A reverse mapping cross-interface tomography method

Abstract

The present invention discloses a reverse mapping cross - interface tomography method. First, a reverse ray - tracing relationship is established. The ray starts from a point on the pixel coordinate system of the projection, passes through the lens center to a unique corresponding point on a certain voxel layer of the target to be measured. Then, a reverse mapping relationship is established. Next, the projection weight coefficient is directly calculated according to the intersection volume fraction of the reverse - traced light path and the spherical voxel. Finally, the point spread function is obtained. The present invention not only solves the problem of projection distortion in tomography in a limited space, but also only requires the reverse mapping relationship from the pixel projection in two - dimensions to the voxel in the three - dimensional target field, without involving the forward projection process from the voxel to the pixel, avoiding the time - consuming mapping relationship conversion step, saving a large amount of computing resources, and improving the computing efficiency.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical imaging, and particularly relates to a reverse mapping cross-interface tomography method. Background Technique

[0002] Tomography reconstructs the three-dimensional spatial distribution of a selected target from projections obtained by simultaneous measurements from different perspectives, and is widely used in flow and combustion problems. According to the type of measurement environment, the tomography problem can be divided into two types: confined space and open space. Signals emitted by the measured targets in the open space are directly received by the image sensor, and these targets generally have a preset characteristic spatial distribution (dye solution with uniform dye concentration, premixed conical flame, etc.). Tomography reconstruction technology is often used to study the three-dimensional distribution of flame combustion and fluid flow characteristics, such as velocity field, concentration, flame surface characteristics, and temperature. However, in actual situations, combustion and flow often occur in a confined space, and the environmental conditions, flow, and flame presentation modes are more complex than those in the open space, which poses a great challenge to the analysis of flow or combustion mechanisms.

[0003] However, for the study of confined space problems, many previous studies have ignored the projection distortion caused by the continuous refraction of light passing through a transparent medium. In a confined space, the light path passes through the optical wall and undergoes two refractions. If ray tracing is directly performed from the voxels in the measurement area to the projection pixels, a large number of rays need to be emitted from each position in the measurement domain to find the only light path passing through the optical center of the lens, and a large number of iterative steps are required in the algorithm application, which is very time-consuming. Although in some two-dimensional optical diagnostic techniques, perpendicularity of the optical axis of the image sensor to the transparent medium surface can reduce the refraction effect, when performing three-dimensional tomography measurements, signals need to be received by the sensor from multiple different angles, and it is impossible to make each image sensor perpendicular to the medium surface. Therefore, the projection will inevitably be affected by light refraction, introducing a large computational error into the tomography reconstruction. Moreover, compared with the projection measured in the open space, the projection obtained by measuring through a planar medium only has an overall pixel shift, but when measuring through a transparent medium with a curved surface (such as an internal combustion engine cylinder), not only will pixel shift occur, but also signal distribution distortion will occur, resulting in a reduction in the accuracy of the reconstruction result. For this problem, relevant cross-interface three-dimensional tomography algorithms have been developed, such as the three-dimensional cross-interfaces computed tomography (CICT) imaging method.

[0004] However, in the past, when calculating the mapping relationship between projection pixels and voxels, the algorithm always first established the reverse ray tracing relationship from the two-dimensional projection to the three-dimensional area to be measured, then used a mathematical model to convert the reverse ray tracing relationship into the forward ray tracing relationship (i.e., from the three-dimensional target to the two-dimensional projection), and finally calculated the point spread function. The calculation is very time-consuming, especially when the measurement accuracy requirements are high and the discrete size of the pixel voxels is very small, the time consumed increases exponentially. Summary of the Invention

[0005] In view of this, the present invention provides a reverse mapping cross-interface tomography method, that is, the RMCICT (Reversal-Mapping Cross-Interfaces Computed Tomography) imaging method, which adopts a simpler imaging model to avoid the time-consuming mapping relationship conversion step, and effectively improves the calculation speed while ensuring the reconstruction calculation accuracy.

