CN113409184A - Color image description method based on sixteen-element polar harmonic-Fourier moment - Google Patents

Color image description method based on sixteen-element polar harmonic-Fourier moment Download PDF

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CN113409184A
CN113409184A CN202110427850.XA CN202110427850A CN113409184A CN 113409184 A CN113409184 A CN 113409184A CN 202110427850 A CN202110427850 A CN 202110427850A CN 113409184 A CN113409184 A CN 113409184A
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CN113409184B (en
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王春鹏
张清华
夏之秋
马宾
李健
李琦
王晓雨
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Qilu University of Technology
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Abstract

The invention relates to a color image description method based on hexadecimal polar harmonic-Fourier moments, which comprises the following steps of a, representing a group of multi-view color images as a group of pure hexadecimal fS(r, θ); b. construction of images f using radial basis functions of polar harmonic-Fourier moments (PHFMs)SSixty-ary polar-fourier moments (SPHFMs) of (r, θ); c. using the right sixteen-element order harmonic-Fourier moment
Figure DDA0003030240850000011
Or the order sixty-digit harmonic-Fourier moment
Figure DDA0003030240850000012
Reconstructed image fS(r, θ). The invention can simultaneously encode all color components of all views of a multi-view color image by using the imaginary part of the sixteen element number, and can simultaneously process the components, and the internal relation among the components is reserved. The method has good robustness, and can be used forThe method can effectively resist geometric attacks such as rotation, scaling, shearing, aspect ratio change and the like, various noise attacks, filtering attacks, JPEG (joint photographic experts group) compression attacks and the like, can process the multi-view color image as a whole, and can adapt to more complex application scenes.

Description

Color image description method based on sixteen-element polar harmonic-Fourier moment
Technical Field
The invention relates to the technical field of image processing, in particular to a multi-view color image description method, and specifically relates to a multi-view color image description method based on sixteen element polar harmonic-Fourier moments.
Background
In the digital technology age, it is a very common practice to analyze complex image objects using algorithms. It is important to have an automatic method that is interpretable, robust, efficient, and computationally efficient, capable of representing salient features of an object. The image moment has strong geometric invariance and global feature description capability, is an excellent image description feature, and has become a hotspot in the field of image analysis. In recent years, various moments have been widely used for image reconstruction, image detection, object classification, digital watermarking, image compression, and other applications.
The ability of moments to represent objects in a low-dimensional feature space has many useful features in that it reduces the dimensionality of the original object for fast processing, the same points in the low-dimensional feature space represent all affine transformed versions of the original object, and the feature coefficients representing the high-dimensional space are highly independent, thus minimizing information redundancy and providing compactness of the data. In recent years, the research on moments has been greatly developed, and a series of moments for plane gray scale image processing, which can be divided into orthogonal moments and non-orthogonal moments, appear. The non-orthogonal moments play an important role in image analysis and processing, but the basis functions are relatively simple, information redundancy exists, and the image reconstruction is difficult. The orthogonal moments effectively solve this problem and have become the main research direction in the field of image moments in recent years.
However, these moments are used to process gray images, and with the development of networks and media, the application field of color images is more and more extensive. The study of color moments has also been greatly advanced in recent years. The application of the quaternion theory on moments reserves the correlation among color channels of the color image, and has important significance for the development of the moments of the color image.
The quaternion moment theory is only suitable for processing a single color image, and the research on the moment of processing of a multi-view color image does not have a good way at present.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an image description method which applies the sixteen element number theory to the multi-view color image matrix, can simultaneously process all components of all views of the multi-view color image and can keep the integrity of the image.
