[0069] Map all sampling points and their corresponding signed distances back to the two-dimensional parameterized space of the theoretical three-dimensional model to generate a two-dimensional bias distance field.

[0070] Spatial interpolation and smoothing are performed on the two-dimensional deviation distance field to eliminate noise caused by uneven point cloud density or small registration errors.

[0071] The processed deviation distance field is remapped back to three-dimensional space to generate a surface profile deviation field that is consistent with the surface geometry of the theoretical three-dimensional model, but with a deviation value attached to each point.

[0072] When the surface profile deviation field is visualized in different colors or contour lines, it intuitively shows the unevenness or smoothness of the inner surface of the Zisha teapot relative to the theoretical model.

[0073] Compared with the prior art, the beneficial effects of the present invention are:

[0074] Based on the phase continuity of different regions in the surface phase shift map, this method identifies and divides complete measurement regions into occluded regions. It uses the topological properties of the phase field itself for discrimination; phase-continuous regions correspond to surface geometric coherence and valid measurement information, while phase discontinuities indicate geometric occlusion or missing information. Compared to conventional segmentation methods that rely on image grayscale or edge features, this method avoids recognition failures caused by weak surface texture and uneven reflection within the cavity. It directly utilizes the inherent mathematical properties of phase data, ensuring that the accuracy of region segmentation is unaffected by image contrast. This provides a reliable data foundation for subsequent phase unwrapping and 3D reconstruction, guaranteeing the computational accuracy of the initial point cloud data within the effective region.

[0075] The measured preliminary 3D contour model is spatially registered with the standard theoretical model to calculate the residual distribution in multiple spatial dimensions, i.e., the surface contour deviation field. By analyzing the numerical characteristics and spatial distribution patterns of this deviation field, a measurement analysis report is generated to guide subsequent processes. Discrete 3D point cloud differences are transformed into field data with clear spatial locations and magnitude distributions. The report not only presents the overall deviation amplitude but also accurately describes the specific distribution pattern, gradient direction, and aggregation of deviations on the inner cavity surface, as well as key locations such as the spout root and the body transition. This ensures that the measurement results are not merely isolated sets of geometric dimensions but are directly linked to specific trimming positions and adjustment amounts, achieving effective transformation from inspection data to production operations. Attached Figure Description

[0076] Figure 1 This is a schematic diagram illustrating the working principle of the optical measurement-based three-dimensional contour measurement method for the inner cavity surface of a Zisha teapot as described in this invention.

[0077] Figure 2A flowchart illustrating the construction of a multi-band spectral light source system and its projection;

[0078] Figure 3 A flowchart for analyzing and generating surface phase shift maps;

[0079] Figure 4 A diagram showing the iterative convergence characteristics of Poisson surface reconstruction;

[0080] Figure 5 The distance field is a two-dimensional deviation of the inner surface of the Zisha teapot. Detailed Implementation

[0081] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0082] Please see Figure 1 This invention provides a method for measuring the three-dimensional contour of the inner surface of a Zisha teapot based on optical measurement. The method includes: constructing a multi-band spectral light source system, projecting beams of specific wavelengths onto the inner surface of the target Zisha teapot at a preset sequence of incident angles, and acquiring a multi-band interference fringe image formed by reflection from the inner surface, while simultaneously recording real-time ambient light noise data at each incident angle. Subsequently, based on the correlation between the morphological distortion of the interference fringe image and the ambient light noise data, a surface phase shift map is generated, and based on the phase continuity of different regions in the map, the complete measurement area and the occluded area of ​​the inner surface are identified and divided. A pixel-by-pixel phase unwrapping operation is performed on the complete measurement area, mapping the wrapped phase to an absolute phase distribution field. Then, based on the geometric constraint relationship between the absolute phase distribution field and the known parameters of the projected beam, an initial three-dimensional point cloud data set of the inner surface is generated point by point. Next, the boundary geometric information of the occluded area is fused, and hole inference and surface smoothing extension processing are performed on the initial three-dimensional point cloud data set to form a complete preliminary three-dimensional contour model. Finally, the preliminary three-dimensional contour model is spatially registered with the theoretical three-dimensional model of the inner cavity of a standard Zisha teapot. The residual distribution of the registered model and the theoretical model in each spatial dimension is calculated to generate a surface contour deviation field. Based on the numerical characteristics and spatial distribution pattern of the deviation field, a measurement and analysis report is output to guide subsequent processes.

[0083] In one embodiment of the present invention, see [reference] Figure 2The system is configured with multiple solid-state light sources, each capable of independently modulating intensity and wavelength. These light sources form a ring-shaped light source array, the axis of which must be strictly aligned with the central axis of the spout of the Zisha teapot during installation. The set beam combination includes at least three different center wavelengths, each corresponding to an independent measurement spectral band. A set of incident angle sequences is predefined for each measurement spectral band, containing multiple discrete angle values ​​from grazing incidence to near-normal incidence. The light source array is controlled to operate sequentially according to the measurement spectral bands, switching the projection angle sequentially within each band based on its corresponding incident angle sequence. During each beam projection, a high-speed image sensor is synchronously triggered to capture an image of the reflected light field on the inner cavity surface. The precise beam parameters corresponding to each image capture are recorded, including the current effective wavelength, current incident angle, and current beam intensity. The raw image stream is received from the high-speed image sensor and classified and stored according to the measurement spectral band identifier and incident angle identifier in the beam parameters. Background subtraction processing is performed on each classified image; the subtracted background is the environmental background image acquired without actively projected beams. The alternating bright and dark fringe pattern is extracted from the image after background subtraction and defined as the interference fringe image formed under the current projection conditions. Within each exposure time window for acquiring the interference fringe image, ambient light intensity data is continuously sampled using an independent ambient light sensor. The average value and variance of the ambient light intensity data within this exposure time window are calculated, and these average value and variance are recorded together as the real-time ambient light noise data corresponding to this interference fringe image. An index mapping relationship is established between the interference fringe image, its beam parameters, and the real-time ambient light noise data, thus constructing a multi-spectral interferometric image database with environmental labels.