[0006] The present invention is realized by the following technical solutions:

[0007] A reverse mapping cross-interface tomography method, based on the imaging of the target to be measured in a transparent hollow cylindrical cylinder sleeve on a camera outside the cylinder sleeve, includes the following steps:

[0008] Step S1: Establish a pixel array coordinate system for camera imaging and a voxel space coordinate system inside the cylinder sleeve;

[0009] Step S2: Perform reverse ray tracing to establish a reverse mapping relationship from the pixel array coordinate system to the voxel space coordinate system;

[0010] Step S3: According to the reverse mapping relationship in Step S2, obtain the projection weight coefficient of each voxel;

[0011] Step S4: Based on the projection weight coefficient of each voxel in Step S3, establish a point spread function matrix from the voxels on all voxel layers to the CCD plane according to the reverse mapping relationship, and realize the imaging of the target to be measured placed in the cylinder sleeve on the CCD plane.

[0012] Further, the specific method of Step S1 is:

[0013] The method of establishing the pixel array coordinate system for camera imaging is: the camera is simplified into an imaging system composed of a CCD plane containing a number of pixel arrays of the same size and a convex lens. A two-dimensional Cartesian coordinate system o-xz is defined with the center point of the CCD plane as the origin, the x direction is the horizontal axis of the CCD plane, and the z direction is the vertical axis of the CCD plane;

[0014] The method for establishing the voxel space coordinate system within the cylinder liner is as follows: The cylindrical space enclosed by the cylinder liner is discretized into two or more voxel layers, each voxel layer being parallel to a meridian plane within the cylindrical space enclosed by the cylinder liner. Each voxel layer is composed of a number of voxel blocks of the same size. The center of the bottom surface of the cylinder liner is set as the origin O, and a three-dimensional Cartesian coordinate system O-XYZ is defined, where the direction perpendicular to the voxel layer is the Y direction, the central axis of the cylinder liner is the Z direction, and the X direction is perpendicular to the Y and Z directions.

[0015] Furthermore, the voxel is spherical.

[0016] Furthermore, the specific method of step S2 is as follows:

[0017] Step S21: Conduct reverse ray tracing: Select any one voxel layer as the current voxel layer. For a point on the CCD plane, emit a ray passing through the center of the lens that passes through the outer and inner surfaces of the cylinder liner and intersects the current voxel layer at a point. According to the theorem of light propagation and Snell's law, calculate the coordinates of the point on the current voxel layer, that is, obtain the coordinates of the corresponding point on the current voxel layer for a point on the CCD plane.

[0018] Step S22, establish a reverse mapping relationship: Based on the reverse ray tracing in step S21, for the i-th point A i ' on the CCD plane, according to the reverse ray tracing in step S12, trace to its corresponding point A ji on the j-th voxel layer in the voxel space coordinate system, and establish a reverse mapping relationship from the pixel array coordinate system to the voxel space coordinate system.

[0019] Furthermore, the further introduction of step S21 is as follows:

[0020] S211: Use the calibration plate as the object to be measured and place it on any voxel layer within the cylinder liner. Select any point A' on the CCD plane and let a ray emitted from A' pass through the center C of the lens and intersect the outer surface of the cylinder liner at point E, and calculate the incident angle α of the ray at point E Ei , and the specific formula is as follows:

[0021]

[0022] where is the incident ray vector at point E, is the normal vector at point E;

[0023] S212, calculate the exit angle α of the ray at point E according to Snell's law Ee , and the specific formula is as follows:

[0024]

[0025] Among them, n air is the refractive index of light in air, and n quar t z is the refractive index of light in the cylinder liner material;

[0026] S213. According to the light emergence angle α Ee of the light, determine the intersection point F of the light and the inner surface of the cylinder liner, and calculate the incident angle α Fi of the incident light at point F. The specific formula is as follows:

[0027]

[0028] Among them, is the incident light vector at point F, is the normal vector at point F;

[0029] S214. According to the incident angle α Fi of the incident light at point F and Snell's law, calculate the emergence angle α Fe of the emergent light at point F. The specific formula is as follows:

[0030]

[0031] S215. According to the emergence angle α Fe of the emergent light at point F, determine the intersection point A of the light and the calibration plate, and then obtain the coordinates of the corresponding point A on the calibration plate of any point A' on the CCD plane.