The complex number can be extended to 16 dimensions and is called a sixteen element number, a sixteen element number consisting of a real part and fifteen imaginary parts:
x＝x0+x1e1+x2e2+x3e3+x4e4+x5e5+x6e6+x7e7+x8e8+ x9e9+x10e10+x11e11+x12e12+x13e13+x14e14+x15e15
wherein x1，x2，…，x15Is the real part, e1，e2，…，e15Is in imaginary units;
the conjugate of the sixteen element number is defined as:
Figure RE-GDA0003207736620000021
the norm of the sixteen element number is:
Figure RE-GDA0003207736620000022
if the real part of the sixteen element number is 0 (x)00), then the sixteen element number x is referred to as a pure sixteen element number. If the norm of a pure hexadecimal number is 1(| x | ═ 1), then x is referred to as the unit hexadecimal number;
polar harmonic-Fourier moments (abbreviated PHFMs) of the polar coordinate image f (r, θ) are defined as follows:
Figure RE-GDA0003207736620000023
wherein P isnmIs a polar harmonic-Fourier moment (PHFMs), N (N belongs to N) is an order, m (m belongs to Z) is a repetition degree, exp (-jm theta) is an angular Fourier factor, Tn(r) is the radial basis function:
Figure RE-GDA0003207736620000024
Tn(r) is orthogonal within the range of r is more than or equal to 0 and less than or equal to 1:
Figure RE-GDA0003207736620000025
wherein deltanoIs the kronecker function.
From the nature of the angular Fourier factor, the basis function Hnk(r,θ)＝Tn(r) exp (jk θ) is orthogonal within the unit circle:
Figure RE-GDA0003207736620000026
wherein
Figure RE-GDA0003207736620000027
Is Hol(r, theta) conjugate, where r is 0-1, theta is 0-2 pi,
Figure RE-GDA0003207736620000028
is a normalization factor;
as can be seen from the orthogonal function theory, the image reconstruction function of the original image f (r, θ) can be expressed as:
Figure RE-GDA0003207736620000029
the invention provides a color image description method based on sixteen-element polar harmonic-Fourier moments, which comprises the following steps,
a. representing a set of multi-view color images as a set of pure sixteen-element numbers fS(r, θ) (the number of sixteen elements may represent a multi-view color image of no more than five views, and a five-view color image is taken as an example in the present invention):
fS(r,θ)＝fr1(r,θ)e1+fg1(r,θ)e2+fb1(r,θ)e3+fr2(r,θ)e4+fg2(r,θ)e5+fb2(r,θ)e6+ fr3(r,θ)e7+fg3(r,θ)e8+fb3(r,θ)e9+fr4(r,θ)e10+fg4(r,θ)e11+fb4(r,θ)e12+ fr5(r,θ)e13+fg5(r,θ)e14+fb5(r,θ)e15
wherein f isr1(r,θ)，fg1(r,θ)，fb1(r,θ)，…，fr5(r,θ)，fg5(r,θ)，fb5(r, theta) each represents fSRed, green, and blue components of 1 st to 5 th viewing angles of (r, θ);
b. construction of polar images f using radial basis functions of polar harmonic-Fourier moments (PHFMs)SSixty-ary polar-Fourier moments (SPHFMs) of (r, θ),
Figure RE-GDA0003207736620000031
Figure RE-GDA0003207736620000032
wherein
Figure RE-GDA0003207736620000033
Representing the right SPHFMs, and is,
Figure RE-GDA0003207736620000034
represents the left SPHFMs, Tn(r) is the radial basis function of the polar harmonic-Fourier moments of the sixteen elements, μ is the unit pure sixteen element:
Figure RE-GDA0003207736620000035
Figure RE-GDA0003207736620000036
same multi-view color image fSThe relationship of the right and left SPHFMs of (r, θ) is as follows:
Figure RE-GDA0003207736620000037
because f isS(r, θ) is a pure sixteen-element number matrix, so
Figure RE-GDA0003207736620000038
Therefore:
Figure RE-GDA0003207736620000039
c. using the right sixteen-element order harmonic-Fourier moment
Figure RE-GDA00032077366200000310
Or the order sixty-digit harmonic-Fourier moment
Figure RE-GDA00032077366200000311
Can approximately reconstruct the image fS(r, θ), the formula is as follows:
Figure RE-GDA0003207736620000041
Figure RE-GDA0003207736620000042
further, the harmonic-Fourier moments of the right sixteen elements
Figure RE-GDA0003207736620000043