[0084] In the specific implementation, a sophisticated multi-band spectral light source system is constructed and operated. This system consists of multiple solid-state light sources with independently modulated intensity and wavelength, arranged in a physical ring to form a complete ring light source array. During installation, the geometric axis of the ring light source array must precisely coincide with the central axis of the spout of the teapot being tested to ensure that the projected beam can uniformly cover the inner surface of the cavity. In the specific implementation, a beam combination containing at least three different center wavelengths is defined for the system, with each center wavelength independently defining a measurement spectrum. A sequence of incident angles is predefined for each measurement spectrum, containing multiple discrete angle values ​​from grazing incidence to near-normal incidence. The control unit drives the ring light source array to operate sequentially according to the measurement spectrum. Within the working cycle of each measurement spectrum, the projection angle of each solid-state light source is switched sequentially according to the incident angle sequence defined for that spectrum.

[0085] Each time a beam of light is projected at a specific wavelength and angle, a synchronous trigger signal is sent to the high-speed image sensor. The high-speed image sensor then captures the reflected light field on the surface of the inner cavity of the teapot and generates a raw image. The precise beam parameters corresponding to each image capture event are recorded synchronously, including the current effective wavelength, current incident angle, and current beam intensity. After receiving a continuous stream of raw images from the high-speed image sensor, the system automatically classifies and stores the raw image stream based on the measurement spectral segment identifier and incident angle identifier corresponding to each image. In specific implementation, background subtraction is performed on each classified image. The subtracted background image is the environmental background image acquired by the same high-speed image sensor under the condition that all actively projected solid-state light sources are turned off.

[0086] The clearly visible alternating bright and dark fringe pattern in the image after background subtraction is extracted and defined as the interference fringe image formed under the current specific projection conditions. Within the entire exposure time window of each interference fringe image acquired by the high-speed image sensor, a high-sensitivity ambient light sensor, independent of the imaging system, continuously samples the ambient light intensity. The average value and variance of the ambient light intensity sampling data within each exposure time window are calculated, and the average value and variance are recorded together as the real-time ambient light noise data corresponding to that interference fringe image. In some embodiments, the ambient light sensor can be placed near the ring light source array to more accurately sense changes in the illumination of the measurement environment. Finally, the system establishes a strict index mapping relationship between each interference fringe image and its beam parameters and real-time ambient light noise data, forming a structured multi-spectral interference image database with environmental labels. In some embodiments, the driving current of the solid-state light source can be fine-tuned according to the real-time ambient light noise data to compensate for the potential impact of ambient light changes on fringe contrast. Optionally, the recorded beam intensity parameter is the calibrated actual emitted light power value. In practice, the current incident angle in the beam parameters is the physical deflection angle of the optical structure relative to the axis of the ring light source array.

[0087] It is understandable that establishing a multi-spectral interferometric image database with environmental labels is fundamental to achieving high-precision phase resolution. Optionally, for image frames with excessively large fluctuation variance in real-time ambient light noise data, the system can mark them as low-quality data and reduce their weight or trigger retesting in subsequent processing. In specific implementations, the sampling frequency of ambient light intensity data is much higher than the image acquisition frame rate to ensure that light intensity fluctuations during exposure can be captured. An example of light source modulation is shown in the following equation:

[0088]

[0089] in: This indicates the output intensity of the modulated solid-state light source. Indicates the reference output intensity. This represents the variance of illumination fluctuations in real-time ambient light noise data. It is a constant factor related to the sensor response and the ambient light intensity baseline.

[0090] In one embodiment of the present invention, see [reference] Figure 3 For each interference fringe image in the multi-band interferometric image database, its fringe contrast and fringe spatial frequency are calculated. The calculated fringe contrast is compared with the illumination fluctuation variance in the corresponding real-time ambient light noise data. If the fluctuation variance exceeds a preset threshold, the grayscale value of the interference fringe image is corrected by variance-based weighted filtering. A two-dimensional Fourier transform is performed on the corrected interference fringe image to extract the fundamental frequency component representing the surface height change in the spatial frequency domain. The fundamental frequency component is reconstructed into a complex amplitude image containing phase information through inverse Fourier transform. The phase angle is extracted from the complex amplitude image to obtain a wrapped phase map, where each pixel value represents the relative phase within the range of negative π to positive π. The wrapped phase maps obtained under all measurement bands and all incident angles are weighted and fused according to their corresponding beam parameters to generate a comprehensive, highly redundant surface phase shift map. The phase value at each location point in this map is constrained by multiple independent measurement results. The phase gradient is calculated on the surface phase shift map to obtain the phase change rate of each pixel in the row and column directions. A phase continuity decision threshold is set, and the surface phase shift map is traversed. Connected pixel regions with phase change rates less than the decision threshold in both row and column directions are marked as high-confidence regions. Pixels with phase change rates greater than the decision threshold in either row or column direction are marked as phase abrupt change points. Using the phase abrupt change points as boundaries, closed regions enclosed by these points, with smooth internal phase changes but unable to connect to high-confidence regions, are marked as potential occlusion regions. The phase value distribution pattern of potential occlusion regions is analyzed. If the phase distribution exhibits irregular jumps or constant characteristics, it is ultimately confirmed as an occlusion region. All regions in the surface phase shift map except for occlusion regions are uniformly defined as complete measurement regions, and binary mask images are generated for both complete measurement regions and occlusion regions.

