CN113592995B - Multi-reflection light separation method based on parallel single-pixel imaging - Google Patents
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Abstract
The invention designs a multi-reflection light separation method based on parallel single-pixel imaging, which is used for decomposing aliased light rays in a multi-reflection light surface by using the parallel single-pixel imaging, and can finish the separation of one-time, two-time and three-time and more reflection light rays in the multi-reflection light rays. Firstly, projecting sinusoidal gray scale stripes to a scene of the measured multiple reflected lights through a projector, and acquiring modulation information in the scene by a camera; secondly, phase subtraction is carried out according to an image result acquired by a camera to obtain a Fourier coefficient, and the Fourier coefficient is subjected to inverse Fourier transform to obtain an image of the light transmission coefficient under the view angle of the projector; and then separating the primary reflected light and the secondary reflected light according to the epipolar constraint and the three-dimensional model respectively, thereby realizing the separation of the surfaces of the multiple reflected lights. The method is the inverse process of traditional illumination rendering, can directly obtain the composite illumination result of scene information through a camera-projector system and separate aliased light, and plays an important role in promoting the development of optical measurement, computer vision and computer graphics.
Description
Technical Field
The invention relates to a multi-reflection light separation method based on parallel single-pixel imaging, which uses the parallel single-pixel imaging in the fields of light transmission and photogrammetry, and combines the traditional three-dimensional measurement technology to finish the separation of primary, secondary and multi-reflection light components on the multi-reflection light surface. The invention mainly belongs to the fields of computational imaging and computer vision.
Background
The multiple reflected light is effectively an aliasing of light in space, resulting in multiple sequentially reflected light aliases together, and when collected by the light detector, the detector receives light intensity information that is effectively the result of the multiple reflected light aliases. In the field of photogrammetry, the decomposition of the multi-reflection light rays can help to reconstruct real three-dimensional scene information, and the measurement accuracy is improved; in the field of computer graphics, as virtual scenes are often rendered through a rendering equation, the propagation process of light rays from a light source to the scenes is simulated, illumination information such as multiple reflection lights is added in the propagation process, so that the scene information is more real, the separation of the multiple reflection lights is actually a reverse process of rendering, the separation of the reflection lights can help to verify the authenticity of rendering, and theoretical basis and real measurement data are provided for the virtual scenes.
For example, the parallel single-pixel imaging method disclosed in patent publication No. cn110264540a published by chinese patent application researches the light intensity information received by a single detector pixel, analyzes the light intensity information to obtain the illumination information corresponding to the pixel, and the multi-reflection light is actually a part of the illumination information, so that from theory, the parallel single-pixel imaging should be able to complete the identification and separation of various components in the multi-reflection light.
Disclosure of Invention
The invention provides a multi-reflection light separation method based on parallel single-pixel imaging, which expands the basic principle of parallel single-pixel imaging to the problem of aliased light separation, and realizes the identification and separation of multi-reflection light components under complex illumination conditions through the uniqueness of a parallel single-pixel algorithm. A flow chart of a multi-reflection light separation method based on parallel single-pixel imaging is shown in figure 1.
The basic principle of the invention is based on that by transplanting parallel single-pixel imaging into a traditional array camera, each camera pixel is regarded as a single-pixel detector, the collected light intensity information is subjected to Fourier inverse transformation processing to obtain a light transmission coefficient image, a direct reflection point is identified in the light transmission coefficient image through polar constraint, and then a secondary reflection point is identified and separated through a three-dimensional model, so that the separation of primary, secondary and multiple reflection light components is completed.
The invention is different from other separated reflected light rays in that the invention realizes the reverse reduction from measurement data to the image of the multiple reflected light components, and is unique in that the invention does not acquire the surface material information and the space three-dimensional structure of the measured scene in advance, and the identification and separation of the multiple reflected light components are realized for the static unknown scene, which is the most unique and direct advantage of the invention.