For example, in step b, the multi-view color image fSRight sixty-digit harmonic-Fourier moment of (r, theta)
Figure RE-GDA0003207736620000044
The method is obtained by calculating PHFMs of each component of each visual angle of the multi-visual-angle color image, the multi-visual-angle color image is integrally processed through the relation between the imaginary part of the sixteen element number and the image component, and the calculation process is as follows:
Figure RE-GDA0003207736620000045
wherein:
Figure RE-GDA0003207736620000051
Figure RE-GDA0003207736620000052
Figure RE-GDA0003207736620000053
Figure RE-GDA0003207736620000054
Figure RE-GDA0003207736620000055
Figure RE-GDA0003207736620000056
Figure RE-GDA0003207736620000057
Figure RE-GDA0003207736620000058
Figure RE-GDA0003207736620000059
Figure RE-GDA00032077366200000510
Figure RE-GDA0003207736620000061
Figure RE-GDA0003207736620000062
Figure RE-GDA0003207736620000063
Figure RE-GDA0003207736620000064
Figure RE-GDA0003207736620000065
Figure RE-GDA0003207736620000066
wherein P isnm(fr1)，Pnm(fg1)，Pnm(fb1)，…，Pnm(fr5)，Pnm(fg5)，Pnm(fb5) Each represents fSPolar harmonic-fourier moments (PHFMs) of the red, green and blue components of view angles 1 to 5 of (r, θ), re (p) refers to the real part of complex number p, im (p) refers to the imaginary part of complex number p. Each component of the sixteen-element polar harmonic-fourier moments (SPHFMs) can be represented as a combination of real and imaginary parts of the PHFMs for a single view component of the multi-view color image.
Furthermore, image reconstruction based on the sixteen polar harmonic-Fourier moments is obtained by reconstructing each component of each view angle, and the multi-view color image f in the step cSThe detailed image reconstruction process of (r, θ) is as follows:
Figure RE-GDA0003207736620000071
wherein:
Figure RE-GDA0003207736620000081
Figure RE-GDA0003207736620000082
Figure RE-GDA0003207736620000083
Figure RE-GDA0003207736620000084
Figure RE-GDA0003207736620000085
Figure RE-GDA0003207736620000086
Figure RE-GDA0003207736620000087
Figure RE-GDA0003207736620000088
Figure RE-GDA0003207736620000089
Figure RE-GDA00032077366200000810
Figure RE-GDA00032077366200000811
Figure RE-GDA00032077366200000812
Figure RE-GDA00032077366200000813
Figure RE-GDA00032077366200000814
Figure RE-GDA00032077366200000815
Figure RE-GDA0003207736620000091
wherein the content of the first and second substances,
Figure RE-GDA0003207736620000092
is a matrix close to 0 and is,
Figure RE-GDA0003207736620000093
Figure RE-GDA0003207736620000094
reconstructed images representing red, green and blue components of the multi-view color image at view angles 1 to 5 respectively,
Figure RE-GDA0003207736620000095
are respectively Anm，Bnm，Cnm，…，QnmThe reconstruction matrix of (a) is constructed,
Figure RE-GDA0003207736620000096
Figure RE-GDA0003207736620000097
Figure RE-GDA0003207736620000098
Figure RE-GDA0003207736620000099
Figure RE-GDA00032077366200000910
Figure RE-GDA00032077366200000911
Figure RE-GDA00032077366200000912
Figure RE-GDA00032077366200000913
Figure RE-GDA00032077366200000914
Figure RE-GDA00032077366200000915
Figure RE-GDA00032077366200000916
Figure RE-GDA00032077366200000917
Figure RE-GDA00032077366200000918
Figure RE-GDA00032077366200000919
Figure RE-GDA00032077366200000920
Figure RE-GDA00032077366200000921
the invention constructs a new multi-view color image sixteen-element number polar harmonic-Fourier moment algorithm based on the theory of sixteen element number and image moment, can simultaneously process all color components of all views of the multi-view color image, can effectively resist geometric attacks such as rotation, scaling, shearing, aspect ratio change and the like, various noise attacks, filtering attacks, JPEG compression attacks and the like, can integrally process the multi-view color image, and can adapt to more complex application scenes.