[0091] In practical implementation, for each interference fringe image in the multi-band interferometric image database, the system calculates its fringe contrast and fringe spatial frequency. Fringe contrast reflects the clarity of bright and dark fringes in the image, while fringe spatial frequency reflects the distribution characteristics of fringe density. The calculated fringe contrast is compared juxtaposed with the illumination fluctuation variance in the corresponding real-time ambient light noise data, and a judgment is made based on a preset variance threshold: if the illumination fluctuation variance in the real-time ambient light noise data exceeds the preset threshold, then a variance-based weighted filtering correction is performed on the grayscale value of each pixel in the current interference fringe image to suppress random noise introduced by rapid fluctuations in ambient light.

[0092] In practice, a two-dimensional Fourier transform is performed on the interference fringe image after grayscale correction, converting the image from the spatial domain to the spatial frequency domain. In the spatial frequency domain, the algorithm identifies and extracts the fundamental frequency components characterizing the height variation of the inner surface of the Zisha teapot. Through inverse Fourier transform, the extracted fundamental frequency components are reconstructed into a complex amplitude image containing rich phase information. Phase angle information is extracted from the complex amplitude image, and a wrap-around phase map is generated. Each pixel value in the wrap-around phase map represents the relative phase within the range of negative π to positive π. The wrap-around phase maps calculated from all measured spectral bands and all incident angles obtained from the multi-spectral interferometric image database are weighted and fused according to the beam parameters corresponding to each wrap-around phase map. The weighting factor can include wavelength weight and incident angle weight, thereby generating a comprehensive, highly redundant surface phase shift map. The final phase value of each position point in the surface phase shift map is constrained by multiple independent measurement results.

[0093] In some embodiments, the specific operation of weighted filtering correction can be expressed in the following form:

[0094]

[0095] in: Indicates the corrected image in coordinates grayscale value at that location Indicates the original image in coordinates grayscale value at that location This represents the variance of illumination fluctuation in the real-time ambient light noise data corresponding to this image. Indicates The average gray value within a local neighborhood window centered on the center. It is a preset correction intensity coefficient.

[0096] Phase gradient calculations are performed on the final generated surface phase shift map. These calculations are performed along both the row and column directions of the image, yielding the phase change rate of each pixel in the surface phase shift map in the row and column directions. A phase continuity decision threshold is set. The system iterates through each pixel in the surface phase shift map, marking connected pixel regions where both the row and column phase change rates are less than the phase continuity decision threshold as high-confidence regions. Pixels where either the row or column phase change rate is greater than the phase continuity decision threshold are marked as phase abrupt change points.

[0097] Using identified phase abrupt change points as natural boundaries, the algorithm searches for closed regions enclosed by these points, where the internal pixel phase changes are gradual but cannot connect to any high-confidence regions. These closed regions are marked as potential occlusion regions. The phase value distribution pattern of all pixels within each potential occlusion region is analyzed, with the judgment criteria including statistical characteristics and spatial patterns. If the phase distribution of a potential occlusion region exhibits irregular jumps or constant characteristics, then the potential occlusion region is finally confirmed as an occlusion region. Irregular jumps are characterized by extremely high variance in phase values ​​and no spatial correlation, while constant characteristics are characterized by a variance in phase values ​​close to zero. All regions in the surface phase shift map, except for all finally confirmed occlusion regions, are uniformly defined as complete measurement regions. The system generates a binary mask image for both complete measurement regions and occlusion regions, where the mask pixel value corresponding to the complete measurement region is "true," and the mask pixel value corresponding to the occlusion region is "false."

[0098] In one embodiment of the invention, a binary mask image generated for the complete measurement region is loaded, and only pixels with true mask values ​​are processed. Starting from a seed pixel within the complete measurement region in the surface phase offset map, the phase value of the seed pixel is set as an absolute phase zero. A flood-fill algorithm is used to propagate phase unwrapping from the seed pixel to surrounding neighboring pixels. During propagation, the wrapped phase difference between the current pixel and its neighboring pixels is calculated. If the absolute value of this phase difference exceeds π, an integer multiple of 2π is added to or subtracted from the absolute phase of the neighboring pixels, such that the absolute value of the absolute phase difference between the current pixel and its neighboring pixels is less than or equal to π. The number of integer multiples of 2π added to or subtracted for each pixel is recorded; this number is called the phase transition order. After traversing all pixels within the complete measurement region, two result data fields are generated: one is the absolute phase distribution field composed of the absolute phase values ​​of each pixel, and the other is the order distribution field composed of the phase transition orders of each pixel. A mapping model is established from the image pixel coordinate system to the object space coordinate system of the inner cavity of the Zisha teapot. This mapping model includes the intrinsic parameters of the image sensor, the extrinsic parameters of the multi-band spectral light source system, and the beam projection geometry. For each pixel in the absolute phase distribution field, based on its absolute phase value and combined with the wavelength and incident angle in the beam parameters used to generate that phase value, the total optical path difference from the light source to the inner cavity surface point corresponding to the current pixel and then to the sensor is calculated. Based on the triangulation principle and the total optical path difference, the three-dimensional spatial coordinates of the inner cavity surface point corresponding to the current pixel relative to the optical center of the sensor are calculated. Simultaneously, the consistency of the calculated three-dimensional spatial coordinates is checked using the phase transition order corresponding to the current pixel. If the order difference of the neighboring points contradicts the calculated depth change trend, the local phase recalculation process is initiated. The three-dimensional spatial coordinates corresponding to all verified pixels, the estimated surface normal vector, and the reflectivity information from the original interference fringe image are combined to form the initial three-dimensional point cloud data set of the inner cavity surface. This set has missing data at the spatial locations corresponding to the occluded areas.

