Method for synthesizing image representing appearance of surface under diffused illumination

Abstract

A method for synthesizing a diffused image (S) representative of the appearance of a surface under diffused illumination comprises: a) obtaining at least two directional images (D1, D2, D3) of the surface, each directional image having been acquired along a predefined viewing direction under directional illumination of the surface from a predefined illumination direction; b) for each directional image, determining a plurality of statistical parameters ({A1, n, m}, {A2, n, m}, {A3, n, m}) representative of a statistical distribution of pixel values in the respective directional image; c) predicting a plurality of probability distribution parameters ({Ap, n, m}) representing a predicted probability distribution function of pixel values in the diffusion image using statistical parameters associated with the at least two directional images as predictors, and d) determining pixel values of the diffusion image based on samples from the predicted probability distribution function.

Description

Technical Field

[0001] The present invention relates to a method for synthesizing a diffuse image representing the appearance of a surface under diffuse illumination, to a corresponding computer program, and to an imaging spectrophotometer configured to perform the method. Background Technology

[0002] Under defined lighting and viewing conditions, the visual impression of a real material or object in its environment is referred to as "appearance" in the relevant professional field. Appearance is known to be the result of a complex interaction of the following different factors: - Define the geometric factors of the scene, objects, and lighting and viewing conditions; - Optical properties, which describe the interaction between light and the material of the object being viewed; and - Physiological factors that affect the perception (response) of the human visual system.

[0003] In many industrial applications, it is desirable to perform measurements to characterize the appearance of materials or objects. In such measurements, multiple optical properties of a material or object are determined under one or more sets of lighting and viewing conditions. A wide variety of tools, varying in complexity, have been proposed for this purpose.

[0004] An exemplary application is in motor vehicle repair. When a damaged motor vehicle part is replaced with a new one in a body shop, the new part needs to be painted so that its visual appearance perfectly matches that of the original part. The same applies if the damaged part needs to be repainted. For this purpose, it is desirable to determine the visual appearance of the original part by measurement and, based on that measurement, define a paint formula that will achieve a close match to the appearance of the original part.

[0005] Motor vehicle paints often contain effect pigments that cause angularly visible behavior, meaning they produce an appearance that strongly depends on lighting and viewing direction. For example, special effect flake pigments may produce a shimmering effect that changes dramatically with lighting or viewing direction. As another example, interference pigments can cause angular color change, meaning the color gradually changes as the lighting or viewing direction changes. Effect pigments are also used in other materials, such as the plastic materials used in many household items.

[0006] Various industry standards have proposed sets of suitable measurement geometries for characterizing materials containing effect pigments. ASTM E2194-14 (2017) defines a set of at least three measurement geometries for materials containing metallic effect pigments. ASTM E2539-14 (2017) defines additional measurement geometries for characterizing materials containing interference pigments.

[0007] Effect paints can produce not only colors visible at angles, but also localized variations on the surface of a viewed object, known as "texture." Two aspects of texture can be distinguished: visual texture characterizes spatial variations in color and reflectivity, while surface texture characterizes the three-dimensional shape of a surface at a scale discernible to the human eye. Visual texture typically differs under directional lighting (such as direct sunlight) and diffuse lighting (such as on a cloudy day). Directional lighting can produce patterns of very bright "flakes," caused by direct reflection from thin flakes of pigment in the top layer of paint. This effect is often referred to as glitter, shine, sparkle, or shimmer. Diffuse lighting produces localized variations in brightness with much lower contrast, often referred to as graininess, diffuse roughness, image grain, or granularity.

[0008] Handheld multi-angle imaging spectrophotometers are known for characterizing paint coatings containing effect pigments, combining multi-angle color measurements with image-based texture measurements. One example is the MA-Tx series measurement device, available from X-Rite, GrandRapids, Michigan, USA. The system architecture of the MA-Tx series is described in US20140152990A1. The device is configured to measure measurement points on a sample surface that define a measurement plane. The device includes a mechanical arcuate structure defining the system plane. The arcuate structure houses up to seven directional illumination systems for illuminating the measurement points from different angles within the system plane, and it houses two detector systems for picking up light already reflected from the measurement points at normal angles of 15° and 45° within the system plane. Additionally, a diffuse illumination system is provided to illuminate the measurement points from a range of directions at large angles relative to the system plane. The detector system with a 45° normal angle is implemented as a spectral pickup system that couples the collected light into an optical fiber and then into a spectrometer. A detector system with a 15° normal angle is implemented as a multiplexed optical system combining a combined spectral pickup channel and an RGB color camera at the same viewing angle. Spectral measurements and image acquisition share the same light source. Therefore, this device can quickly and accurately evaluate and verify the color, glitter, and graininess characteristics of effect finishes.

[0009] The measuring apparatus disclosed in US20140152990A1 is capable of generating images of measurement points under diffuse illumination at a normal angle of 15° using a diffuse illumination system and an RGB color camera. This geometry is referred to as the "r15d" measurement geometry. In practice, the resulting images are typically not used for quantitative determination of texture features. Instead, they are usually used only for preview purposes, providing a realistic visual impression of the measurement points under diffuse illumination.

[0010] However, not all multi-angle imaging spectrophotometers include a diffuse illumination system. Currently, it is not possible to provide a realistic preview of the measurement point under diffuse illumination using equipment lacking a diffuse illumination system. Summary of the Invention

[0011] The object of this invention is to provide a method that can provide a true visual impression of a measurement point under diffuse illumination without requiring a diffuse illumination system.

[0012] This objective is achieved by the method according to claim 1. Further embodiments of the invention are set forth in the dependent claims.

[0013] In a first aspect, the present invention provides a method for synthesizing an image representing the appearance of a surface under diffuse illumination. In this disclosure, an image obtained under diffuse illumination is referred to as a "diffuse image." A diffuse image comprises an array of pixels, referred to herein as "diffuse image pixels." Each diffuse image pixel has at least one pixel value, referred to herein as a "diffuse image pixel value." For example, if the diffuse image is a grayscale image, each diffuse image pixel may have exactly one pixel value. If the diffuse image is a color image, each diffuse image pixel may have three or more pixel values, each pixel value being a color value or a spectral value along color coordinates in a suitable color space.

[0014] The method includes: a) Obtain at least two orientation images of a measurement point on a surface, each orientation image having been acquired at the measurement point under directional illumination from an illumination direction along a viewing direction, the illumination and / or viewing direction being different between the at least two orientation images, each orientation image comprising an array of orientation image pixels, each orientation image pixel having at least one orientation image pixel value; b) For each orientation image, determine multiple statistical parameters, which represent the statistical distribution of orientation image pixel values ​​in the corresponding orientation image; c) Using statistical parameters associated with at least two directional images as a predictor, a plurality of probability distribution parameters are predicted, the probability distribution parameters representing a predicted probability distribution function of pixel values ​​of a diffuse image; d) Determine the pixel values ​​of the diffuse image based on samples from the predicted probability distribution function.