The technical solution of the invention is as follows: firstly, generating sinusoidal gray scale stripes suitable for the method according to a Fourier transform parallel Shan Xiangsu imaging method, projecting the modulated gray scale stripes into a scene to be tested according to frequency transformation by using a projector, and shooting and sampling the scene and the mixed scene modulated by the stripes by using a calibrated camera; after shooting is finished, obtaining an optical transmission coefficient image under a projector visual angle corresponding to each single pixel on a camera pixel through phase subtraction and inverse Fourier transform; performing polar constraint processing on the light transmission coefficient, and identifying and separating out primary reflection light spots; and reconstructing according to a stereoscopic vision principle to obtain a three-dimensional point cloud, establishing a light propagation model, and identifying and separating secondary reflected light components according to a secondary reflected light criterion. The method mainly comprises the following steps:
(1) Before the projector and the camera are placed and a scene to be measured, the projector should generate sinusoidal gray scale stripes to be projected in advance, the projector projects the stripes, then light is aliased on a propagation path, and a camera end acquires an aliased light intensity image.
(2) According to the principle of multi-step phase shift, carrying out phase subtraction on four phase images under each frequency to obtain a Fourier coefficient, and carrying out inverse Fourier transform on the Fourier coefficient;
(3) Processing all camera pixels (2), wherein each pixel point can obtain an optical transmission coefficient image;
(4) According to the light transmission coefficient image, decomposing primary reflected light (direct reflected light) and indirect reflected light by adopting an epipolar constraint principle;
(5) And reconstructing a three-dimensional point cloud data model according to a stereoscopic vision principle, and decomposing the indirect reflected light component according to a secondary reflection separation model to obtain secondary reflected light and three or more reflected light.
The expression for the multi-reflected aliased ray mentioned in step (1) is:
wherein I is out (x, y) is the aliasing intensity of the multiple reflected light received by a certain camera pixel (x, y), h (x, y; m, n) is the light transmission coefficient of the light from the projector pixel (m, n) to the camera pixel (x, y), I in (m, n) is the intensity of the emitted light from the projector pixel (m, n), I e (x, y) is the ambient light intensity.
The light transmission coefficient image mentioned in step (3) is located at the projector viewing angle, the resolution is consistent with the projector, and the multiple reflection light surface generally has a plurality of light spots, and for a certain pixel (m, n), it represents that the light emitted by the point on the projector array reaches the current camera pixel (x, y) through several reflections in space, and the corresponding relation between the two is just reflected in the light transmission coefficient image.
In the step (4), the primary reflection light of the camera belongs to a component which is directly emitted from a certain pixel of the projector and is directly received by the camera through primary reflection, so that the constraint condition of polar lines in stereoscopic vision is met, in the light transmission coefficient, only the primary reflection light meets the condition by calculating the polar lines of the camera pixel corresponding to the view angle of the projector, and therefore, the separation of the primary reflection light can be completed by the method.
The three-dimensional model designed in the step (5) has the principle expression of separating secondary reflected light and three or more reflected light as follows:
δ(m,n；x,y)≤θ d
because of the uniqueness of secondary reflection light propagating in space, the secondary reflection light can generate double reflection as shown in the figure on the curved surface of the material of the multi-reflection light, and the propagation path of the secondary reflection light after the second reflection is consistent with that of the primary reflection light to form an aliased light, so that the secondary reflection light is separated before the secondary reflection light is separated. For a certain point Y on the curved surface, incident light is emitted by a certain pixel (m, n) of the projector, and then the light is reflected by the point Y on the curved surface to reach another point X on the curved surface and then reflected to a point (X, Y) on the camera pixel to form secondary reflection light. Let the light incident on Y be L and the light reflected by Y to X be R, where i (m, n; X, Y) and R (m, n; X, Y) are the incident angle and the reflection angle of the light at Y point, respectively, and the two above formulas represent the angular relationship of the secondary reflected light from a certain pixel (m, n) of the projector to a certain pixel (X, Y) of the camera when the secondary reflection occurs for the first time. According to the above steps, a certain pixel value collected by the camera can be subjected to inverse fourier transform to obtain a light transmission coefficient image, primary reflected light can be screened out by a polar constraint method, at this time, the value of a primary reflection light spot is set to 0 on the light transmission coefficient image, and an indirect reflection light component is reserved; meanwhile, according to the matching relation between the primary reflected light and the camera pixels, the three-dimensional coordinates corresponding to each camera pixel in space can be calculated. Thus, for each camera pixel, a light transmission coefficient image containing only indirectly reflected light components can be reconstructed, all points in the light transmission coefficient image are traversed, and the light that satisfies the threshold condition can be determined to be secondarily reflected light according to the above formula.