[0099] In practice, the system loads a binary mask image generated for the complete measurement area and determines the processing range based on the pixel logic values ​​of the binary mask image. Subsequent phase unwrapping operations are performed only on pixels with a mask value of "true" in the binary mask image. A pixel is selected from within the complete measurement area in the surface phase offset map as the starting seed pixel. The selection criterion for the starting seed pixel is usually that it is located in a region with stable phase value and high signal-to-noise ratio. The absolute phase value of the starting seed pixel is initially set to zero.

[0100] A flood-fill algorithm is used to propagate phase unwrapping from the initial seed pixel to its surrounding neighboring pixels. The flood-fill algorithm grows regions using either 4-connected or 8-connected neighborhood rules. During phase unwrapping propagation, for each currently processed pixel, the algorithm calculates the wrapped phase difference between the current pixel and each of its neighboring pixels. The wrapped phase difference is the direct subtraction of the original wrapped phase values ​​of the two pixels in the surface phase shift map. If the absolute value of the calculated wrapped phase difference exceeds π, then an integer multiple of 2π is added to or subtracted from the absolute phase value of the neighboring pixels. The sign and value of the integer multiple are determined based on the principle that the absolute value of the absolute phase difference between the current pixel and its neighboring pixels is less than or equal to π. The specific number of integer multiples of 2π added to or subtracted from the absolute phase value of each pixel is recorded; this number is defined as the phase transition order of that pixel. After the flood filling algorithm traverses all pixels with a mask value of "true" within the complete measurement area, it generates two core data fields: the first data field is the absolute phase distribution field composed of the final absolute phase value of each pixel; the second data field is the order distribution field composed of the phase transition order of each pixel.

[0101] In some embodiments, the starting seed pixel can be manually specified or located by automatically searching for the region with the smallest phase gradient. An accurate mapping model is established from the image pixel coordinate system of the high-speed image sensor to the object space coordinate system of the teapot's inner cavity. This mapping model includes the intrinsic parameter matrix and distortion coefficients of the high-speed image sensor, the extrinsic parameter matrix of the multi-band spectral light source system relative to the world coordinate system, and the geometric optical path model of the beam projection. In practical implementation, establishing a precise mapping model from the image pixel coordinate system of the high-speed image sensor to the object space coordinate system of the inner cavity of the Zisha teapot requires, firstly, obtaining the intrinsic parameter matrix and distortion coefficients of the image sensor through a calibration process. The intrinsic parameter matrix includes core parameters such as focal length and principal point coordinates, while the distortion coefficients characterize the radial and tangential distortions caused by the lens. Secondly, determining the extrinsic parameter matrix of the multi-band spectral light source system relative to the world coordinate system through spatial calibration defines the position and orientation transformation relationship of the light source array. Finally, combining the geometric optical path model of beam projection, which describes the complete path of light emitted from the light source, reflected by the inner cavity surface, and reaching the sensor based on a specific wavelength and incident angle sequence, a nonlinear mapping relationship between pixel coordinates and object-space three-dimensional coordinates is constructed, providing a geometric basis for subsequent phase-to-three-dimensional coordinate conversion. For each effective pixel in the absolute phase distribution field, based on the absolute phase value of the pixel and combined with the wavelength and incident angle in the original beam parameters used to generate this absolute phase value, the total optical path difference from the light source point in the ring light source array to the inner cavity surface point corresponding to the pixel and then reflected to the image plane of the high-speed image sensor is calculated through geometric optical relationships.

[0102] Based on the principle of triangulation and the calculated total optical path difference, the system calculates the three-dimensional spatial coordinates of the inner surface point of the teapot relative to the optical center of the high-speed image sensor in the object space by solving a set of geometric equations containing the positions of the light source, sensor, and surface points. While calculating the three-dimensional spatial coordinates of each pixel, the system performs spatial consistency verification using the phase transition order recorded in the order distribution field for that pixel. Specifically, this involves comparing the phase transition order difference between the pixel and its neighboring pixels and analyzing whether this difference logically matches the depth change trend calculated from the initial three-dimensional spatial coordinates. If a contradiction occurs, a local phase recalculation process is triggered, and a new path is selected in the contradictory region for phase unwrapping. The three-dimensional spatial coordinates corresponding to all pixels that pass the spatial consistency verification are summarized, and a surface normal vector is estimated for each point, along with reflectivity information extracted from the corresponding original interference fringe image. This information is then combined to form the initial three-dimensional point cloud data set of the inner surface. It is understandable that, since the mask value of the occluded area in the binary mask image is "false", the initial 3D point cloud data set will naturally have data missing at the spatial location corresponding to the occluded area, forming point cloud holes.

[0103] In practice, the transformation from absolute phase values ​​to three-dimensional spatial coordinates relies on a geometric constraint equation that incorporates phase information. An example is shown below:

[0104]

[0105] in: This represents the axial depth of a point on the inner cavity surface under a specific simplified geometric model. This indicates the wavelength of the beam that produces this phase. This represents the absolute phase value in the absolute phase distribution field. This indicates the angle of incidence of the light beam.

[0106] In one embodiment of the present invention, the boundary pixel coordinates of all occluded regions are extracted from the binary mask image of the occluded region. These boundary pixel coordinates are then back-projected into three-dimensional space, and the corresponding boundary three-dimensional points are found in the initial three-dimensional point cloud data set. The normal curvature and torsion of the boundary three-dimensional points along the tangent of the occluded region boundary are analyzed, and the orientation of the surface within the occluded region is inferred using differential geometry principles. Based on the inferred surface orientation, a Poisson surface reconstruction equation is constructed using minimum curvature change as a constraint condition. Solving the Poisson surface reconstruction equation generates a triangular mesh surface patch that can smoothly connect the known three-dimensional point clouds surrounding the occluded region. This triangular mesh surface patch is seamlessly stitched and fused with the initial three-dimensional point cloud data set to obtain a continuous, hole-free triangular mesh model, which is defined as a complete preliminary three-dimensional contour model.