Drawings
FIG. 1 is a schematic diagram of a description method of a multi-view color image based on sixteen-element number-Fourier moment according to the present invention;
FIG. 2 is an original image of a multi-view color image used in an experiment according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a multi-view color image represented by a set of sixteen elements according to the present invention
Fig. 4 is a schematic diagram of amplitude variation mean value versus error data of an image reconstructed by using different maximum moment orders on an original image and SPHFMs according to an embodiment of the present invention.
Detailed Description
In order to clearly illustrate the technical features of the present invention, the present invention is further illustrated by the following detailed description with reference to the accompanying drawings.
A color image description method based on sixteen-element polar harmonic-Fourier moment comprises the following steps,
a. representing a set of multi-view color images as a set of pure sixteen-element numbers fS(r, θ) (the number of sixteen elements may represent a multi-view color image of not more than five views, and a five-view color image is taken as an example in this embodiment):
fS(r,θ)＝fr1(r,θ)e1+fg1(r,θ)e2+fb1(r,θ)e3+fr2(r,θ)e4+fg2(r,θ)e5+fb2(r,θ)e6+ fr3(r,θ)e7+fg3(r,θ)e8+fb3(r,θ)e9+fr4(r,θ)e10+fg4(r,θ)e11+fb4(r,θ)e12+ fr5(r,θ)e13+fg5(r,θ)e14+fb5(r,θ)e15
wherein f isr1(r,θ)，fg1(r,θ)，fb1(r,θ)，…，fr5(r,θ)，fg5(r,θ)，fb5(r, theta) each represents fSRed, green, and blue components of 1 st to 5 th viewing angles of (r, θ);
b. construction of polar images f using radial basis functions of polar harmonic-Fourier moments (PHFMs)SSixty-ary polar-Fourier moments (SPHFMs) of (r, θ),
Figure RE-GDA0003207736620000101
Figure RE-GDA0003207736620000102
wherein
Figure RE-GDA0003207736620000103
Representing the right SPHFMs, and is,
Figure RE-GDA0003207736620000104
represents the left SPHFMs, Tn(r) is the radial basis function of the polar harmonic-Fourier moments of the sixteen elements, μ is the unit pure sixteen element:
Figure RE-GDA0003207736620000105
Figure RE-GDA0003207736620000111
same multi-view color image fSThe relationship of the right and left SPHFMs of (r, θ) is as follows:
Figure RE-GDA0003207736620000112
because f isS(r, θ) is a pure sixteen-element number matrix, so
Figure RE-GDA0003207736620000113
Therefore:
Figure RE-GDA0003207736620000114
c. using the right sixteen-element order harmonic-Fourier moment
Figure RE-GDA0003207736620000115
Or the order sixty-digit harmonic-Fourier moment
Figure RE-GDA0003207736620000116
Can approximately reconstruct the image fS(r, θ), the formula is as follows:
Figure RE-GDA0003207736620000117
Figure RE-GDA0003207736620000118
further, the harmonic-Fourier moments of the right sixteen elements
Figure RE-GDA0003207736620000119
For example, in step b, the multi-view color image fSRight sixty-digit harmonic-Fourier moment of (r, theta)
Figure RE-GDA00032077366200001110
The method is obtained by calculating PHFMs of each component of each visual angle of the multi-visual-angle color image, the multi-visual-angle color image is integrally processed through the relation between the imaginary part of the sixteen element number and the image component, and the calculation process is as follows:
Figure RE-GDA0003207736620000121
wherein:
Figure RE-GDA0003207736620000131
Figure RE-GDA0003207736620000132
Figure RE-GDA0003207736620000133
Figure RE-GDA0003207736620000134
Figure RE-GDA0003207736620000135
Figure RE-GDA0003207736620000136
Figure RE-GDA0003207736620000137
Figure RE-GDA0003207736620000138
Figure RE-GDA0003207736620000139
Figure RE-GDA00032077366200001310
Figure RE-GDA0003207736620000141
Figure RE-GDA0003207736620000142
Figure RE-GDA0003207736620000143
Figure RE-GDA0003207736620000144
Figure RE-GDA0003207736620000145
Figure RE-GDA0003207736620000146
wherein P isnm(fr1)，Pnm(fg1)，Pnm(fb1)，…，Pnm(fr5)，Pnm(fg5)，Pnm(fb5) Each represents fSPolar harmonic-fourier moments (PHFMs) of the red, green and blue components of view angles 1 to 5 of (r, θ), re (p) refers to the real part of complex number p, im (p) refers to the imaginary part of complex number p. Each component of the sixteen-element polar harmonic-Fourier moments (SPHFMs) can be expressed as multiplesPerspective color images are a combination of real and imaginary parts of PHFMs for individual components of a single perspective.