[0032] Furthermore, the specific method of step S3 is as follows: Select more than three feature points on the pixels on the CCD plane. Based on the inverse mapping relationship, form an inverse tracking light path. According to the inverse tracking light path and the intersection volume fraction of the voxels, obtain the projection weight coefficient of the voxels.

[0033] Furthermore, the way to form the inverse tracking light path is as follows: Select the four vertices of any pixel on the CCD plane as feature points, namely points H, I, J, and K. According to the inverse mapping relationship, obtain four inverse rays, and form an inverse tracking light path with these four rays as the boundaries.

[0034] Furthermore, the way to obtain the projection weight coefficient of the voxels according to the inverse tracking light path and the intersection volume fraction of the voxels is as follows: Obtain all the voxels where the light path intersects with all the voxel layers, calculate the percentage of the volume of each voxel intersecting with the light path in the volume of a single voxel, and this percentage is the projection weight coefficient of each voxel.

[0035] Further, convert the actually frustum-shaped reverse-tracing optical path into a cylindrical optical path, where the area of the cylindrical end face is the same as that of the frustum-shaped end face.

[0036] Advantages:

[0037] (1) For the reverse mapping cross-interface tomography method provided by the present invention, first establish the reverse ray tracing relationship. The ray starts from a point on the pixel coordinate system on the projection, passes through the lens center to the unique corresponding point on a certain voxel layer of the target to be measured, then establish the reverse mapping relationship, and then directly calculate the projection weight coefficient according to the intersection volume fraction of the reverse-tracing optical path and the spherical voxel. Finally, obtain the point spread function. This method not only solves the problem of tomographic imaging projection distortion in a limited space, but also only requires the reverse mapping relationship from the pixels in two dimensions to the voxels in the three-dimensional target field, without involving the forward projection process from voxels to pixels, avoiding the time-consuming mapping relationship conversion step, saving a large amount of computing resources, and improving the computing efficiency.

[0038] (2) The present invention respectively establishes a two-dimensional pixel array coordinate system on the CCD plane and a three-dimensional voxel space coordinate system. According to the principle of light propagation, for any point on the CCD plane, the unique corresponding point on a certain voxel layer in the three-dimensional voxel space coordinate system is traced back, realizing the one-to-one correspondence between the points on the two-dimensional pixel array coordinate system and the points in the three-dimensional voxel space coordinate system.

[0039] (3) In the present invention, spherical voxel blocks are adopted. The spherical voxel blocks are isotropic and are more in line with the characteristics of voxel light signal emission in practice than cubic voxel blocks, eliminating the projection error from cameras at different angles and improving the measurement accuracy.

[0040] (4) By using the principle of light propagation and Snell's law to calculate the light propagation trajectory, for any point on the CCD plane, the unique corresponding point on a certain voxel layer in the three-dimensional voxel space coordinate system is traced back, solving the problem of tomographic imaging projection distortion caused by the refraction of light by the inner and outer walls of the cylinder liner in the limited space of the cylinder liner.

[0041] (5) The present invention selects feature points on pixels on more than three CCD planes and performs reverse ray tracing to form a reverse tracing optical path. All the optical signals that the pixels can receive are included in the reverse tracing optical path. The voxels on all voxel layers that intersect with the optical path are all the voxels that contribute to the signal projection of the pixels. Therefore, the volume fraction can be used to calculate the projection weight coefficient. Using the volume fraction to calculate the projection weight coefficient eliminates the need for forward projection, that is, there is no need to obtain the projection point coordinates of each point on each voxel layer on the CCD plane through linear fitting based on projection similarity, thereby avoiding the time-consuming mapping relationship conversion step, simplifying the calculation steps, and saving computing resources.

[0042] (6) The four vertices of any pixel on the CCD plane of the present invention are used as feature points. Compared with the selection of other feature points on the pixel, it can better reflect the true projection relationship of pixel reverse mapping.

[0043] (7) In the present invention, the reverse tracing optical path is approximated as a cylinder, which is convenient for calculating the intersection volume of the cylinder and the sphere mathematically under the condition of little influence on the calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic flowchart of the RMCICT imaging method;

[0045] Figure 2 is a schematic diagram of the reverse ray tracing relationship on the calibration plate;

[0046] Figure 3 is a schematic diagram of the optical path intersection model; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The following examples are given in conjunction with the drawings to describe the present invention in detail.