[0107] In practical implementation, the initial 3D point cloud dataset and the corresponding binary mask image of the occluded region are used as input. The goal is to generate a continuous preliminary 3D contour model. The system first extracts the boundary pixel coordinates of all marked occluded regions from the binary mask image of the occluded region. The extraction operation is completed by scanning the binary mask image and identifying edge pixels whose mask values ​​change from "true" to "false". The extracted boundary pixel coordinates of the occluded region are then back-projected into 3D space according to the camera imaging model. This back-projection process utilizes a known mapping model from the image pixel coordinate system to the object space coordinate system to find the boundary 3D points in the initial 3D point cloud dataset that precisely correspond to these 2D boundary pixels.

[0108] The geometric properties of the boundary 3D points along the tangential direction of the occluded region boundary are analyzed. The normal curvature and torsion at each boundary 3D point are calculated. The normal curvature describes the degree of bending of the surface in the boundary tangential direction, and the torsion describes the twisting characteristics of the boundary curve itself. By combining the normal curvature and torsion information using differential geometry principles, the orientation of the surface within the occluded region can be inferred. Based on the inferred surface orientation, the system constructs a Poisson surface reconstruction equation with minimizing curvature change as a constraint. The Poisson surface reconstruction equation transforms the surface fitting problem into a Poisson equation that solves the least squares problem between the gradient field of the scalar function and the indicator vector field. Solving the Poisson surface reconstruction equation, a smooth scalar field is calculated through discretization and iterative numerical methods. Isosurfaces are extracted from the scalar field to generate triangular mesh surface patches that can smoothly connect the known 3D point clouds around the occluded region. The generated triangular mesh surface is seamlessly stitched and fused with the initial 3D point cloud data set. The mesh fusion operation includes vertex resampling, edge alignment and mesh smoothing, and finally a triangular mesh model with a continuous surface and no holes is obtained. This triangular mesh model is defined as a complete preliminary 3D contour model.

[0109] In some embodiments, the normal curvature of the boundary 3D point can be estimated by fitting a local quadratic surface to the boundary point and its neighboring points. To clearly illustrate the geometric properties involved in the boundary point analysis, refer to Table 1, which shows a simplified example of the geometric properties of the boundary 3D point.

[0110] Table 1: Geometric Attributes of Boundary 3D Points

[0111]

[0112] It is understandable that the normal curvature listed in the table... With torsion It is a key differential geometric quantity for inferring the surface orientation within the occluded region. A discretized solution form of the Poisson surface reconstruction equation can be expressed as:

[0113]

[0114] in: This represents the Laplacian operator matrix on a discrete triangular mesh. Let represent the scalar field vector to be solved. Denotes the divergence operator, This represents the indicator vector field constructed by the boundary three-dimensional point constraints. Solving this equation yields... Then, a complete triangular mesh can be generated by extracting specific isosurfaces.

[0115] See Figure 4 In the convergence analysis of Poisson surface reconstruction, the evolution of residual error and curvature change intuitively reflects the stability of the reconstruction process. Specifically, the residual error (red curve) characterizes the fitting deviation between the current scalar field and the indicator vector field during the Poisson equation solution process, while the curvature change (green curve) quantifies the degree of local geometric fluctuation of the triangular mesh surface during iteration. As the number of iterations increases, the residual error shows a monotonically decreasing trend, converging from approximately 0.09 initially to near 0, reflecting the numerical stability of the Poisson equation solution; the curvature change simultaneously decreases from approximately 0.025 to around 0.005, indicating that the surface gradually becomes smoother. During parameter evolution, both fluctuate significantly in the early iteration stage (0-10 iterations), corresponding to the rapid adjustment of the initial scalar field; in the later iteration stage (30-50 iterations), the rate of change slows down, indicating that the surface is close to a stable solution. The key parameter characteristics of this figure are: the residual error approaches 0 when the iteration terminates (50 times), and the curvature change stabilizes at the order of 0.005, which verifies the convergence effectiveness of Poisson surface reconstruction in occluded region completion.

[0116] In one embodiment of the invention, key feature geometric elements are extracted from the theoretical three-dimensional model of the inner cavity of a standard Zisha teapot. These elements include the ridge line at the junction of the spout and the body, the maximum circumference of the inner wall of the teapot, and the center point of the bottom. Corresponding feature geometric elements measured in practice are extracted from the corresponding positions of the preliminary three-dimensional contour model through geometric fitting. An iterative nearest-point algorithm is used to calculate the optimal spatial rigid body transformation parameters, which include three translations and three rotations, with the goal of minimizing the overall distance between the measured feature geometric elements and the theoretical feature geometric elements. Using the calculated optimal spatial rigid body transformation parameters, the complete preliminary three-dimensional contour model is rotated and translated as a whole to align its spatial orientation with the theoretical three-dimensional model of the inner cavity of the standard Zisha teapot. The root mean square error between the corresponding points of the feature geometric elements of the two models after registration is calculated. If this root mean square error is less than the tolerance value, the registration is considered successful, and the final registration transformation matrix is ​​recorded. A dense set of sampling points is generated on the surface of the theoretical three-dimensional model according to a predetermined spatial sampling density. For each sampling point on the surface of the theoretical 3D model, the nearest point is found on the registered preliminary 3D contour model, and the signed distance between the two is calculated. The sign of this signed distance indicates whether the measured surface is outside or inside the theoretical surface. All sampling points and their corresponding signed distances are mapped back to the 2D parametric space of the theoretical 3D model, generating a 2D deviation distance field. This 2D deviation distance field is then spatially interpolated and smoothed to eliminate noise caused by uneven point cloud density or small registration errors. The processed deviation distance field is remapped back to 3D space to generate a surface contour deviation field that matches the geometry of the theoretical 3D model surface but with a deviation value for each point. When this surface contour deviation field is visualized in different colors or as contour lines, it visually represents the unevenness or smoothness of the inner surface of the Zisha teapot relative to the theoretical model.