[0015] In this method, a diffuse image is synthesized based on at least two images already acquired under directional illumination. In this disclosure, these images are referred to as "directional images." Measurement points may have very different appearances under directional and diffuse illumination. For example, for effect paint, a measurement point may exhibit a strong shimmering effect, which may be highly dependent on the lighting and viewing direction, but may be absent or greatly reduced under diffuse illumination. Therefore, it may be difficult to directly predict the appearance of a measurement point under diffuse illumination based on its appearance under directional illumination. The proposed method is based on the understanding that although measurement points have different appearances under different lighting conditions, there may be a strong correlation between certain statistical properties of the pixel value histograms of the directional and diffuse images. This invention proposes predicting the statistical properties of the diffuse image and determining the pixel values ​​of the diffuse image in such a way that their actual statistical properties approximately match the predicted statistical properties. This is achieved by determining the predicted probability density function (PDF) of the pixel values ​​of the diffuse image and sampling from this probability density function using a suitable sampling method.

[0016] In an advantageous embodiment, determining the statistical parameters involves fitting a PDF with a maximum value and two independent “heavy” tails that decay to zero over a range longer than a Gaussian distribution to the distribution of pixel values ​​in the corresponding oriented image, and determining the statistical parameters based on the resulting PDF. This PDF can, in particular, be a PDF of Johnson’s SU distribution. Experiments have shown that Johnson’s SU distribution generally reproduces well the most important properties of the histograms of pixel values ​​in both oriented and diffuse images.

[0017] Advantageously, at least four statistical parameters are determined for each orientation image. If the orientation image is a color image defined in a color space with three or more dimensions, this is preferably performed separately for each dimension of the color space. Notably, Johnson's SU distribution is defined by four parameters.

[0018] It may be advantageous to define the statistical parameter as a percentile of the cumulative density function (CDF), which represents the statistical distribution of oriented image pixel values ​​in the corresponding oriented image. Specifically, the statistical parameter can be defined as a percentile of the CDF, which corresponds to a PDF that has been fitted to the distribution of oriented image pixel values ​​in the corresponding oriented image. Experiments have shown that specifying the statistical parameter as a percentile of the CDF can increase the robustness of the prediction algorithm. This percentile will also be referred to as the "anchor" below.

[0019] The pixel values ​​of a diffuse image are based on samples from a predicted probability distribution function. If only random samples from the predicted PDF are used to determine the pixel values ​​of a diffuse image, without any further image processing, the pixel values ​​of adjacent pixels will be statistically uncorrelated. This may not accurately reflect reality because camera systems typically used to capture images of measurement points have limited resolution, and therefore, real diffuse images often exhibit short-range spatial correlations between the pixel values ​​of different pixels. Other effects may also contribute to spatial correlation.

[0020] To account for spatial correlation, determining the pixel values ​​of a diffuse image can include: d1) Synthesize a preimage with multiple preimage pixels, wherein for each preimage pixel, a preimage pixel value is calculated, wherein the calculation of the preimage pixel value includes random sampling from a prediction probability distribution function; and d2) Determine the diffuse image pixel values ​​from the pre-image pixel values ​​in such a way that short-range spatial correlations arise between the diffuse image pixel values.

[0021] In this method, a pre-image is synthesized whose pixel values ​​can be substantially uncorrelated, and a diffuse image is determined from the pre-image through an image processing operation that causes short-range correlation between adjacent pixels.

[0022] Specifically, determining the diffuse image pixel values ​​based on the pre-image pixel values ​​can include one or both of the following: Resize the pre-image or the image derived from it by adjusting the size factor to obtain a diffuse image; and / or A blurring operation is applied to the pre-image or the image derived therefrom to obtain a diffuse image.

[0023] In this way, diffuse image pixel values ​​will typically have increased short-range spatial correlation compared to pre-image pixel values.

[0024] Blur operations can include convolving a pre-image with a point spread function (particularly a circular (isotropic) point spread function). In this way, the diffraction effect in the camera system of the measuring device is simulated.

[0025] In some embodiments, the range of spatial correlations between pixels in the actual diffuse image may be known in advance. In other embodiments, this range may be unknown. In such embodiments, it may be desirable to predict the spatial correlations in the synthetic diffuse image directly from the orientation image. To this end, the method may include: For each orientation image, determine at least one spatial autocorrelation parameter; and When determining pixel values ​​for a diffuse image, the spatial autocorrelation parameter of the orientation image should be considered. The method preferably includes predicting the spatial autocorrelation parameters of the diffuse image and using the spatial autocorrelation parameters of the diffuse image to determine the pixel values ​​of the diffuse image.

[0026] Specifically, the spatial autocorrelation parameter of the orientation image pixels can be an additional input parameter of a prediction algorithm for predicting the probability distribution parameters of the diffuse image pixel values, and the output value of the prediction algorithm can include the spatial autocorrelation parameter of the diffuse image, for example, in the form of a scaling factor or blur parameter, such as in the form of a length scaling parameter of a point spread function convolved with the pre-image.

[0027] In some embodiments, the directional image and diffuse image may each have only one pixel value per pixel; for example, they may be grayscale images, where the pixel value represents the intensity or brightness of the pixel. In other embodiments, each diffuse image pixel may have at least three diffuse image pixel values, each diffuse image pixel value being a color value in a color space having at least three color space dimensions. Similarly, each directional image pixel may have at least three directional image pixel values, each directional image pixel value being a color value in said color space. In this case, steps a) and b) of the method described above can be performed separately for each color space dimension. Using statistical parameters of all color space dimensions as a predictor, prediction step c) is advantageously performed together for all color space dimensions. Prediction step c) can then provide probability distribution parameters of the diffuse image pixel values ​​for all color space dimensions accordingly.

[0028] If the orientation image is a color image with at least three color values, it is typically acquired in a three-color color space (e.g., RGB), where the color values ​​represent the intensities of three different colors. In such a color space, the pixel color values ​​of the orientation image can exhibit strong correlations between different color space dimensions. It is then advantageous to transform the orientation image to a second color space, in which, compared to the original color space, the pixel color values ​​of the orientation image have reduced correlations between different color space dimensions. In particular, this is advantageous if the second color space has a hue dimension, a saturation dimension, and an intensity or lightness dimension. Specifically, the color space can be a well-known HSV or HSL color space, for which the transformation from RGB can be performed in a particularly efficient manner.

[0029] The method may include performing correlation analysis (e.g., principal component analysis) on image pixel values ​​along different color space dimensions in a first color space to determine a second color space as the color space that minimizes the correlation between image pixel color values ​​along different color space dimensions in the second color space.

[0030] Even in a color space with minimized correlation, undesirable correlations may still exist between image pixel values ​​along different color space dimensions. These correlations can be particularly pronounced if flashes are present in the oriented image. Therefore, it may be advantageous to separate flash pixels from background pixels and process them separately. In this way, undesirable correlations between color space dimensions can be further reduced, and more realistic results can be achieved. For example, flash pixels can be identified using a simple thresholding algorithm that identifies pixels above a certain intensity threshold as flash pixels, or through more complex algorithms such as edge detection algorithms.