[0048] This embodiment provides a reverse mapping cross-interface tomography method based on the imaging of a target to be measured in a transparent hollow cylindrical cylinder sleeve on a camera outside the cylinder sleeve. The cylinder sleeve is made of quartz material.

[0049] Referring to the attached Figure 1 , the method includes the following steps:

[0050] Step S1: Establish a pixel array coordinate system for camera imaging and a voxel space coordinate system inside the cylinder sleeve. The specific method is as follows:

[0051] Referring to the attached Figure 2 , the specific method for establishing the pixel array coordinate system for camera imaging is as follows: The camera is simplified into a CCD plane (i.e., the camera plane in Figure 2 ) containing a number of pixel arrays of the same size and a convex lens (i.e., Figure 2An imaging system composed of lenses) defines a two-dimensional Cartesian coordinate system o-xz with the center point of the CCD plane as the origin. The x-direction is the horizontal axis of the CCD plane, and the z-direction is the vertical axis of the CCD plane;

[0052] See the appendix Figure 2 and the appendix Figure 3 The method of establishing the voxel space coordinate system in the cylinder liner is as follows: The cylindrical space enclosed by the cylinder liner is discretized into two or more voxel layers. Each voxel layer is parallel to a meridian plane (i.e., a section passing through the axis of the cylindrical cylinder liner) within the cylindrical space enclosed by the cylinder liner. Each voxel layer is composed of several spherical voxel blocks (i.e., voxels) of the same size; Set the center of the bottom surface of the cylinder liner as the origin O, and define a three-dimensional Cartesian coordinate system O-XYZ, where the direction perpendicular to the voxel layer is the Y-direction, the central axis of the cylinder liner is the Z-direction, and the X-direction is perpendicular to the Y and Z directions.

[0053] It should be noted that each voxel layer is composed of several spherical voxel blocks (i.e., voxels) of the same size. The spherical voxel blocks are isotropic and more in line with the characteristics of voxel emission of light signals in practice than cubic voxel blocks, eliminating the projection error from cameras at different angles and improving the measurement accuracy.

[0054] Step S2: Perform reverse ray tracing to establish the reverse mapping relationship from the pixel array coordinate system to the voxel space coordinate system, which is specifically introduced as follows:

[0055] Step S21: See the appendix Figure 2 The specific method of performing reverse ray tracing is as follows: Select any voxel layer as the current voxel layer. For a point on the CCD plane, emit a ray passing through the center of the lens, which passes through the outer and inner surfaces of the cylinder liner and intersects the current voxel layer at a point. According to the theorem of light propagation and Snell's law, calculate the coordinates of the point on the current voxel layer, that is, obtain the coordinates of the corresponding point on the current voxel layer for the point on the CCD plane. The specific example is introduced as follows:

[0056] S211: Use the calibration plate as the target to be measured and place it on any voxel layer within the cylinder liner. Select any point A' on the CCD plane. Let a ray emitted from A' pass through the center C of the lens and intersect the outer surface of the cylinder liner at point E, and calculate the incident angle α of the ray at point E Ei , and the specific formula is as follows:

[0057]

[0058] where is the incident ray vector at point E, is the normal vector at point E (towards the direction adapting to the cylindrical axis of the cylinder liner);

[0059] S212. Calculate the exit angle α of the light ray at point E according to Snell's law. The specific formula is as follows: Ee , specifically as follows:

[0060]

[0061] where n air is the refractive index of light in air, and n quartz is the refractive index of light in the cylinder liner material;

[0062] S213. Determine the intersection point F of the light ray and the inner surface of the cylinder liner according to the exit angle α of the light ray, and calculate the incident angle α of the incident light ray at point F. The specific formula is as follows: Ee , specifically as follows: Fi , specifically as follows:

[0063]

[0064] where is the incident light ray vector at point F, and is the normal vector at point F;

[0065] S214. Calculate the exit angle α of the exit light ray at point F according to the incident angle α of the incident light ray at point F and Snell's law. The specific formula is as follows: Fi , specifically as follows: Fe , specifically as follows:

[0066]

