Method and system for snapshot multi-spectral light field imaging
10645281 ยท 2020-05-05
Assignee
Inventors
Cpc classification
H04N5/2226
ELECTRICITY
H04N23/11
ELECTRICITY
G06T3/4053
PHYSICS
G02B17/0848
PHYSICS
H04N23/951
ELECTRICITY
International classification
Abstract
A method for generating high resolution multi-spectral light fields is disclosed. The method may include capturing a multi-perspective spectral image which includes a plurality of sub-view images; aligning and warping the sub-view images to obtain low resolution multi-spectral light fields; obtaining a high resolution dictionary and a low resolution dictionary; obtaining a sparse representation based on the low resolution multi-spectral light fields and the low resolution dictionary; and generating high resolution multi-spectral light fields with the sparse representation and the high resolution directory. Each sub-view image is captured with a different perspective and a different spectral range. The multi-perspective spectral image is obtain with one exposure.
Claims
1. A method for generating high resolution multi-spectral light fields, comprising: capturing a multi-perspective spectral image with one exposure, wherein the multi-perspective spectral image includes a plurality of sub-view images and each sub-view image is captured with a different perspective and a different spectral range; aligning and warping the sub-view images to obtain low resolution multi-spectral light fields; obtaining a high resolution dictionary and a low resolution dictionary; obtaining a sparse representation based on the low resolution multi-spectral light fields and the low resolution dictionary; and generating high resolution multi-spectral light fields with the sparse representation and the high resolution directory.
2. The method of claim 1, wherein the high resolution directory and the low resolution directory are co-trained.
3. The method of claim 1, further comprising: using a robust selective normalized cross correlation to obtain a pixel correspondence among the sub-view images.
4. The method of claim 1, further comprising: estimating differences in depth of views of the sub-view images by a depth from defocus technique.
5. The method of claim 1, wherein the sub-view images are warped to each other by using a disparity map.
6. The method of claim 1, further comprising: correcting view distortions in the multi-perspective spectral image by analyzing reflectance geometry and re-projecting each pixel to a virtual focal plane.
7. The method of claim 1, wherein the low resolution multi-spectral light fields include nine spectral bands.
8. The method of claim 1, wherein the high resolution multi-spectral light fields have a resolution of no more than 5 nm.
9. The method of claim 1, further comprising: capturing the multi-perspective spectral image using a digital camera and a plurality of spectral-coded catadioptric mirrors.
10. The method of claim 9, wherein each catadioptric mirror is coated with a different spectral reflective coating.
11. The method of claim 9, wherein the catadioptric mirrors form a 33 array.
12. The method of claim 9, wherein each catadioptric mirror has a spherical surface.
13. A snapshot plenoptic imaging system for capturing images to generate high resolution multi-spectral light fields, the system comprising: a plurality of spectral-coded catadioptric mirrors, wherein each catadioptric mirror is coated with a different spectral reflective coating; a digital camera configured to capture a multi-perspective spectral image, wherein the multi-perspective spectral image includes a plurality of sub-view images and each sub-view image is captured with a different perspective and a different spectral range; and an image processing unit configured to align and warp the sub-view images to obtain low resolution multi-spectral light fields and generate high resolution multi-spectral light fields based on the low resolution multi-spectral light fields.
14. The system of claim 13, wherein the image processing unit is configured to obtain a high resolution dictionary and a low resolution dictionary; obtain a sparse representation based on the low resolution multi-spectral light fields and the low resolution dictionary; and generate the high resolution multi-spectral light fields with the sparse representation and the high resolution directory.
15. The system of claim 13, wherein the high resolution directory and the low resolution directory are co-trained.
16. The system of claim 13, wherein the image processing unit is configured to use a robust selective normalized cross correlation to obtain a pixel correspondence among the sub-view images.
17. The system of claim 13, wherein the image processing unit is configured to estimate differences in depth of views of the sub-view images by a depth from defocus technique.
18. The system of claim 13, wherein the sub-view images are warped to each other by using a disparity map.
19. The system of claim 13, wherein the image processing unit is configured to correct view distortions in the multi-perspective spectral image by analyzing reflectance geometry and re-projecting each pixel to a virtual focal plane.
20. The system of claim 13, wherein the low resolution multi-spectral light fields include nine spectral bands.
21. The system of claim 13, wherein the high resolution multi-spectral light fields have a resolution of no more than 5 nm.
22. The system of claim 13, wherein the catadioptric mirrors form a 33 array on a plane.
23. The system of claim 13, wherein each catadioptric mirror has a spherical surface.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) The accompanying drawings, which constitute a part of this disclosure, illustrate several non-limiting embodiments and, together with the description, serve to explain the disclosed principles.