[0031] More specifically, the method may include identifying flash pixels in the orientation image, where flash pixels represent flash points, and removing the flash pixels from the orientation image to obtain an orientation background image. Steps a) through d) can then be performed using only the orientation background image to obtain a synthesized diffuse background image. Optionally, simulated flash points can ultimately be inserted into the diffuse background image to obtain the final diffuse image. Simulated flash points can also be obtained by applying steps a) through d) to the flash pixels of the orientation image. In step c), it may be advantageous to use a common prediction algorithm that has statistical parameters for both the orientation background image and the flash points in the orientation image in its input, and probability distribution parameters for both the diffuse background image and the simulated flash points in its output.

[0032] The prediction algorithm used to determine the probability distribution parameters can be a machine learning algorithm trained using a training dataset that includes statistical parameters of at least two measured orientation images and one measured diffuse image for each of a plurality of surfaces. For each surface, the statistical parameters of the measured orientation images act as the predictor, while the statistical parameters of the measured diffuse image act as the target value. The statistical parameters can be determined as described above, for example, as percentiles (“anchors”) of the CDF. The machine learning algorithm can be, for example, a regression algorithm, particularly a regression gradient boosting algorithm.

[0033] In another aspect, the present invention provides a computer program including instructions that, when executed by a computer, cause the computer to perform the methods disclosed herein. The computer program may be provided on a non-volatile computer-readable data carrier on which the computer program is stored.

[0034] The present invention also provides an imaging spectrophotometer, comprising: At least one directional light source is used to illuminate the measurement point on the sample surface from at least one predefined illumination direction; At least one image detector is used to acquire images of the measurement points along a predefined viewing direction; and Processing circuitry configured to perform the methods of this disclosure. Attached Figure Description

[0035] Preferred embodiments of the invention are described below with reference to the accompanying drawings, which are for illustrative purposes and not for limiting the scope of the invention. In the drawings, Figure 1 A perspective view of a multi-angle spectrophotometer according to the prior art is shown; Figure 2 It shows Figure 1 A perspective view of the measurement array of the multi-angle spectrophotometer in the image; Figure 3 It shows in Figure 1 Illustrations of possible measurement geometries in handheld measuring devices; Figure 4 A schematic flowchart illustrating an embodiment of the method according to the present disclosure is shown; Figure 5 Three graphs illustrating a typical distribution of pixel values ​​in the HSV color space are shown; Figure 6 A plot illustrating Johnson's SU distribution for three different parameter sets is shown. Figure 7 A graph illustrating the determination of the percentiles of the cumulative density function is shown; Figure 8 An image patch showing the detection of flashes in the illustrated image; and Figure 9 A schematic block diagram of a hardware-oriented multi-angle spectrophotometer according to the present disclosure is shown. Detailed Implementation

[0036] In this disclosure, singular references may also include plural ones. Specifically, unless the context otherwise indicates, the word “a” (“a” or “an”) may refer to one or more.

[0037] The term "visual appearance," or simply "appearance," should be broadly understood as the way in which an object reflects and transmits light, including but not limited to how an individual viewing the object perceives its color and surface texture under various viewing conditions. Appearance also includes instrumental measurements of how an object reflects and transmits light.

[0038] One aspect of visual appearance is color. The “color” of an object is determined by the portion of the spectrum of incident white light that is reflected or transmitted but not absorbed. The color of an object can be described by “color values” in any color space (such as a three-color space like RGB or CIEXYZ, or any other color space like HSV, HSL, or CIELAB (L*a*b*)), or it can be described in any format as spectral data representing the spectral response of a material to incident light.

[0039] Another aspect of visual appearance is texture. The term "texture" should be broadly understood to refer to spatial variations in appearance across a material surface, both at microscopic or mesoscopic scales (i.e., scales at which individual structural elements are typically not perceptible to the naked eye) and macroscopic scales (i.e., scales at which individual structural elements are perceptible to the naked eye). Texture as understood in this disclosure includes phenomena such as graininess, glitter, and variations in surface morphology. Texture can be described using "texture properties." In the context of this disclosure, the term "texture property" should be broadly understood to encompass any form of data capable of quantifying at least one aspect of texture. Examples of texture properties include global texture properties, such as global glitter parameters.

[0040] A spectrophotometer is a device used to determine the reflectance and / or transmittance properties of a surface or material when illuminated with visible light (as a function of wavelength, i.e., the spectral response of the object). Different types of spectrophotometers are known, with varying geometries and optimized for different purposes. Some types of spectrophotometers (called multi-angle spectrophotometers) are capable of determining spectral information for multiple combinations of different illumination and viewing directions. Imaging spectrophotometers also have imaging capabilities, meaning they can include one or more cameras to capture one or more digital images of an object.

[0041] An "image" can be an image of an actual sample surface acquired with a digital camera, or it can be a composite image. An image can take the form of a two-dimensional array of image elements ("pixels"), each pixel having one or more pixel values. Pixel values ​​can represent reflectance at a pixel location at a specific wavelength, average reflectance over a specific wavelength range, or average reflectance across all visible light wavelengths. Therefore, in some embodiments, an image can be provided as an array of pixel values. In other embodiments, an image can be provided in a compressed or transformed form.

[0042] The term "directional illumination" refers to the situation where light is guided from a light source along a narrow range of illumination directions to a measurement point (also known as the measurement area) on the sample surface. Reflected light from the measurement area can be detected by a digital camera along the viewing direction. It should be understood that, due to the limited aperture of the light source and the size of the measurement point, the range of directions along which light can propagate from the light source to the measurement area is always limited. "Illumination direction" should be understood as the direction along which light propagates from the center of the light source aperture to the center of the measurement point. The angular range of the actual direction in which the light source illuminates the measurement point can typically be narrow, for example, less than 10°, preferably less than 8° (as specified in standard ATSM 2194-14), or even less than 5°. Similarly, due to the limited camera aperture and the size of the measurement point, the range of directions along which light can propagate from the measurement point to the camera and be recorded by the camera's image detector is always limited. "Viewing direction" or "observation direction" should be understood as the direction along which light propagates from the center of the measurement point to the center of the camera aperture. Similarly, the angular range of the light direction from the measurement point to the camera aperture can typically be narrow, such as less than 10°, preferably less than 8° (as specified in standard ATSM2194-14), or even less than 5°.

[0043] The term "mirror direction" refers to the direction in which light incident on the measurement point along the illumination direction is reflected by the sample surface in a mirror-like manner. The term "aspheric angle" refers to the angle between the viewing direction and the mirror direction. The aspheric angle can be defined in the plane spanned by the illumination direction and the mirror direction. When measured from the mirror direction of the sample surface toward the normal direction, the aspheric angle is then considered positive. The term "normal angle" refers to the angle between the illumination or viewing direction and the normal to the measurement plane.