Furthermore, image reconstruction based on the sixteen polar harmonic-Fourier moments is obtained by reconstructing each component of each view angle, and the multi-view color image f in the step cSThe detailed image reconstruction process of (r, θ) is as follows:
Figure RE-GDA0003207736620000151
wherein:
Figure RE-GDA0003207736620000161
Figure RE-GDA0003207736620000162
Figure RE-GDA0003207736620000163
Figure RE-GDA0003207736620000164
Figure RE-GDA0003207736620000165
Figure RE-GDA0003207736620000166
Figure RE-GDA0003207736620000167
Figure RE-GDA0003207736620000168
Figure RE-GDA0003207736620000169
Figure RE-GDA00032077366200001610
Figure RE-GDA00032077366200001611
Figure RE-GDA00032077366200001612
Figure RE-GDA00032077366200001613
Figure RE-GDA00032077366200001614
Figure RE-GDA00032077366200001615
Figure RE-GDA0003207736620000171
wherein the content of the first and second substances,
Figure RE-GDA0003207736620000172
is a matrix close to 0 and is,
Figure RE-GDA0003207736620000173
Figure RE-GDA0003207736620000174
reconstructed images representing red, green and blue components of the multi-view color image at view angles 1 to 5 respectively,
Figure RE-GDA0003207736620000175
are respectively Anm，Bnm，Cnm，…，QnmThe reconstruction matrix of (a) is constructed,
Figure RE-GDA0003207736620000176
Figure RE-GDA0003207736620000177
Figure RE-GDA0003207736620000178
Figure RE-GDA0003207736620000179
Figure RE-GDA00032077366200001710
Figure RE-GDA00032077366200001711
Figure RE-GDA00032077366200001712
Figure RE-GDA00032077366200001713
Figure RE-GDA00032077366200001714
Figure RE-GDA00032077366200001715
Figure RE-GDA00032077366200001716
Figure RE-GDA00032077366200001717
Figure RE-GDA00032077366200001718
Figure RE-GDA00032077366200001719
Figure RE-GDA00032077366200001720
Figure RE-GDA00032077366200001721
the invention is further analyzed and illustrated by the following experiments.
1. Rotational invariance
Rotating 5 visual angles of the multi-view color image by 5 degrees, 15 degrees, 30 degrees, 45 degrees, 65 degrees and 90 degrees respectively, calculating the SPHFMs (sinusoidal pulse width modulation) amplitudes of the original multi-view color image and the rotated multi-view color image respectively, and expressing the amplitude change rate of the rotated image relative to the original image by Mean Relative Error (MRE). The amplitude and rate of change of SPHFMs for a multi-view color image after rotation by different angles are shown in Table 1.
TABLE 1 amplitude change rates of rotated multiview color images SPHFMs
Figure RE-GDA0003207736620000181
Experiments show that after the image is subjected to rotation transformation, the amplitude of SPHFMs of the multi-view color image is almost unchanged, and MRE is less than 0.005. Thus, the SPHFMs of a multi-view color image have rotational invariance.
2. Scaling invariance
The scaling ratios of 5 views of the multi-view color image are 0.5, 0.75, 1.25, 1.5, 1.75 and 2, and the comparison of the amplitudes and the change rates of the SPHFMs of the multi-view color image after scaling according to different ratios is shown in Table 2.