[0067] S215. Determine the intersection point A of the light ray and the calibration plate according to the exit angle α of the exit light ray at point F, and then obtain the coordinates of the corresponding point A on the calibration plate of any point A' on the CCD plane. Fe , specifically as follows:

[0068] It should be noted that referring to the appendix Figure 2 , if there is no refraction of the light ray by the cylinder liner, according to the pinhole model, point A on the calibration plate would be point A'' on the CCD plane. The distance between point A' and point A'' shows the projection distortion caused by the refraction of the cylinder liner. Step S21 calculates the propagation trajectory of the light by using the principle of light propagation and Snell's law. For any point on the CCD plane, it backtracks to the unique corresponding point on a certain voxel layer in the three-dimensional voxel space coordinate system, solving the problem of tomographic imaging projection distortion caused by the refraction of the inner and outer walls of the cylinder liner in the limited space of the cylinder liner.

[0069] Step S22. The specific method for establishing the reverse mapping relationship is as follows: Based on the reverse ray tracing in step S21, for the i-th point A on the CCD plane i', according to the reverse ray tracing in step S12, the corresponding point A on the j-th voxel layer in the voxel space coordinate system is traced for all of them. ji , establish the reverse mapping relationship from the pixel array coordinate system to the voxel space coordinate system.

[0070] Step S3: Obtain the projection weight coefficient of each voxel according to the reverse mapping relationship in step S2. The specific method is as follows: Select feature points on pixels on more than three CCD planes. Based on the reverse mapping relationship, form a reverse tracing optical path. Obtain the projection weight coefficient of the voxel according to the intersection volume fraction of the reverse tracing optical path and the voxel. The specific example is as follows:

[0071] S31: Refer to the appendix Figure 3 , select the four vertices of any pixel on the CCD plane as feature points, namely points H, I, J, and K. According to the reverse mapping relationship, obtain four reverse rays, and form a reverse optical path (Line-of-sight, LOS) with these four rays as the boundaries, that is, the reverse tracing optical path.

[0072] It should be noted that all the optical signals that the pixel HIJK can receive are included in the reverse tracing optical path, and the voxels on all the voxel layers that intersect with the optical path are all the voxels that contribute to the signal projection of the pixel HIJK.

[0073] S32: Obtain all the voxels where the optical path intersects with all the voxel layers, and calculate the percentage of the volume of each voxel intersecting with the optical path in the volume of a single voxel. The percentage is the projection weight coefficient of each voxel;

[0074] Furthermore, when calculating the projection weight coefficient, approximate the actually frustum-shaped optical path as a cylindrical optical path, and the area of the end face of the cylinder is the same as the area of the end face of the frustum.

[0075] It should be noted that assuming that the voxel emits optical signals uniformly, it can be considered that the larger the volume of the voxel intersecting with the optical path and the closer the center of the sphere is to the reverse tracing optical path, the more the contribution to the optical signal of the pixel. Therefore, the volume fraction can be used to calculate the projection weight coefficient. Approximating the optical path as a cylinder is convenient for calculating the intersection volume of the cylinder and the sphere in mathematics.

[0076] Step S4: Based on the projection weight coefficient of each voxel in step S3, establish the point spread function matrix from the voxels on all the voxel layers to the CCD plane according to the reverse mapping relationship, and realize the imaging of the target to be measured placed in the cylinder liner on the CCD plane.