[0044] The "HSV color space" is an example of a color space with hue coordinates, saturation coordinates, and intensity or lightness coordinates. More specifically, the HSV color space can be considered an example of a polar coordinate representation of the RGB color space. The coordinates hue (H), saturation (SV), and value (V) in this color space can be calculated from RGB values ​​as follows: in in, .

[0045] Alternative definitions of the transformation from RGB to HSV have been proposed in the literature and may also be used; this disclosure is not limited to the specific definition of the transformation.

[0046] The HSL color space is another example of the polar coordinate representation of the RGB color space. For HSV, the hue coordinate H is calculated, and the saturation coordinate S is calculated. L The brightness L can be calculated based on the RGB values ​​as follows: .

[0047] "Edge detection" refers to various mathematical methods designed to identify edges in digital images where there are abrupt changes in image brightness or discontinuities.

[0048] The term "database" refers to an organized collection of data that can be accessed electronically by a computer system. In a simple embodiment, a database can be a searchable electronic file in any format. Examples include Microsoft Excel™ spreadsheets or searchable PDF documents. In a more complex embodiment, the database can be a relational database maintained by a relational database management system using a language similar to SQL.

[0049] The term "computer" or "computing device" refers to any device that can automatically perform sequences of arithmetic or logical operations when instructed by a program. A computer can take the form of a desktop computer, laptop computer, tablet computer, smartphone, programmable digital signal processor, etc., but is not limited to these. A computer typically includes at least one processor and at least one memory device. A computer can be a subunit of another device (such as an appearance capture device). A computer can be configured to establish a wired or wireless connection with another computer (including a computer used for querying a database). A computer can be configured to couple via a wired or wireless connection to data input devices such as a keyboard or computer mouse and / or data output devices such as a monitor or printer.

[0050] A processor is an electronic circuit that performs operations on an external data source, particularly a memory device.

[0051] A "memory device," or simply "memory," is a device used to store information for use by a processor. Memory devices can include volatile memory, such as random access memory (RAM), and non-volatile memory, such as read-only memory (ROM). In some embodiments, a memory device can include a non-volatile semiconductor memory device, such as (E)EPROM or flash memory, which may take the form of, for example, a memory card or solid-state drive. In some embodiments, a memory device can include a high-capacity storage device with mechanical components, such as a hard disk. A memory device can store programs executed by a processor. Non-volatile memory devices can also be referred to as non-volatile computer-readable media.

[0052] A "program" is a collection of instructions that can be executed by a processor to perform a specific task.

[0053] A “wired connection” is a connection via an electrical conductor. A wired connection may include one or more cables. A “wireless connection” is a connection that includes the electromagnetic transmission of information between two or more points that are not connected by an electrical conductor. Wireless connections include connections via WiFi™, Bluetooth™, 3G / 4G / 5G mobile networks, optical communication, infrared, etc.

[0054] An exemplary multi-angle spectrophotometer with imaging capabilities exist Figure 1 and Figure 2 An exemplary handheld measuring device that can be used in the context of this disclosure is shown. Figure 1 and Figure 2 The handheld measuring device is a multi-angle spectrophotometer with imaging capabilities, as described in more detail in document US20140152990A1, the contents of which are incorporated herein by reference in their entirety for the purpose of teaching handheld multi-angle spectrophotometers with imaging capabilities. However, the invention is not limited to any particular type of handheld measuring device, and any handheld measuring device including at least one light source and at least one camera with an image detector can be used.

[0055] exist Figure 1 and Figure 2 The handheld measuring device shown is configured to capture the appearance of the surface of the object being measured (hereinafter referred to as the "sample surface"). In the following description, the term "measuring array" is understood to mean the sum of the components of the handheld measuring device used to illuminate a measurement area on the sample surface, capture light reflected from that measurement area, and convert it into a corresponding electrical signal. The term "device normal" is understood to mean an imaginary straight line that is fixed relative to the device and extends substantially through the center point of the measuring opening, and is perpendicular to the sample surface when the measuring device is placed on a flat sample surface. The plane of the measuring opening is generally parallel to the measurement point on the sample surface, such that the device normal is also perpendicular to the measuring opening. The term "perpendicular" is understood to mean the direction of the device normal. Therefore, "perpendicular section" should be understood to mean a planar section in a plane containing or parallel to the device normal. In the following description of the measuring device, the direction and / or angle are relative to the device normal, which is spatially fixed relative to the measuring device.

[0056] Figure 1 The handheld measuring device shown is generally indicated by the reference numeral HMD. It includes a housing H that houses the measuring array and electronic control circuitry (in... Figure 2(symbolically indicated by a box with reference numeral 300 in the figure), the electronic control circuit controls and reads out the measuring array and analyzes the signals received from the measuring array. Two gripping parts 1 and 2 are implemented laterally on the housing H. The wrist strap 3 is arranged on the upper side of the housing H. The display 4 is located on the front side of the housing H. The operating mechanism (not shown) is arranged on the upper side of the housing H.

[0057] The lower side of the housing H includes a housing base 5 reinforced by a substrate 7, which has a measurement opening 6. The housing base 5 includes a hole (not indicated by reference numerals) in the area of ​​the measurement opening 6, allowing light to exit the interior of the housing through the hole and the measurement opening 6, and conversely, allowing light from the outside to enter the interior of the housing through the measurement opening 6 and the hole. Three support members 7a, 7b, and 7c are arranged around the measurement opening 6 on the substrate 7, facilitating accurate positioning of the measuring device even on curved measuring surfaces, such that the device normal perfectly or at least approximately coincides with the normal of the sample surface at the center point of the measurement point.

[0058] Device normal at Figure 1 The reference numeral DN is used in the attached drawing. It is perpendicular to the substrate 7 and extends through the center point of the measuring opening 6.

[0059] Setting up the measurement array Figure 2 The diagram shows an electric arc body 10, which is fixedly held within a housing H, and optical and / or photoelectric components of the measurement array are arranged within the electric arc body 10. In the exemplary embodiment shown, these components include seven directional illumination systems 21, 22, 23, 24, 25, 26, and 27, and three detectors (pickup devices) 31, 32, and 33. Furthermore, a diffuse illumination system 28 is also arranged adjacent to the measurement opening 6.

[0060] Seven directional illumination systems 21-27 illuminate the measurement points on the sample surface along different fixed illumination directions relative to the device normal DN. For example, the optical axes of the directional light sources 21 to 27 can be oriented relative to the device normal at normal angles of -60°, -45°, -30°, -20°, 0°, +30°, and +65°, as shown below. Figure 3 As shown in the diagram. All seven directional light sources 21 to 27 are arranged such that their optical axes lie in a common plane containing the device normal DN, hereinafter referred to as the system plane SP. Each directional light source 21-27 may include a white LED and at least one optical component (e.g., one or more lenses) to produce a collimated or focused beam along the corresponding illumination direction. Figure 3 The sample surface 11 and measurement point 12 are also indicated.