TABLE 2 comparison of amplitude change rates of scaled multi-view color images SPHFMs
Figure RE-GDA0003207736620000182
Experiments show that after the image is subjected to scaling transformation, the amplitude values of the SPHFMs of the multi-view color image are almost unchanged, and the MRE is less than 0.01. Thus, the SPHFMs of the multi-view color image have scale invariance.
3. Filtering attacks
Filtering attacks of 3 multiplied by 3 and 5 multiplied by 5 types of Gaussian filtering, Average filtering and Wiener filtering are respectively added to an original image of the multi-view color image, and the robustness of the SPHFMs to different types of filtering attacks is verified through experiments. The SPHFMs amplitude comparison and MRE comparison of the attacked image to the original image are shown in the following tables.
TABLE 3 SPHFMs amplitude change rate comparison of multi-view color images after Filter attack
Figure RE-GDA0003207736620000191
From the experimental results, it can be seen that the amplitude of the SPHFMs of the multi-view color image is almost unchanged after different types of filtering attacks, and the MRE is less than 0.005. Thus, the SPHFMs are robust to different types of filtering attacks.
4. Noise attack
Noise attacks of 0.001, 0.00 and 0.005 types of Gaussian noise and Salt and pepper noise are added to the original image respectively, and the robustness of the SPHFMs to different types of noise attacks is verified through experiments. The SPHFMs amplitudes of the attacked image and the original image were calculated separately, and the comparison results and MRE comparisons are shown in the following table.
TABLE 4 amplitude change rate comparison of multi-view color images SPHFMs after noise attack
Figure RE-GDA0003207736620000192
It can be seen that the amplitude of the SPHFMs of the multi-view color image is almost unchanged after the multi-view color image is attacked by different types of noise, and the MRE is less than 0.01. Thus, the SPHFMs are robust against different types of noise attacks.
5. JPEG compression attack
JPEG compression attack with quality factors of 30, 50, 70 and 90 is carried out on an original image of the multi-view color image, and the robustness of the SPHFMs to the compression attack with different degrees is verified through experiments. The amplitude values of the SPHFMs of the image subjected to the compression attack and the original image are compared, the MRE of the attacked image is calculated, and the obtained experimental results are shown in the following table.
TABLE 5 comparison of amplitude change rates of multi-view color images SPHFMs after JPEG compression attack
Figure RE-GDA0003207736620000201
From experimental results, after the JPEG compression attack, the amplitude values of the SPHFMs of the multi-view color image are almost unchanged, and the MRE is less than 0.005, which shows that the SPHFMs can resist the JPEG compression attack well.
6. Original image reconstruction
For verifying the image reconstruction performance of the SPHFMs, the maximum moment order N is selectedmax10,20, …,100, the reconstruction error is measured as the Mean Square Reconstruction Error (MSRE). As shown in fig. 4, reconstructed images of the SPHFMs at different maximum moment orders versus 5 views of the Art set of images are presented, and the data under each reconstructed image is the MSRE of the reconstructed image. As can be seen from the data in fig. 4, the image reconstruction performance of the SPHFMs is similar for different viewing angles of the multi-view color image, and the image reconstruction performance of the SPHFMs gradually increases as the maximum moment order increases.
Finally, it should be further noted that the above examples and descriptions are not limited to the above embodiments, and technical features of the present invention that are not described may be implemented by or using the prior art, and are not described herein again; while the foregoing embodiments and drawings are merely illustrative of the present invention and not intended to limit the same, the present invention has been described in detail with reference to the preferred embodiments, and it will be understood by those skilled in the art that changes, modifications, additions or substitutions may be made therein without departing from the spirit and scope of the invention, wherein the sixteen-polar harmonic-fourier moment is one of the sixteen-polar moments, and the same object may be achieved by replacing the sixteen-polar harmonic-fourier moment with another sixteen-polar moment, and the invention shall fall within the scope of the claims of the invention.