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DETAILED DESCRIPTION OF THE EMBODIMENTS
(8) Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments consistent with the present invention do not represent all implementations consistent with the invention. Instead, they are merely examples of systems and methods consistent with aspects related to the invention.
(9) In accordance with embodiments of the present disclosure, an SPI system including a data capturing unit and a data processing unit is provided. The data capturing unit captures a multi-perspective spectral image and transmits it to the data processing unit. The data processing unit performs ray-wise distortion correction, spectral image registration and spectral signal recovery. The ray-wise distortion correction corrects view distortions in the multi-perspective spectral image. The spectral image registration is to align and warp sub-view images of the multi-perspective spectral image to generate low resolution MLFs. The spectral signal recovery is to generate high resolution MLFs based on the low resolution MLFs.
(10) 1. System Overview
(11)
(12) As shown in
(13) 2. Data Capturing Unit
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(15) TABLE-US-00001 TABLE 1 Mirror Type Spherical Material BK7 Glass Radius 32.5 mm Baseline 70.0 mm Coating Type Spectral reflective coating Spectral Range 400 nm-700 nm Sensor Resolution 5760 3840 Field-of-View >100 Spectral Resolution <10 nm MLF Resolution 1000 1000 3 3 30
(16) 2.1 Data Capturing Method
(17) As shown in
(18) 3. Data Processing Unit
(19) As shown in
(20) 3.1 Ray-Wise Distortion Correction
(21) The use of catadioptric mirrors provides a wide field of view (FOV), and also causes strong view distortions in the captured images. Each of the multi-perspective image includes 9 distorted sub-view images from different perspectives. To correct the distortions in the sub-view images with different perspectives, a ray-wise distortion correction method can be applied by analyzing reflectance geometry of the catadioptric mirrors and re-projecting each pixel (ray) to a virtual focal plane. The sub-view images present non-single view projections of the scene, since each of the sub-view image is captured at a different perspective. Since baselines between any two adjacent sub-view images are the same, the distorted sub-view images may be re-projected by using geometric modeling as illustrated in
(22) In
tan .sub.i.Math.(lr sin )=r.Math.cos
where is the direction of surface normal. For any given .sub.i, can be obtained as:
(23)
Based on the law of reflection, the equivalent incident .sub.i and l can be obtained as follows:
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(25) A virtual focal plane can be defined by the position of the virtual camera, i.e., l. According to the above-discussed equations, setting an FOV as 100, the equivalent incident .sub.i and l can be obtained for all incident rays. By re-projecting each pixel (ray) to the virtual focal plane, the sub-view image from one catadioptric mirror can be corrected from view distortions. The geometric modeling of a single catadioptric mirror can be simply extended to a mirror array due to the mirror's rotational symmetry of its spherical surface. In some embodiments, the distance from the camera to a catadioptric mirror/may not be a constant for all mirrors in a planar array configuration.
(26) 2.2 Spectral Image Registration
(27) The multi-perspective image with the corrected sub-view images is transmitted to the spectral image registration 320 for spectral image registration. The objective of the spectral image registration is to align and warp the sub-view images to any perspective so that a datacube of a multi-spectral light field can be constructed on each perspective. In other words, for each particular sub-view image, align and warp the other sub-view images to the particular sub-view image. Then on each perspective, a datacube, which includes a light field of a plurality of different spectral bands can be constructed. Here, a band refers to a section of light spectrum. In some embodiments, a multi-perspective image may include 9 different perspectives and 9 different spectral bands. By performing the spectral image registration on the multi-perspective image, 9 multi-spectral datacubes, each of which includes 9 spectral bands, are constructed on each perspective respectively. These MLFs included in these datacubes are called low resolution MLFs in this disclosure.
(28) Traditional image registration methods, such as, patch-based stereo, optical flow, etc., fail to register spectral images, as the spectral images share no intensity consistency. This disclosure presents a spectral image registration method to obtain disparity maps by utilizing both a cross-spectrum feature descriptor and depth from defocus technique. This method can align spectral images and generate high quality disparity maps, and warp the sub-view images to each other based on the disparity maps.
(29) 2.2.1 Cross-Spectrum Feature Descriptor
(30) A feature descriptor is a type of feature representation chosen to stand for a feature in image processing. In this disclosure, the robust selective normalized cross correlation (RSNCC), is adopted as a cross-spectrum feature descriptor. RSNCC is a robust matching metric for spectral images.