[0061] Two of the three detectors 31-33 constitute a spectral measurement channel; the third detector constitutes a spatially resolved color measurement channel (imaging channel). The detectors receive measurement light reflected from the region of the illuminated measurement point of the measured object at viewing angles of +15° and +45° in the system plane SP. The two detectors 31 and 32 forming the spectral measurement channel include two spectrally resolved detectors (e.g., spectrometers) 31a and 32a, to which the measurement light is fed via lenses and optical fibers 31c and 32c. The detector 33 forming the spatially resolved measurement channel includes an image detector in the form of a color-enabled (RGB) camera 33a, to which the measurement light is applied via a beam splitter and a lens (not shown). The beam splitter is located in the pickup optical path of detector 32 and guides a portion of the measurement light laterally from the arc body 10 to the camera 33a at a viewing angle of +15°. Therefore, detectors 32 and 33 share the measurement light and receive it at exactly the same viewing angle.

[0062] The measurement geometry is the opposite of ASTM E2194-14 (2017) and ASTM E2539-14 (2017), which define two specular illuminations at 15° and 45° and six specular spectral channels at 0°, 30°, 65°, -20°, -30° and -60° for measuring metallic and pearlescent effect pigments, with an additional directional light source 22 at a -45° angle for use in conjunction with a pickup device 31 to measure gloss.

[0063] Two spectrometers, 31a and 32a, perform spectral analysis on the measurement light fed to them at viewing angles of 45° and 15°, respectively, and each measurement produces a set of spectral measurements, each corresponding to an intensity within a different wavelength range. Spectrometers 31a and 32a do not perform spatial analysis on the measurement light; that is, they perform spectral analysis on the entire amount of measurement light they receive.

[0064] The RGB camera 33a resolves spatially and spectrally the measurement light fed to it at a 15° viewing angle. Based on the three colors RGB, the spectral resolution is limited to three channels. The RGB camera accordingly generates a raw dataset of 3*n measurements per measurement, where n is the number of pixels resolved.

[0065] A diffuse illumination system 28 is provided, enabling the measuring device to also support measurement modes with diffuse illumination conditions. The diffuse illumination system 28 is configured as LED backlighting, which directly illuminates the measured object from a relatively large solid angle. It includes two rows of white light sources in the form of light-emitting diodes arranged on both sides of the measuring opening 6, and two inclined diffuser films, each assigned to one row, for uniform illumination. The two rows of LEDs can be controlled separately by the control circuit 300.

[0066] This measuring device enables the acquisition of an "orientation image" of the measurement surface under illumination from seven different directions, and a "diffuse image" of the measurement surface under diffuse illumination. Orientation images are frequently analyzed to determine the texture properties of the sample surface. In contrast, diffuse images are typically used only for preview purposes, providing a realistic impression of the visual appearance of the measurement point under diffuse illumination conditions, such as under overcast skies.

[0067] However, not all multi-angle imaging spectrophotometers include a diffuse illumination system. In such cases, it is impossible to provide a realistic preview image under diffuse illumination conditions. This disclosure addresses this shortcoming.

[0068] Exemplary embodiments of the methods according to this disclosure Figure 4 An exemplary embodiment of the method according to this disclosure is shown.

[0069] Initially, for three different measurement geometries, images D1, D2, and D3 (“direction images”) of the measurement points under directional illumination are obtained. For example, the direction images might have been obtained using the combination described above. Figures 1-3 The imaging multi-angle spectrophotometer discussed acquires and retrieves the images from its memory. In this example, the illumination directions of the three images are assumed to be normal angles of 0°, 30°, and 65° relative to the device normal, respectively, and for all three images, the viewing direction is assumed to be a normal angle of 15° in the system plane; that is, the viewing directions are assumed to be aspherical angles of 15°, 45°, and 80°, respectively. According to standard colorimetric practice, these measurement geometries are named r15as15, r15as45, and r15as80, respectively.

[0070] Each of the orientation images D1, D2, and D3 can be a color image. Specifically, each pixel in each orientation image can be represented by three pixel values, each a color value at a coordinate in a three-dimensional color space. As will be explained in more detail below, it is advantageous in this case to provide images D1, D2, and D3 in a color space with hue, saturation, and lightness coordinates (e.g., HSV or HSL color spaces) because the statistical correlation between pixel values ​​at different color coordinates is generally lower for such color spaces than for RGB. If the orientation images have already been acquired by an RGB camera, the RGB values ​​can therefore be converted to the preferred color space first.

[0071] Then, a statistical analysis is performed on each of the orientation images D1, D2, and D3 to determine the statistical parameters representing the statistical distribution of pixel values ​​in the corresponding orientation image (“pixel value histogram”). This is performed separately for each color coordinate n in the color space. The resulting statistical parameters for each color coordinate n can be specified as A. i,n,m The indexes i=1, ...,3 identify the measurement geometry, the indexes n=1, ...,3 identify the color coordinates, the indexes m=1, ...,M identify specific statistical parameters, and M specifies the total number of statistical parameters for each orientation image and each color coordinate.

[0072] For example, the statistical parameters can be determined as follows. First, histogram data can be generated for the corresponding image and color coordinates. For this, the entire range of possible pixel values ​​can be divided into a series of intervals (“bins”), and for each bin, the number of pixels whose pixel values ​​are within that bin can be determined. These bins can be specified as continuous, non-overlapping intervals, which may or may not have equal sizes. For example, for hue coordinates (which can range from 0° to 360°), 360 bins of size 1° can be specified, or 180 bins of size 2° can be specified, and so on. The histogram data can be normalized to a total area of ​​1, defined as the sum of the products of the bin size and the number of pixels in each bin. Next, a predefined probability distribution function (PDF) can be fitted to the histogram data. As will be explained in more detail below, a well-suited PDF is Johnson's SU distribution, defined by four parameters. A particularly useful method for determining the four statistical parameters characterizing said distribution will also be described below.

[0073] The statistical parameters {A} that have been determined in this way i,n,m The set of parameters {A} for the predicted probability distribution of the PDF is then fed into a prediction algorithm. p,n,m The PDF is predicted to represent the distribution of pixel values ​​at the same measurement points under diffuse illumination. As will be explained in more detail below, the prediction algorithm can be a machine learning (ML) algorithm that has been previously trained on a suitable training dataset.

[0074] Next, random sampling is performed using the predicted PDF to determine the pixel values ​​of the pre-image P. The size of the pre-image P can then be adjusted to obtain the final composite image S. For this purpose, the pre-image P can have a smaller size than the final composite image S. Resizing imparts a degree of short-range correlation to the pixel values ​​of neighboring pixels in the final composite image S, addressing the natural graininess in the image under diffuse illumination caused by the limited resolution of the detection optics. This will be explained in more detail below. Instead of resizing, or in addition to resizing, blurring can be applied to the pre-image P to obtain the final composite image S. Specifically, the pre-image P can be blurred by convolving it with a point spread function that simulates the response of a camera system in a spectrophotometer to a point object. In this case, the pre-image can have the same size as the final composite image. Resizing and blurring can also be combined.