The invention has the advantages that:
(1) The invention aims at the three-dimensional scene with the multi-reflection light surface, can complete the separation work of the primary component, the secondary component and the tertiary and more components in the multi-reflection light on the premise of unknown surface materials and three-dimensional morphology, and is different from the traditional separation research, the past multi-reflection light separation or the separation based on given surface material information or ideal lambertian surface, or the separation of the direct component and the indirect component is completed only once, and the decomposition of the higher-order reflection light is not completed. The decomposition of the secondary reflected light can help the accurate establishment of BRDFs and BSSDFs models and the verification of rendering effects in the fields of optics and computer graphics.
(2) A visual representation of the light from the light source to the collector is provided. By introducing parallel single-pixel imaging, the invention directly reconstructs the light transmission coefficient of the light rays in the process from the projector to the camera, and in a two-dimensional image of the light transmission coefficient, the representation result composed of the reflected light in each order can be directly observed. This means that the propagation of light can be directly visualized in the light transmission coefficient, providing a basis for decomposing the individual components.
(3) And (5) separating secondary reflected light of the unknown scene. On the premise of unknown scene morphology and surface materials, the problem of decomposing the light reflected for multiple times is solved. The invention starts from parallel single-pixel imaging, reconstructs an optical transmission coefficient image through the parallel single-pixel imaging, and can screen secondary reflected light meeting judgment conditions in the range of a reflected light lobe according to the propagation path of the secondary reflected light and a Phong model after a three-dimensional model is established.
In summary, the invention provides a multi-reflection light surface separation method based on parallel Shan Xiangsu imaging, light transmission coefficients are restored through parallel single-pixel imaging, and in the light transmission coefficients, the components can be separated one by one according to the respective characteristics of multi-reflection light components of one time, two times and more than three times, so that the separation of the reflection components on the multi-reflection light surface is realized, and the separation result is displayed by a two-dimensional image.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
FIG. 2 is a schematic illustration of the propagation of light from a projector array to a camera array. In the figure, 1 is a primary reflection light propagation path, 2 is a secondary reflection light path, 3 is a tertiary reflection light path, 4 is a stripe projector, 5 is a pixel on a projector array, 6 is a scene of measured multi-reflection light, 7 is a multi-reflection light aliasing light received by a camera, 8 is a pixel on a camera array, and 9 is a camera.
Fig. 3 is a schematic diagram of the light transmission coefficient obtained by the pixel. In the figure, 8 denotes a pixel on the camera array, 9 denotes a camera, 10 denotes an image of the light transmission coefficient, and 11 denotes a line corresponding to the pixel on the image.
Fig. 4 is a schematic diagram of secondary reflection light separation. In the figure, 1 is a primary reflection light propagation path, 2 is a secondary reflection light path, 4 is a stripe projector, 7 is a multi-reflection light aliasing ray received by a camera, 8 is a pixel representation on a camera array, 9 is a camera, 12 is a computer, 13 is a curved surface representation of a scene of the measured multi-reflection light, 14 is a gray sine stripe emitted by the projector, 15 is a normal line of a certain point of a reflection surface 13, and 16 and 17 respectively represent an incident angle and a reflection angle of the secondary reflection light at the point.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and the specific embodiments.
The invention provides a multi-reflection light separation method based on parallel single-pixel imaging, which is characterized in that a flow chart is shown in figure 1, gray sine stripes are projected by a stripe projector, the stripes are received by camera pixels through multi-reflection light scene reflection, a two-dimensional image of a light transmission coefficient is obtained through inverse Fourier transform, on the basis of the two-dimensional image, primary reflection light rays are screened out through polar constraint, a stereoscopic vision relationship is established between the primary reflection light rays and projector pixel points, three-dimensional reconstruction data are obtained, a separation model of secondary reflection light is established on the basis, secondary reflection light is separated from indirect light components through secondary reflection light criteria, and finally the separation of primary, secondary and three-time and more reflection light components is completed. A schematic diagram of the formation of aliased light rays from the multiple reflected light in space is shown in fig. 2. The invention specifically operates as follows:
1. and (3) calibrating the stripe projector and the camera to obtain a space pose relation between the stripe projector and the camera, and generating gray sine stripes with the characteristic of parallel single pixels, so as to ensure that a modulation pattern projected by the projector can be acquired by the camera. The projector projects a modulation pattern, and the camera is triggered to acquire images of the scene to obtain a series of scene images combining the scene with the stripes.