[0117] In practical implementation, the system takes a complete preliminary 3D contour model and a pre-stored theoretical 3D model of the inner cavity of a standard Zisha teapot as inputs. It then performs spatial orientation registration and contour deviation analysis. First, the system extracts a set of key geometric features from the theoretical 3D model of the inner cavity of the standard Zisha teapot. These key geometric features include the spatial ridge line at the junction of the spout and body, the maximum circumference of the inner wall of the teapot, and the center point of the bottom. From the corresponding anatomical positions of the complete preliminary 3D contour model, the system extracts the corresponding measured geometric features using least-squares fitting or geometric feature detection algorithms. For example, it obtains the actual maximum circumference by fitting a cylindrical surface to a point cloud and obtains the actual ridge line at the junction of the spout and body through edge detection.

[0118] An iterative nearest-point algorithm is employed, with the optimization objective being to minimize the overall distance between the actually measured feature geometric elements and the theoretical feature geometric elements extracted from the theoretical 3D model. The overall distance is typically defined as the sum of the squares of the Euclidean distances between corresponding point pairs. An optimal set of spatial rigid body transformation parameters is calculated, including translations along the three coordinate axes and rotations around them. Using these optimal parameters, the complete preliminary 3D contour model undergoes overall rotation and translation transformations to align its spatial orientation with the theoretical 3D model of the standard Zisha teapot's inner cavity. The root mean square error (RMSE) between corresponding points of the feature geometric elements in the two models after registration is calculated. RMSE is a quantitative indicator of registration accuracy; if the calculated RMSE is less than a preset tolerance value, the spatial orientation registration is considered successful, and the final applied spatial rigid body transformation parameters are recorded as the final registration transformation matrix for subsequent use. On the surface of the theoretical 3D model, a dense set of sampling points is generated according to a predetermined spatial sampling density. This set of sampling points should uniformly cover the entire inner cavity surface of the theoretical 3D model. For each sampling point on the surface of the theoretical 3D model, the nearest point in space is found on the preliminary 3D contour model after spatial pose registration. The signed distance between the theoretical sampling point and the nearest measured point is calculated. The value of the signed distance represents the magnitude of the deviation, and its sign indicates whether the measured surface point is outside or inside the theoretical surface. Generally, a positive value is defined as the measured surface being convex, and a negative value as the measured surface being concave. All sampling points and their corresponding signed distance data are mapped to a two-dimensional parameterized space through the parameterized unfolding method of the theoretical 3D model, thereby generating a two-dimensional deviation distance field. The two-dimensional deviation distance field is stored in the form of a pixel grid, and each pixel value represents the signed distance of the corresponding parameter position.

[0119] Spatial interpolation and smoothing are performed on the generated two-dimensional deviation distance field. Spatial interpolation is used to fill in the blank grids caused by parametric mapping, and smoothing is used to suppress high-frequency noise caused by uneven point cloud density or small residual errors in registration. The two-dimensional deviation distance field after interpolation and smoothing is then remapped back to three-dimensional space according to its mapping relationship with the surface of the theoretical three-dimensional model, generating a surface profile deviation field that is completely consistent with the geometry of the surface of the theoretical three-dimensional model, but with each point on the surface having a quantized deviation value.

[0120] In some embodiments, the operation of finding the nearest point can be accelerated using a KD-Tree data structure. (Signed distance) The calculation can be expressed in the following form:

[0121]

[0122] in: Indicates signed distance. This represents the coordinates of the sampling points on the surface of the theoretical 3D model. This represents the coordinates of the nearest point found on the initial 3D contour model after registration. Represents theoretical sampling points The unit normal vector at that location, It is a symbolic function. Represents the vector dot product. It represents the magnitude of the vector.

[0123] See Figure 5 This image presents the processed two-dimensional deviation distance field visualization results. A two-dimensional parametric space is constructed using X and Y coordinates (unit: mm). The signed distance (unit: mm) of the measured surface of the teapot's inner cavity relative to the theoretical model is represented by color mapping: in the color gradient, positive values ​​(warm colors) correspond to convexity of the measured surface, and negative values ​​(cool colors) correspond to concavity, with a range of -7.5 mm to 10.0 mm. Specifically, this image maps the signed distance of sampling points on the surface of the theoretical three-dimensional model to the two-dimensional parametric space, and then performs spatial interpolation and smoothing. Warm-colored areas (such as near Y coordinate 0 and X coordinates -2 to 2) reflect convex deviations of the measured surface relative to the theoretical model at corresponding positions within the inner cavity, while cool-colored areas (such as near X and Y coordinates ±8) correspond to concavity deviations. The color distribution visually reflects the convex-concave distribution characteristics of the teapot's inner cavity surface contour relative to the theoretical model, providing a quantitative basis for the spatial distribution of surface deviations for subsequent process optimization.