(31) At step 401, by using RSNCC, pixel correspondence among the sub-view images can be established. The detailed computational process may be explained in the following equations. Denoting a central view as I.sub.1 and its neighboring view as I.sub.2, a matching cost function E.sub.rsncc can be computed as:
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Here, d is a pixel disparity, p is a pixel position, M[I.sub.1] and M[I.sub.2] stand for gradient magnitudes of images I.sub.1 and I.sub.2. I.sub.1(p) and I.sub.2(p+d) are pixels' feature vectors in path p in I.sub.1 and patch p+d in I.sub.2 respectively.
(33) 2.2.2 Depth from Defocus
(34) At step 402, differences in the depth of views (DOVs) of sub-view images can be estimated by a depth from defocus technique. The depth from defocus technique is a method that estimates a scene depth from a stack of refocused images with a shallow DOV. The depth from defocus method can be performed by fusing a multi-spectral focal stack. The multi-spectral focal stack, including a plurality of views: I.sub.1, I.sub.2, . . . can be generated by refocusing the multi-spectral light field at a serial of depths. Then a patch-wise refocusing energy metric can be computed as:
(35)
Here, M[ ] stands for a gradient magnitude of an image, U is a small patch centered at p.
(36) 2.2.3 Optimization
(37) At step 403, a disparity map for each perspective can be obtained by optimizing an energy function. The energy function utilizes both results from RSNCC and the depth from defocus, and can be constructed as following:
E(d,p)=.Math.E.sub.rsncc(d,p)+.Math.E.sub.rf(d,p)+P(d,p)
Here, and are weight coefficients, and P(d,p) is a smooth penalty. The disparity map can be defined as:
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This is an optimization problem, and can be solved by graph cuts algorithm. Graph cuts is a type of algorithm used to solve a variety of energy minimization problems which employ a max-flow/min-cut optimization. At step 404, other sub-view are warped to the central view using the disparity map D.sub.map(p), so that a multi-spectral datacube at the central view can be obtained. At step 405, the same registration and warping process are repeated for every perspective, and 9 multi-spectral datacubes can be obtained. Accordingly, the low resolution MLFs can be obtained at step 405.
(39) 2.3 Spectral Signal Recovery
(40) The low resolution MLFs have a low spectral resolution, including only 9 spectral bands. Traditional SPI solutions are also limited to either spectral or spatial resolution. To overcome these limitations and increase spectral resolution, the SPI system, in some embodiments, can adopt a sparse reconstruction algorithm to generate high resolution multi-spectral light fields. The sparse reconstruction algorithm is a learning-based reconstruction algorithm, which is used for acquiring, representing and compressing high-dimensional signals. The multi-spectral signals can be sparsely represented under an over-complete dictionary, and the spectral sparsity of the multi-spectral signals allows compressed sensing of the signals. Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Shannon-Nyquist sampling theorem. Representing a signal involves the choice of the so-called dictionary, which is a set of elementary signals used to decompose the signal. When the dictionary forms a basis, the signal can be uniquely represented as a linear combination of the elementary signals. Over-complete indicates that the number of basis is more than the dimensionality of the signals. Finding a sparse representation of a signal in a given over-complete dictionary is to find the corresponding sparse coefficients in the linear combination of the elementary signals.
(41) The spectral-coded catadioptric mirrors are able to sense the 5D plenoptic function compressively. Therefore, the high resolution MLFs can be generated computationally by using a spectral dictionary. A spectral dictionary can be learned from a publicly available multi-spectral image database. In some embodiments, the database can be retrieved from http://www.cs.columbia.edu/CAVE/databases/multispectral/. The database consists of 32 scenes, and each scene includes full spectral resolution reflectance data from 400 nm to 700 nm at 10 nm steps (31 bands total). With the obtained dictionary, the sparse reconstruction algorithm is able to improve the low resolution MLFs to a high resolution MLFs from 30 nm to no more than 10 nm.
(42) The obtained low resolution MLFs are input to the spectral signal recovery unit 330.
(43) At step 501, two dictionaries can be obtained from the publicly available multi-spectral database: a high resolution dictionary D.sub.h and a corresponding low dictionary D.sub.l. Both are used to generate the high resolution multi-spectral high fields. The detailed method can be explained as following.