2. For the two-dimensional image acquired by the camera, the fourier coefficient can be obtained after the phase subtraction, and the light transmission coefficient as shown in fig. 3 can be obtained by performing inverse fourier transform. The light transmission coefficient is an aliasing result of the multiple reflection light component, and the expression is:
wherein I is out (x, y) is the light intensity of the mixed light received by the camera pixel, h (x, y; m, n) is the light transmission coefficient of the projector coordinate (m, n) corresponding to the camera array coordinate (x, y), and is shown as a bright point in the light transmission coefficient in fig. 3, and the separation principle of the multiple reflection light is as follows:
h n (x,y；m,n)＝h(x,y；m,n)·M n (x,y；m,n) (2)
wherein M is n (x, y; m, n) is a mask that reflects light n times in a certain order, and the expression is:
in the formula (3), cn represents whether the current reflected light logically belongs to the required nth reflected light, if the current reflected light logically belongs to the required nth reflected light, the current reflected light is set to be 1, otherwise, the current reflected light is 0, (2) the light transmission coefficient of the multiple reflected light is calculated in the mathematical logic, and the key point of the invention is that the mask representation of the primary, secondary and tertiary reflected light and above is obtained, so that the separation result is obtained. Fig. 3 illustrates a process of recovering a light transmission coefficient from a certain pixel of a camera.
3. The primary reflected light is separated from the light transmission coefficient image. In fig. 3, 9 is a camera, 8 is a pixel on the camera array, and the pixel is subjected to inverse fourier transform to obtain an image at the viewing angle of the projector, where the size of the image is the resolution of the projector, and some bright spots in the image represent light transmission coefficients of reflected light in different orders, and for separating primary reflected light, the characteristic of primary reflected light compared with indirect light should be found. Because the primary reflection light represents the primary reflection of the light in the measured scene in the propagation process and reaches the camera pixel, the primary reflection light spot is selected and screened by the polar constraint in the step, as shown in the figure, 10 is a light transmission coefficient image, 11 is the polar line of the pixel on the light transmission coefficient image, the light spot in the polar line threshold range is judged according to the polar line, and the sum of the pixel values is the light intensity I of the primary reflection light received by the pixel 1 And (x, y), processing all pixels according to the method to obtain a two-dimensional separation result of primary reflected light.
4. The three-dimensional structure of the measured surface can be obtained through three-dimensional visual three-dimensional reconstruction through the primary reflection light spots and the corresponding camera pixel points. With this three-dimensional result, a separation model for separating the secondary reflected light can be established, as shown in fig. 4.
Because of the uniqueness of secondary reflection light propagating in space, the secondary reflection light can generate double reflection as shown in the figure on the curved surface of the material of the multi-reflection light, and the propagation path of the secondary reflection light after the second reflection is consistent with that of the primary reflection light to form an aliased light, so that the secondary reflection light is separated before the secondary reflection light is separated. For a certain point Y on the curved surface, incident light is emitted by a certain pixel (m, n) of the projector, and then the light is reflected by the point Y on the curved surface to reach another point X on the curved surface and then reflected to a point (X, Y) on the camera pixel to form secondary reflection light. Let the light incident on Y be L, the light reflected by Y to X be R, and the following equation is given according to the reflection characteristics of light:
wherein i (m, n; x, Y) and r (m, n; x, Y) are the incident angle and the reflection angle of the light at the Y point, respectively, and the above two expressions represent the angular relationship of the secondary reflected light from a certain pixel (m, n) of the projector to a certain pixel (x, Y) of the camera when the secondary reflected light is reflected for the first time. According to the above steps, a certain pixel value collected by the camera can be subjected to inverse fourier transform to obtain a light transmission coefficient image, primary reflected light can be screened out by a polar constraint method, at this time, the value of a primary reflection light spot is set to 0 on the light transmission coefficient image, and an indirect reflection light component is reserved; meanwhile, according to the matching relation between the primary reflected light and the camera pixels, the three-dimensional coordinates corresponding to each camera pixel in space can be calculated. Thus, for each camera pixel, a light transmission coefficient image can be reconstructed that contains only indirectly reflected light components, including indirect light from some pixels on the projector, bringing all the spot coordinates into the following formula:
δ(m,n；x,y)≤θ d (7)
wherein K is L And K G Representing the reflectance of the lambertian and smooth surfaces, respectively, ranging from 0 to 1, and representing the reflectance characteristics of the non-smooth and smooth surfaces, respectively. The parameter s represents the roughness of the current surface, the numerical value of the metal material is larger than that of other materials, once the final calculation result delta (m, n; x, y) is smaller than a given threshold value, the light rays from (m, n) to (x, y) are judged to belong to secondary reflection light, each camera pixel can be screened in sequence, the corresponding secondary reflection light rays are selected from the reverse tracking angle of the light rays, after screening, the light spot pixel values meeting the conditions are reserved in the light transmission coefficient image, the rest is set to be 0, and then the numerical value of each light transmission coefficient image is added, so that the final secondary reflection light separation result is obtained.