[0075] Circular point spread function (PSF) in Figure 4 The diagram is schematically shown in the form of a two-dimensional profile (not to scale). Any suitable PSF can be used, such as an Airy disk or a 2D Gaussian function. If a point spread function is used, its parameters (particularly the length scaling parameters of the PSF, such as the virtual aperture size) can be easily determined empirically (e.g., by fitting the short-range correlation in the synthetic image to the short-range correlation of the orientation image, as described in more detail below), or by directly measuring the PSF of the spectrophotometer's camera system using a calibration sample. Since PSF typically exhibits very small inter-instrumental variations within the same model of instrument, determining the PSF only once for each spectrophotometer model may be sufficient.

[0076] Typical pixel value histogram Figure 5 Three graphs illustrating typical statistical distributions of pixel values ​​in oriented or diffuse images in the HSV color space are shown. For simplicity, the data are represented as continuous curves rather than typical histogram-type graphs. However, these graphs can be considered as histograms of pixel values. Each of these distributions exhibits a single peak with two independent tails.

[0077] Choice of probability distribution function Based on experience, a good PDF that can be fitted to histogram data has been found to be Johnson's SU distribution, a well-known four-parameter distribution that resembles a Gaussian distribution with two independent heavy tails. Its PDF is defined as follows: For four different sets of parameters γ, δ, ξ, and λ, the PDF is in Figure 6 As shown in the figure, Johnson's SU distribution is entirely specified by these four parameters.

[0078] In contrast, the simple Gaussian distribution leads to poorer results because it has no heavy tail. Furthermore, the gamma distribution has proven to be poor in most cases because it lacks a heavy left tail.

[0079] Characteristic probability distribution function While the parameters γ, δ, ξ, and λ fully specify Johnson's SU distribution, it has been empirically found that these parameters are not ideal predictors for subsequent prediction algorithms. For example, they are sensitive to noise or small image variations. Instead, a different method has been developed to characterize the histogram of pixel values, where the corresponding cumulative density function (CDF) is considered, and the percentiles of the CDF are used as predictors. In the following text, these percentiles will be referred to as "anchors." Since Johnson's SU distribution has four parameters, four "anchors" are sufficient to fully specify this distribution.

[0080] The determination of the "anchor" is in Figure 7 As shown in the figure, Figure 7 An exemplary CDF of Johnson's SU distribution is shown, along with the 20th, 40th, 60th, and 80th percentiles, which are labeled A, B, C, D, and E respectively. i,n,1 A i,n,2 A i,n,3 and A i,n,4 Once the PDF has been fitted into histogram data, the corresponding CDF and its percentiles, or "anchors," can be easily determined and used directly as predictors. They are continuous, have well-defined ranges (e.g., in the HSV color space, H ranges from 0° to 360°, and S and V range from 0 to 1), and are robust to small perturbations in the input. This makes anchors an excellent choice for predictors in prediction algorithms.

[0081] Prediction Algorithm For prediction, machine learning algorithms (ML algorithms) are advantageously used. Given that the input and output data are tabular, regression algorithms, especially gradient boosting regression algorithms, are well-suited. In one embodiment, the XGBoost software library is used to implement the prediction algorithm. The XGBoost model is a robust, out-of-the-box ML model that is well-suited for tabular data, works correctly without fine-tuning, and accepts predictors of different scales. No preprocessing, centering, or scaling is required.

[0082] To train the algorithm, a training dataset containing training data from a large number of surfaces can be used. For each surface, I ≥ 2 measured orientation images and one measured diffuse image can be provided. For each orientation image, M anchors (e.g., four anchors) can be determined for each of the N color space dimensions, resulting in a total of N ⋅ M ⋅ I anchors. Similarly, for the diffuse image, M anchors can be determined for each of the N color space dimensions. The N ⋅ M ⋅ I anchors associated with the orientation images can be used as inputs to the prediction algorithm (predictor), and the N ⋅ M anchors associated with the diffuse image can be used as target values ​​for the prediction algorithm (“training data”).

[0083] In one embodiment, a database comprising data from 1937 surfaces was used as the training dataset. The data for each surface included I=3 measured orientation images of geometries r15as15, r15as45, and r15as80, and one measured diffuse image of geometry r15d. All images were converted to the HSV color space, which has N=3 color space dimensions. For each orientation image and each color space dimension, M=4 anchors were computed, resulting in a total of N⋅M⋅I=3⋅3⋅4=36 predictors and N⋅M=12 targets. The XGBoost model was trained using this training data.

[0084] Data from an additional 194 surfaces were used as test data. Similarly, 3×3×4=36 anchors were determined as predictors for each surface. Predictions were made using a pre-trained XGBoost model to obtain 3×4=12 anchors for the predicted diffuse image. Based on these anchors, the CDF of Johnson's SU distribution was determined for each color coordinate, and the corresponding PDF was determined. The resulting PDF was compared with the histogram of pixel values ​​from the actual measured diffuse image. A good match was obtained. The PDF was randomly sampled to create a small 178×133 pixel preimage, and this preimage was scaled by a factor of 2.7 to obtain a synthetic diffuse image of 480×360 pixels. The synthetic diffuse image was visually compared with the actual measured diffuse image. For most surfaces, a good visual match was observed.

[0085] Considerations regarding color spaces If only a black-and-white image (e.g., silver paint) is of interest, the above process can be performed on only a single color channel (i.e., the intensity / luminance channel, e.g., as the average of the RGB channels). The same applies if the orientation image exists only as a black-and-white image. For example, some known imaging spectrophotometers consist only of a black-and-white camera.

[0086] On the other hand, if the synthesized diffuse image would be a color image, the following considerations regarding the selection of an appropriate color space apply. In this case, performing the above process in a three-color space like RGB is not optimal because for many surface materials, the pixel values ​​in the three color channels (i.e., along the three dimensions of the color space) are correlated. Therefore, sampling the three color channels independently may result in results that do not quite match reality.

[0087] It is possible to find a color space in which pixel values ​​have the least correlation between color channels and to transform the orientation image into that color space. For example, principal component analysis (PCA) can be performed for this purpose.

[0088] However, such a process is computationally expensive and therefore may be undesirable in real-time applications. It has been found that in many cases, simply using a color space with hue, saturation, and intensity / luminance coordinates (especially the HSV or HSL color spaces) is sufficient. In such color spaces, the correlation between color space dimensions is generally greatly reduced. An added advantage compared to color spaces obtained through PCA is the ease with which color values ​​can be interpreted.