[0077] In summary, the above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A reverse mapping cross - interface tomography method, characterized in that, Based on the imaging of the target to be measured in the transparent hollow cylindrical cylinder liner on the camera outside the cylinder liner, it includes the following steps: Step S1: Establish a pixel array coordinate system for camera imaging and a voxel space coordinate system inside the cylinder liner; Step S2: Perform reverse ray tracing to establish an inverse mapping relationship from the pixel array coordinate system to the voxel space coordinate system; Step S3: According to the inverse mapping relationship in Step S2, obtain the projection weight coefficient of each voxel; Step S4: Based on the projection weight coefficient of each voxel in Step S3, establish a point spread function matrix from the voxels on all voxel layers to the CCD plane according to the inverse mapping relationship, and realize the imaging of the target to be measured placed in the cylinder liner on the CCD plane; The specific method of Step S2 is as follows: Step S21: Perform reverse ray tracing: Select any voxel layer as the current voxel layer. For a point on the CCD plane, emit a ray passing through the center of the lens. After passing through the outer surface and inner surface of the cylinder liner, it intersects with the current voxel layer at a point. According to the theorem of light propagation and Snell's law, calculate the coordinates of the point on the current voxel layer, that is, obtain the coordinates of the corresponding point on the current voxel layer for a point on the CCD plane; Step S22, establish an inverse mapping relationship: Based on the inverse ray tracing in step S21, for the th point on the CCD plane, according to the inverse ray tracing in step S21, trace to its corresponding point on the th voxel layer in the voxel space coordinate system, and establish an inverse mapping relationship from the pixel array coordinate system to the voxel space coordinate system; The specific method of Step S3 is as follows: Select more than three characteristic points on the pixels on the CCD plane. Based on the inverse mapping relationship, form a reverse tracing light path. According to the reverse tracing light path and the intersection volume fraction of the voxel, obtain the projection weight coefficient of the voxel; The formation method of the reverse tracing light path is as follows: Select the four vertices of any pixel on the CCD plane as characteristic points, namely points H, I, J, and K. According to the inverse mapping relationship, obtain four reverse rays, and form a reverse tracing light path with these four rays as the boundaries; The method of obtaining the projection weight coefficient of the voxel according to the intersection volume fraction of the reverse tracing light path and the voxel is as follows: Obtain all the voxels where the light path intersects with all voxel layers, calculate the percentage of the volume of each voxel intersecting with the light path in the volume of a single voxel, and the percentage is the projection weight coefficient of each voxel; Convert the actually frustum-shaped reverse tracing light path into a cylindrical light path, and the end face area of the cylindrical shape is the same as the end face area of the frustum shape.

2. The reverse mapping cross-interface tomography method according to claim 1, wherein The specific method of Step S1 is as follows: The method of establishing the pixel array coordinate system for camera imaging is as follows: The camera is simplified into an imaging system composed of a CCD plane containing a number of pixel arrays of the same size and a convex lens. Define a two-dimensional Cartesian coordinate system o-xz with the center point of the CCD plane as the origin, where the x direction is the horizontal axis of the CCD plane and the z direction is the vertical axis of the CCD plane; The method of establishing the voxel space coordinate system inside the cylinder liner is as follows: Discretize the cylindrical space enclosed by the cylinder liner into more than two voxel layers. Each voxel layer is parallel to a meridian plane inside the cylindrical space enclosed by the cylinder liner. Each voxel layer is composed of a number of voxel blocks of the same size; Set the center of the bottom surface of the cylinder liner as the origin O, and define a three-dimensional Cartesian coordinate system O-XYZ, where the direction perpendicular to the voxel layer is the Y direction, the central axis of the cylinder liner is the Z direction, and the X direction is perpendicular to the Y and Z directions.

3. The reverse mapping cross-interface tomography method according to claim 2, characterized in that, The voxel is spherical.

4. The reverse mapping cross-interface tomography method according to any one of claims 1 to 3, characterized in that The further introduction of the said step S21 is as follows: S211: Use the calibration plate as the target to be measured and place it on any voxel layer in the cylinder liner. Select any point on the CCD plane , and let a light ray emitted from it pass through the center C of the lens and intersect the outer surface of the cylinder liner at point E. Calculate the incident angle of the light ray at point E . The specific formula is as follows: ； Among them, is the incident light vector at point E, is the normal vector at point E; S212, calculate the exit angle of the light ray at point E according to Snell's law , and the specific formula is as follows: ； Among them, is the refractive index of light in air, is the refractive index of light in the cylinder liner material; S213. Determine the intersection point F of the light ray and the inner surface of the cylinder liner according to the light ray exit angle , and calculate the incident angle of the incident light ray at point F . The specific formula is as follows: ； Among them, is the incident light vector at point F, is the normal vector at point F; S214, calculate the exit angle of the exit ray at point F based on the incident angle of the incident ray at point F and Snell's law. The specific formula is as follows: , as follows: ； S215, determine the intersection point A of the light ray and the calibration board according to the exit angle of the exit light ray at point F, and then obtain the coordinates of the corresponding point A of any point on the CCD plane on the calibration board. ​

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