[0124] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0125] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement, characterized in that, include: A multi-band spectral light source system was constructed to project beams of specific wavelengths onto the inner surface of the target purple clay teapot at a preset incident angle sequence, thereby obtaining a multi-band interference fringe image formed by reflection from the inner surface, and simultaneously recording the real-time ambient light noise data corresponding to each incident angle. Based on the correlation between the morphological distortion of the interference fringe image and the real-time ambient light noise data, a surface phase shift map is generated. Based on the phase continuity of different regions in the surface phase shift map, the complete measurement area and the occlusion area of ​​the inner cavity surface are identified and divided. A pixel-by-pixel phase unwrapping operation is performed on the complete measurement area, and the wrapped phase is mapped to an absolute phase distribution field. Based on the geometric constraint relationship between the absolute phase distribution field and the known projection beam parameters, the initial three-dimensional point cloud data set of the inner cavity surface is generated point by point. By fusing the boundary geometry information of the occluded area, hole inference and surface smoothing extension processing are performed on the initial 3D point cloud data set to form a complete preliminary 3D contour model. The preliminary three-dimensional contour model is spatially registered with the theoretical three-dimensional model of the inner cavity of a standard Zisha teapot. The residual distribution of the registered preliminary three-dimensional contour model and the theoretical three-dimensional model in each spatial dimension is calculated to generate a surface contour deviation field. Based on the numerical characteristics and spatial distribution pattern of the surface contour deviation field, a measurement and analysis report is output to guide subsequent processes.

2. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 1, characterized in that, The construction of the multi-band spectral light source system, which projects beams of specific wavelengths onto the inner surface of the target purple clay teapot at a preset incident angle sequence, includes: Multiple solid-state light sources with independently modulated intensity and wavelength are configured to form a ring light source array, the axis of which coincides with the central axis of the mouth of the Zisha teapot; Set up a beam combination containing at least three different center wavelengths, where each center wavelength corresponds to an independent measurement spectrum; A set of incident angle sequences is predefined for each measurement spectral band, the incident angle sequences containing multiple discrete angle values ​​from grazing incidence to near normal incidence; The control light source array works sequentially according to the order of the measurement spectrum segments. Within each measurement spectrum segment, the projection angle is switched sequentially according to its corresponding incident angle sequence. Each time a beam is projected, a high-speed image sensor is synchronously triggered to capture an image of the reflected light field on the surface of the cavity at that moment; Record the precise beam parameters corresponding to each image capture, including the current effective wavelength, the current incident angle, and the current beam intensity.

3. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 2, characterized in that, The process of acquiring a multi-spectral interference fringe image formed by reflection from the inner cavity surface and simultaneously recording real-time ambient light noise data corresponding to each incident angle includes: The raw image stream is received from the high-speed image sensor and classified and stored according to the measurement spectrum segment identifier and incident angle identifier in the beam parameters; Background subtraction is performed on each classified image. The subtracted background is the environmental background image acquired without an active projection beam. Extract the alternating bright and dark stripe pattern from the image after background subtraction, and define the alternating bright and dark stripe pattern as the interference fringe image formed under the current projection conditions; Within each exposure time window for acquiring interference fringe images, ambient light intensity data is continuously sampled using an independent ambient light sensor; Calculate the average value and fluctuation variance of the ambient light intensity data within the exposure time window, and record the average value and fluctuation variance together as the real-time ambient light noise data corresponding to this interference fringe image; An index mapping relationship is established between the interference fringe image and its beam parameters and real-time ambient light noise data to form a multi-spectral interference image database with environmental labels.

4. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 3, characterized in that, The process of generating a surface phase shift map based on the correlation between the morphological distortion of the interference fringe image and real-time ambient light noise data includes: For each interference fringe image in the multi-band interference image database, calculate its fringe contrast and fringe spatial frequency; The calculated fringe contrast is compared with the illumination fluctuation variance in the corresponding real-time ambient light noise data. If the fluctuation variance exceeds a preset threshold, the grayscale value of the interference fringe image is corrected by variance-based weighted filtering. A two-dimensional Fourier transform is performed on the corrected interference fringe image to extract the fundamental frequency components characterizing the surface height variation in the spatial frequency domain. The fundamental frequency components are reconstructed into a complex amplitude image containing phase information through inverse Fourier transform. The phase angle is extracted from the complex amplitude image to obtain a wrapped phase map, where each pixel value of the wrapped phase map represents the relative phase located in the interval from negative π to positive π. The wrap-around phase maps obtained from all measurement spectral segments and all incident angles are weighted and fused according to their corresponding beam parameters to generate a comprehensive, highly redundant surface phase shift map. The phase value of each location point in the surface phase shift map is constrained by multiple independent measurement results.

5. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 1, characterized in that, The method of identifying and delineating the complete measurement area and occlusion area of ​​the inner cavity surface based on the phase continuity of different regions in the surface phase shift map includes: Phase gradient calculations are performed on the surface phase shift map to obtain the phase change rate of each pixel in the row and column directions; Set a phase continuity decision threshold, traverse the surface phase shift map, and mark the connected pixel regions whose phase change rate is less than the decision threshold in both the row and column directions as high confidence regions; Pixels whose phase change rate in the row or column direction is greater than the decision threshold are marked as phase change points; Using the phase abrupt change point as the boundary, the closed region enclosed by it, which has a gentle internal phase change but cannot be connected to the high confidence region, is marked as a potential occlusion region. Analyze the phase value distribution pattern of potential occlusion areas. If the phase distribution shows irregular jumps or constant characteristics, it is finally confirmed as an occlusion area. All regions in the surface phase shift map, except for the occluded regions, are uniformly defined as the complete measurement region, and binary mask images are generated for the complete measurement region and the occluded region respectively.

6. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 5, characterized in that, The step of performing pixel-by-pixel phase unwrapping operations on the complete measurement region, mapping the wrapped phase to an absolute phase distribution field, includes: Load the binary mask image generated for the complete measurement area, and process only the pixels with true mask values; Starting from a seed pixel within the complete measurement region of the surface phase shift map, the phase value of the seed pixel is set as the absolute phase zero. A flood-fill algorithm is used to propagate phase unwrapping from the seed point to the surrounding neighboring pixels; during the propagation process, the wrapping phase difference between the current pixel and its neighboring pixels is calculated. If the absolute value of the phase difference exceeds π, then add or subtract an integer multiple of 2π to the absolute phase of the adjacent pixel, so that the absolute value of the absolute phase difference between the current pixel and the adjacent pixel is less than or equal to π. The number of integer multiples of two π added to or subtracted from each pixel is recorded; this number is called the phase transition order. After traversing all pixels within the complete measurement area, two result data fields are generated: one is the absolute phase distribution field composed of the absolute phase values ​​of each pixel, and the other is the order distribution field composed of the phase transition orders of each pixel.

7. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 6, characterized in that, The process of generating an initial three-dimensional point cloud data set for the inner cavity surface by point-by-point calculation based on the geometric constraint relationship between the absolute phase distribution field and the known projection beam parameters includes: A mapping model is established from the image pixel coordinate system to the object space coordinate system of the inner cavity of the Zisha teapot. The mapping model includes the intrinsic parameters of the image sensor, the extrinsic parameters of the multi-band spectral light source system, and the beam projection geometry. For each pixel in the absolute phase distribution field, based on its absolute phase value, combined with the wavelength and incident angle in the beam parameters used to generate the phase value, the total optical path difference from the light source to the inner cavity surface point corresponding to the current pixel and then to the sensor is calculated. Based on the principle of triangulation and the total optical path difference, the three-dimensional spatial coordinates of the inner cavity surface point corresponding to the current pixel point relative to the optical center of the sensor are calculated. Simultaneously, the phase transition order corresponding to the current pixel is used to perform a consistency check on the calculated three-dimensional spatial coordinates. If the order difference of the neighboring points contradicts the calculated depth change trend, the local phase recalculation process is initiated. The three-dimensional spatial coordinates, surface normal vector estimates, and reflectivity information from the original interference fringe image corresponding to all the verified pixels are combined to form the initial three-dimensional point cloud data set of the inner cavity surface. The initial 3D point cloud dataset has missing data at spatial locations corresponding to the occluded areas.

8. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 7, characterized in that, The boundary geometry information of the fused occlusion region is used to perform hole inference and surface smoothing extension processing on the initial 3D point cloud data set to form a complete preliminary 3D contour model, including: Extract the boundary pixel coordinates of all occluded regions from the binary mask image of the occluded regions; The boundary pixel coordinates of the occluded area are back-projected into three-dimensional space, and the corresponding boundary three-dimensional points are found in the initial three-dimensional point cloud data set. Analyze the normal curvature and torsion of the three-dimensional points along the tangent of the boundary of the occluded region, and use the principles of differential geometry to predict the possible orientation of the surface within the occluded region. Based on the inferred surface orientation, the minimum curvature change is used as a constraint to construct the Poisson surface reconstruction equation; Solve the Poisson surface reconstruction equation to generate a triangular mesh surface that can smoothly connect the known 3D point cloud around the occluded region; The triangular mesh surface is seamlessly stitched and fused with the initial three-dimensional point cloud data set to obtain a triangular mesh model with a continuous surface and no holes. The triangular mesh model is defined as a complete preliminary three-dimensional contour model.

9. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 8, characterized in that, The process of spatially registering the preliminary three-dimensional contour model with the theoretical three-dimensional model of the standard purple clay teapot's inner cavity includes: Key feature geometric elements are extracted from the theoretical three-dimensional model of the inner cavity of a standard Zisha teapot. These key feature geometric elements include the ridge line at the junction of the spout and the body, the maximum circumference of the inner wall of the teapot, and the center point of the bottom of the teapot. The corresponding feature geometric elements are extracted from the actual measured positions of the preliminary 3D contour model through geometric fitting. The iterative nearest point algorithm is used to calculate the optimal spatial rigid body transformation parameters with the goal of minimizing the overall distance between the actual measured feature geometric elements and the theoretical feature geometric elements. The spatial rigid body transformation parameters include three translations and three rotations. Using the calculated optimal spatial rigid body transformation parameters, the complete preliminary three-dimensional contour model is rotated and translated as a whole to align its spatial orientation with the theoretical three-dimensional model of the standard purple clay teapot's inner cavity. Calculate the root mean square error between corresponding points of the feature geometric elements of the two models after registration. If the root mean square error is less than the tolerance value, the registration is considered successful, and the final registration transformation matrix is ​​recorded.

10. The method for measuring the three-dimensional contour of the inner cavity surface of a Zisha teapot based on optical measurement according to claim 9, characterized in that, The residual distribution of the pre-registered 3D contour model and the theoretical 3D model in each spatial dimension generates a surface contour deviation field, including: On the surface of the theoretical 3D model, a dense set of sampling points is generated according to a predetermined spatial sampling density; For each sampling point on the surface of the theoretical 3D model, find the nearest point on the registered preliminary 3D contour model and calculate the signed distance between them. The sign of the signed distance indicates whether the measured surface is outside or inside the theoretical surface. Map all sampling points and their corresponding signed distances back to the two-dimensional parameterized space of the theoretical three-dimensional model to generate a two-dimensional bias distance field. Spatial interpolation and smoothing are performed on the two-dimensional deviation distance field to eliminate noise caused by uneven point cloud density or small registration errors. The processed deviation distance field is remapped back to three-dimensional space to generate a surface profile deviation field that is consistent with the surface geometry of the theoretical three-dimensional model, but with a deviation value attached to each point. When the surface profile deviation field is visualized in different colors or contour lines, it intuitively shows the unevenness or smoothness of the inner surface of the Zisha teapot relative to the theoretical model.

Images