[0089] One problem with color spaces having hue, saturation, and brightness coordinates is that the hue coordinates H are often cyclic, ranging, for example, from 0° to 360°. Before determining the anchors of the hue coordinates (i.e., the percentiles of the CDF), it should preferably be ensured that these anchors are sufficiently far from the 360°→0° boundary. A simple algorithm for this is as follows: if the mode of the H histogram is <100, shift the H histogram by Δ = +180° and take the modulus of 360°; if the mode is >260, shift the H histogram by Δ = -180° and take the modulus of 360°; otherwise, shift by Δ = 0. Then determine the anchors of the shifted H histogram. Finally, shift the anchors by -Δ to obtain the anchors of the distribution at the original positions. After prediction and sampling operations, the hue coordinates H of the resulting composite image should again be taken modulo 360° to remove values ​​<0° or >359°. Of course, other possibilities exist for handling cyclic H coordinates.

[0090] In practice, the camera's optical system can introduce chromatic aberration, which in some cases (such as with silver paint) can cause the H histogram to exhibit bimodality, even if the "true" H distribution is unimodal. This problem can be mitigated by blurring the H channel (and preferably the S channel) of the oriented image with a kernel of sufficient spatial extent to average the chromatic aberration.

[0091] Pre-image In some embodiments, a pre-image is created, which may be a small image (preferably an HDR image), and this small image is then enlarged to the final image size to simulate limited optical resolution. For example, the final image size may be 480 × 360 pixels, and the pre-image size may be 178 × 133 pixels (corresponding to a scaling factor of 2.7). Resizing can be accomplished, for example, using bicubic interpolation or nearest-neighbor interpolation. Nearest-neighbor interpolation is preferred because it does not distort the histogram of pixel values ​​in the pre-image in the HSV color space.

[0092] In other embodiments, the pre-image may already have the final image size and may be blurred to obtain the final image.

[0093] Determining the scale of short-range spatial correlation Spatial correlation in an image can be simply considered as "grain size": the larger the grain, the greater the spatial correlation. However, grain size does not necessarily correspond to the actual size of a feature on the sample surface. For example, in the case of effect pigments containing metallic flakes, the "grain size" may be much larger than the flake size, which is typically in the micrometer range. One reason for this is that the optical resolution of cameras is often too low to resolve very small features at the micrometer scale. Another reason is the saturation of the image sensor: specular reflections from the flakes can cause saturation of a few pixels in the image detector. In this sense, "grain size" is more related to the brightness of individual flashes: the higher the brightness, the larger the flash.

[0094] In the example above, the "particle size" is adjusted by a manually tuned scaling parameter of 2.7. A more systematic approach to studying this parameter is presented below.

[0095] We define a normalized autocorrelation function R(x, y), where x and y are pixel distances along the 2D image direction, and are the real parts of the inverse 2D Fourier transform of the absolute square of the 2D Fourier transform of the normalized V image channels (for the HSV color space), or, in more general terms, the real parts of the luminance coordinates V in the color space: Where “std” represents the standard deviation, and E[V] represents the expected value (mean) of V.

[0096] Starting from the first pixel, the autocorrelation function of the randomly sampled preimage is zero because all image pixels are sampled independently, so there is no spatial correlation. In contrast, the autocorrelation function determined for the actual measured diffuse image tells us that, on average, image features (“granules”) extend over several pixels.

[0097] An autocorrelation parameter can be defined for each image using an autocorrelation function, and this parameter can be used to create spatial correlations in a composite diffuse image, for example, by resizing or blurring. For instance, the autocorrelation parameter can be defined as the average length (measured in pixels) of the autocorrelation function decaying to 1 / e, and this length can be used as a resizing factor. For the instrument used in the example above, this length scales to approximately 2.8 pixels, which explains why scaling the pre-image by a factor of 2.7 results in good results. As another example, the autocorrelation parameter can be the average autocorrelation coefficient at a fixed distance (e.g., a distance of two pixels).

[0098] If the autocorrelation parameter is unknown, it can be automatically determined by the prediction algorithm. For this purpose, the autocorrelation parameter (e.g., the average autocorrelation coefficient at a two-pixel distance) can be determined for each orientation image and can be used as additional input to the prediction algorithm. The same or different autocorrelation parameters for the predicted diffuse image (e.g., resizing or length scaling parameters for the PSF used for blurring) can be one of the outputs of the prediction algorithm. If the prediction algorithm is an ML algorithm, the training dataset should, of course, also include the measured orientation image and the corresponding autocorrelation parameters of the corresponding measured diffuse image.

[0099] Handling flash points Even in a color space with hue, saturation, and brightness coordinates (such as HSV), directional images containing flashes can exhibit strong correlations between color coordinates. This can be explained as follows: flashes are much brighter than the background and have a specific hue (e.g., white). This means that for these points, high brightness (V) is associated with specific H and S values. This correlation can cause synthetic diffuse images to appear unrealistic.

[0100] This can be mitigated by processing the background image and the flash pixels separately. To do this, flash pixels in the orientation image can be identified and separated from the background pixels. This can be done, for example, using a simple thresholding method that considers all pixels with L or V values ​​above a certain threshold as flash pixels, or using more complex methods such as edge detection. The process is as follows: Figure 8 As shown in the figure, Figure 8 A small image patch of a typical orientation image is schematically shown. Most pixels have relatively low brightness (indicated by dark gray shading in the attached figure). However, some pixels appear very bright, such as those around pixel 201. These pixels are considered flash pixels and are removed from the orientation image to create an orientation background image.

[0101] Then, a "diffuse background image" can be synthesized using the directional background image. Similarly, an array of synthesized "diffuse flash pixels" can be synthesized in the same way based on the flash pixels of the directional image. The synthesized flash pixels can then be inserted into the synthesized diffuse background image at random locations.

[0102] Exemplary hardware of the control circuit Figure 9 It shows in Figure 1 and Figure 2 A highly schematic functional diagram of the electronic control circuitry 300 in a handheld measuring device. The processor 310 communicates via a bus system 301 with a non-volatile (ROM) memory 320, a volatile (RAM) memory 330, an input / output (I / O) interface 340, and a communication interface 350. The non-volatile memory 320 may be, for example, a flash memory device. It specifically stores the operating system 321 and several application programs, including prediction software 322 for performing prediction operations and image synthesis software 323 for performing sampling and possible resizing / blurring operations.

[0103] Attached to the input / output interface 340 are a display device 4, one or more control components 9 in the form of one or more buttons, a light source for the lighting system 21-28, and detectors 31-33.

[0104] The communication interface 350 may include one or more of, for example, an Ethernet interface, a WiFi interface, a Bluetooth™ interface, etc. The control circuitry 300 may transmit directional images and / or diffuse images to an external computing device or an external display via the communication interface 350.

[0105] In other embodiments, the prediction and / or image synthesis steps are performed by external circuitry. In this case, the orientation images or anchors already determined for these images are transmitted to the external circuitry via communication interface 350, and prediction parameters for synthesizing diffuse images and / or PDFs of diffuse images are received from the external circuitry via communication interface 350.