(44) Given a training set of high resolution spectral signals: h.sub.1, h.sub.2, . . . , which is obtained from the publicly available database, two dictionaries can be obtained by solving a l.sub.1 norm optimization problem. The l.sub.1 norm optimization problem is a technique commonly used in compressed sensing. In one exemplary embodiment, the sparse reconstruction algorithm can be represented as following:
(45)
Here .sub.i is a sparse coefficient, and l|.sub.i.sub.1 is a term used to penalize .sub.i for not being sparse. The first term is a reconstruction term which tries to force the algorithm to provide a good representation of h.sub.1 and the second term is a sparsity penalty which forces the representation of h.sub.i to be sparse. is a scaling constant to determine the relative importance of these two contributions.
(46)
where S is a known sampling matrix. Denoting spectral reflectance function of the 9 mirrors as R.sub.1, R.sub.2, . . . R.sub.9 and Bayer filter's quantum efficiency as B.sub.R, B.sub.G, B.sub.B, the sampling matrix S is composed as:
(47)
Here, .sub.min and .sub.max stand for a minimum wavelength and a maximum wavelength of an interested spectrum. Two dictionaries D.sub.h and D.sub.l are co-trained so that the high and low resolution multi-spectral signals (h.sub.i and S.Math.h.sub.i) have the same sparse representation, {circumflex over ()}, a set of .sub.i, with respect to the dictionaries.
(48) At step 502, a sparse representation, {circumflex over ()}, can be obtained based on the two dictionaries. As discussed previously, the SPI system senses the compressed MLFs. Low resolution (9 bands) MLFs can be obtained by performing the distortion correction and image registration. For each of the low resolution spectral signal l in the light fields, its corresponding sparse representation under the low resolution dictionary D.sub.l can be solved using LASSO method. LASSO stands for absolute shrinkage and selection operator, and is a regression analysis that performs both variable selection and regulation in order to enhance the prediction accuracy and interpretability of the statistical model it produces. Accordingly, the sparse representation {circumflex over ()} can be solved by the following function:
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Here, k is a sparse parameter.
(50) Since the high and low resolution spectral signals have the same sparse representation {circumflex over ()}, with respect to the dictionaries, the high resolution spectral signal h can be generated using the sparse representation and the high resolution dictionary as following:
h=D.sub.h.Math.{circumflex over ()}
Accordingly, at step 503, the high resolution MLFs can be generated by using the sparse representation and the high resolution dictionary.
(51) The SPI system has the following advantages: 1. It is the first single sensor solution to capture a 5D plenoptic function. Previous solutions employ either a hybrid sensor system or a sensor array to acquire high dimensional light fields. These architectures are bulky in size and expensive. The SPI system in this disclosure uses a single commercial DSLR camera and an optical unit (mirror array) which is portable and less expensive. The single sensor property requires no synchronization, while the synchronization can be very challenging for multiple sensor arrays.
(52) 2. The snapshot property of the SPI system provides a potential for acquiring temporal dimensions. Unlike scanning-based spectral imaging techniques, the SPI records the compressed MLFs in a single exposure, and is applicable for capturing dynamic scene or even multi-spectral light field videos.
(53) 3. Due to the rotational symmetry of spherical mirrors, there is no need to calibrate the orientation of any individual mirror, which is convenient for users to increase the number of mirrors. Also, the spectral range of the SPI system can be extended by replacing some of the mirrors. In some embodiments, the SPI system measures only visible spectral; and in some other embodiments, the system can acquire near infra-red and ultra violet information by using additional spectral-coded mirrors or auxiliary flash devices.
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(55) The various modules, units, and components described above can be implemented as an Application Specific Integrated Circuit (ASIC); an electronic circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor (shared, dedicated, or group) that executes code; or other suitable hardware components that provide the described functionality. The processor can be a microprocessor provided by from Intel, or a mainframe computer provided by IBM.
(56) Note that one or more of the functions described above can be performed by software or firmware stored in memory and executed by a processor, or stored in program storage and executed by a processor. The software or firmware can also be stored and/or transported within any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. In the context of this document, a computer-readable medium can be any medium that can contain or store the program for use by or in connection with the instruction execution system, apparatus, or device. The computer readable medium can include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus or device, a portable computer diskette (magnetic), a random access memory (RAM) (magnetic), a read-only memory (ROM) (magnetic), an erasable programmable read-only memory (EPROM) (magnetic), a portable optical disc such a CD, CD-R, CD-RW, DVD, DVD-R, or DVD-RW, or flash memory such as compact flash cards, secured digital cards, USB memory devices, memory sticks, and the like.
(57) The invention described and claimed herein is not to be limited in scope by the specific preferred embodiments disclosed herein, as these embodiments are intended as illustrations of several aspects of the invention. Indeed, various modifications of the invention in addition to those shown and described herein will become apparent to those skilled in the art from the foregoing description. Such modifications are also intended to fall within the scope of the appended claims.