Claims (4)
1. A multi-reflection light separation method based on parallel single-pixel imaging is characterized in that: the separation process comprises the following steps:
(1) Before placing a projector and a camera and a scene to be measured, the projector projects sinusoidal stripes required for parallel single-pixel imaging, the camera acquires mixed images of the stripes and the scene, and the light intensity acquired by image pixels is a mixture of primary, secondary and multiple reflected light components;
(2) A parallel single-pixel imaging algorithm is carried out on each pixel in the camera, so that a light transmission coefficient image corresponding to the pixel under the view angle of the projector can be obtained, and a plurality of light spots in the light transmission coefficient image reflect the component information of primary, secondary and multiple reflection lights;
(3) Separating primary reflected light from mixed illumination information by adopting an epipolar constraint principle according to the light transmission coefficient image, adding the primary reflected light intensities of all pixels to obtain a primary reflected light separation result image, establishing a three-dimensional model through pixel points and primary reflected light points, and reconstructing to obtain a three-dimensional point cloud model of a measured scene;
(4) According to the characteristics of a secondary reflected light separation model and a propagation path, a secondary reflected light separation algorithm is adopted to decompose the secondary reflected light in the indirect reflected light component to obtain secondary reflected light, and the intensities are added to obtain a secondary reflected light separation result image;
(5) In the light transmission coefficient image, the primary and secondary reflected light components are removed, and the remaining light spots represent three or more reflected light components, and the intensities of which are added to obtain three or more separated result images.
2. The method according to claim 1, characterized in that: the expression for the multi-reflected aliased ray mentioned in step (1) is:
wherein I is out (x, y) is the aliasing intensity of the multiple reflected light received by a certain camera pixel (x, y), h (x, y; m, n) is the light transmission coefficient of the light from the projector pixel (m, n) to the camera pixel (x, y), I in (m, n) is the intensity of the emitted light from the projector pixel (m, n), I e (x, y) is the ambient light intensity.
3. The method according to claim 1, characterized in that: in the step (3), the primary reflection light of the camera belongs to a component which is directly emitted from a certain pixel of the projector and is directly received by the camera through primary reflection, so that the limit condition of polar lines in stereoscopic vision is met, in the light transmission coefficient image, a light spot in a threshold range can be determined by calculating polar lines of the camera pixel corresponding to the view angle of the projector and setting a polar line threshold value, the light spot represents the primary reflection light component, the intensities of the light spots are added, the pixel value of the primary reflection light component can be obtained, the processing is carried out on each pixel, and a result image of the primary reflection light component can be obtained.
4. The method according to claim 1, characterized in that: the principle expression of the secondary reflected light separation algorithm related in the step (4) is as follows:
δ(m,n；x,y)≤θ d
wherein K is L And K G The reflectivities representing the lambertian and bright surfaces, respectively, range from 0 to 1, the parameter s describing the roughness of the surface;
because of the uniqueness of secondary reflection light transmitted in space, the secondary reflection light can occur on a curved surface of a multi-reflection material, for a certain point Y on the curved surface, incident light is emitted by a certain pixel (m, n) of the projector, and reaches another point X after being reflected by the point Y, and finally is received by a camera pixel (X, Y), namely, the secondary reflection light is set as L, the light which is incident on the Y is reflected to the X by the Y and is R, in the above formula, i (m, n; X, Y) and R (m, n; X, Y) are respectively the incident angle and the reflection angle of the light at the point Y, the above two formulas represent the angle relation of the secondary reflection light from the certain pixel (m, n) of the projector to the certain pixel (X, Y) of the camera, and for each camera pixel, after the primary reflection light component is removed, a light transmission coefficient image which only comprises an indirect reflection light component can be reconstructed, candidate points in the light transmission coefficient image can be traversed, and the secondary reflection light can be determined according to the above formula, if the threshold condition is met.
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