[0106] Revise The above combination Figure 3 The method discussed can be easily modified to suit cases where only two combinations of lighting and viewing direction exist, or cases where more than three such combinations exist. This modification is simple.

[0107] In the example above, it is assumed that the measuring device includes multiple directional illumination systems in two or more illumination directions and a single camera in a fixed viewing direction. However, it is also possible to use only a single unidirectional illumination system in the fixed illumination direction and multiple cameras in two or more viewing directions. Combinations of two or more illumination systems and two or more cameras are also possible. If the illumination system and / or camera can be moved between two or more orientations relative to the measurement point, then even providing only a unidirectional illumination system and a single camera may be sufficient. Orientation images can then be acquired sequentially in these orientations.

[0108] The images do not need to be color images. They can be grayscale images where each pixel has only a single pixel value representing the total intensity of reflected light in that pixel. For example, the camera in a multi-angle imaging spectrophotometer can be a monochrome camera. In this case, the synthesized image can also be a grayscale image. In other embodiments, it may be possible to obtain a color image by operating an illumination system to sequentially generate light of different colors, and to acquire images of each color separately.

[0109] Instead of fitting a predefined PDF to histogram data and determining the percentiles of the corresponding CDF, it's also possible to directly determine the percentiles of the cumulative pixel value histogram data. However, in practice, more stable and accurate results can be obtained by first fitting the PDF to the pixel value histogram.

Claims

1. A method for synthesizing a diffuse image (S) representing the appearance of a surface (11) under diffuse illumination, the diffuse image (S) comprising an array of diffuse image pixels, each having at least one diffuse image pixel value, the method comprising: a) obtaining at least two directional images (D1, D2, D3) of a measurement point (12) on the surface (11), each directional image (D1, D2, D3) having been acquired under directional illumination of the measurement point from an illumination direction along a viewing direction, the illumination and / or viewing direction differing between the at least two directional images, each directional image (D1, D2, D3) comprising an array of directional image pixels, each having at least one directional image pixel value; b) for each directional image (D1, D2, D3), determining a plurality of statistical parameters ({A 1,n,m}, {A 2,n,m}, {A 3,n,m}) representative of a statistical distribution of the directional image pixel values in the respective directional image (D1, D2, D3); c) Using statistical parameters associated with the at least two orientation images ({A 1,n,m }, {A 2,n,m }, {A 3,n,m }) as a predictor, predicting multiple probability distribution parameters ({A) p,n,m }), the probability distribution parameter ({A) p,n,m } represents the predicted probability distribution function of pixel values ​​in a diffuse image; d) determining the diffuse image pixel values based on sampling from a predicted probability distribution function.

2. The method according to claim 1, wherein determining statistical parameters ({A 1,n,m}, {A 2,n,m}, {A 3,n,m}) comprises fitting a probability distribution function having one maximum and two independent tails, in particular a Johnson's SU distribution, to the directional image pixel values in each directional image (D1, D2, D3) and determining the statistical parameters based on the probability distribution function thus obtained.

3. The method according to claim 1 or 2, wherein for each directional image (D1, D2, D3) at least four statistical parameters ({A 1,n,m}, {A 2,n,m}, {A 3,n,m}) are determined, where the statistical parameters ({A 1,n,m}, {A 2,n,m}, {A 3,n,m}) are preferably percentiles of a cumulative density function representing the statistical distribution of the directional image pixel values in the respective directional image (D1, D2, D3).

4. The method according to any one of the preceding claims, wherein determining the diffuse image pixel values comprises applying a noise model to create a spatial correlation in the diffuse image (S).

5. The method according to any one of the preceding claims, wherein determining the diffuse image pixel values comprises: dl) synthesizing a pre-image (P) having a plurality of pre-image pixels, wherein for each pre-image pixel a pre-image pixel value is computed, wherein the computation of the pre-image pixel value comprises a random sampling from a predicted probability distribution function; and d2) determining the diffuse image pixel values from the pre-image pixel values in such a way that a spatial correlation between the diffuse image pixel values is induced.

6. The method according to claim 5, wherein determining the diffuse image pixel values from the pre-image pixel values comprises: adjusting the size of the pre-image (P) or an image derived therefrom by an adjustment factor to obtain the diffuse image (S); and / or applying a blurring operation to the pre-image (P) or an image derived therefrom to obtain the diffuse image (S), in particular by convolving the pre-image (P) with a point spread function (PSF).

7. The method according to any one of claims 4-6, comprising: determining at least one spatial autocorrelation parameter for each of the directional images (D1, D2, D3); and considering the spatial autocorrelation parameters of the directional images (D1, D2, D3) when determining the diffuse image pixel values, wherein the method preferably comprises predicting the spatial autocorrelation parameters of the diffuse image and using the spatial autocorrelation parameters of the diffuse image for determining the diffuse image pixel values.

8. The method according to any one of the preceding claims, wherein each diffuse image pixel has at least three diffuse image pixel values, each diffuse image pixel value being a color value in a color space having at least three color space dimensions (H, S, V), wherein each directional image pixel has at least three directional image pixel values, each directional image pixel value being a color value in the color space, wherein steps a) and b) are performed for each of the color space dimensions (H, S, V), respectively, and 9. The method according to claim 8, where the prediction of the probability distribution parameters ({A p,n,m}) is performed for all color space dimensions (H, S, V) together. ​ wherein the directional image is obtained in a first color space, in particular a trichromatic color space, and wherein the method comprises: transforming the directional image pixel color values into a second color space in which the directional image pixel color values have a reduced correlation between different color space dimensions as compared to the first color space, in particular wherein the second color space has a hue dimension (H), a saturation dimension (S), and an intensity or lightness dimension (V), more in particular wherein the color space is an HSV or HSL color space.

10. The method according to claim 8 or 9, comprising: performing a correlation analysis on the directional image pixel values along different color space dimensions in the first color space to determine the second color space as the color space that minimizes the correlation between the directional image pixel color values along different color space dimensions of the second color space.

11. The method according to any one of the preceding claims, comprising: determining glint pixels (201) in the directional image, the glint pixels representing glint points; removing the glint pixels (201) from the directional image to obtain a directional background image; performing steps a) to d) using the directional background image to obtain a synthesized diffuse background image; and optionally inserting simulated glint points into the diffuse background image.

12. The method according to any one of the preceding claims, wherein the probability distribution parameters are predicted using a machine learning algorithm that has been trained using a training data set comprising at least two measured directional images (D1, D2, D3) and one measured statistical parameter of a diffuse image for each of a plurality of surfaces, wherein the machine learning algorithm is preferably a regression algorithm, in particular a regression gradient boosting algorithm.

13. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to any one of the preceding claims.

14. An imaging spectrophotometer, comprising: at least one directional light source (21-27) for illuminating a measurement spot (12) on a sample surface (11) from at least one predefined illumination direction; at least one image detector (33a) for acquiring an image of the measurement spot (12) along a predefined viewing direction; and processing circuitry configured to carry out the method according to any one of claims 1-12.

Images