Claims (3)

1. A multi-view color image description method based on sixteen-element polar harmonic-Fourier moments is characterized by comprising the following steps,
a. representing a set of multi-view color images as a set of pure sixteen-element numbers fS(r, θ) (the number of sixteen elements may represent a multi-view color image of no more than five views, and a five-view color image is taken as an example in the present invention):
fS(r,θ)＝fr1(r,θ)e1+fg1(r,θ)e2+fb1(r,θ)e3+fr2(r,θ)e4+fg2(r,θ)e5+fb2(r,θ)e6+fr3(r,θ)e7+fg3(r,θ)e8+fb3(r,θ)e9+fr4(r,θ)e10+fg4(r,θ)e11+fb4(r,θ)e12+fr5(r,θ)e13+fg5(r,θ)e14+fb5(r,θ)e15
wherein f isr1(r,θ)，fg1(r,θ)，fb1(r,θ)，…，fr5(r,θ)，fg5(r,θ)，fb5(r, theta) each represents fSRed, green and blue components of 1 st to 5 th viewing angles of (r, theta), e1，e2，…，e15Is the imaginary unit of the sixteen element number;
b. construction of polar images f using radial basis functions of polar harmonic-Fourier moments (PHFMs)SSixty-ary polar-Fourier moments (SPHFMs) of (r, θ),
Figure FDA0003030240820000011
Figure FDA0003030240820000012
wherein
Figure FDA0003030240820000013
Representing the right SPHFMs, and is,
Figure FDA0003030240820000014
representing the left SPHFMs, N (N belongs to N) is the order, m (m belongs to Z) is the repetition degree, Tn(r) is the radial basis function of the polar harmonic-Fourier moments of the sixteen elements, μ is the unit pure sixteen element:
Figure FDA0003030240820000015
Figure FDA0003030240820000016
same multi-view color image fSThe relationship of the right and left SPHFMs of (r, θ) is as follows:
Figure FDA0003030240820000017
because f isS(r, θ) is a pure sixteen-element number matrix, so
Figure FDA0003030240820000018
Therefore:
Figure FDA0003030240820000019
c. using the right sixteen-element order harmonic-Fourier moment
Figure FDA00030302408200000110
Or the order sixty-digit harmonic-Fourier moment
Figure FDA00030302408200000111
Can approximately reconstruct the image fS(r, θ), the formula is as follows:
Figure FDA0003030240820000021
Figure FDA0003030240820000022
2. the method as claimed in claim 1, wherein in step b, the multi-view color image f is a multi-view color image based on sixteen polar harmonic-Fourier momentsS(r, theta) ofRight sixteen-element order harmonic-Fourier moment
Figure FDA0003030240820000023
The calculation process is as follows:
Figure FDA0003030240820000024
wherein:
Figure FDA0003030240820000031
Figure FDA0003030240820000032
Figure FDA0003030240820000033
Figure FDA0003030240820000034
Figure FDA0003030240820000035
Figure FDA0003030240820000036
Figure FDA0003030240820000037
Figure FDA0003030240820000038
Figure FDA0003030240820000039
Figure FDA00030302408200000310
Figure FDA0003030240820000041
Figure FDA0003030240820000042
Figure FDA0003030240820000043
Figure FDA0003030240820000044
Figure FDA0003030240820000045
Figure FDA0003030240820000046
wherein P isnm(fr1)，Pnm(fg1)，Pnm(fb1)，…，Pnm(fr5)，Pnm(fg5)，Pnm(fb5) Each represents fSRed, green and blue at 1 to 5 th viewing angles of (r, theta)The polar-Fourier moments (PHFMs) of the color components, Re (p), denote the real part of the complex number p, and im (p) denotes the imaginary part of the complex number p. Each component of the sixteen-element polar harmonic-fourier moments (SPHFMs) can be represented as a combination of real and imaginary parts of the PHFMs for a single view component of the multi-view color image.
3. The method as claimed in claim 1, wherein the multi-view color image f in step c is a multi-view color image based on sixteen polar harmonic-fourier momentsSThe detailed image reconstruction process of (r, θ) is as follows:
Figure FDA0003030240820000051
wherein:
Figure FDA0003030240820000061
Figure FDA0003030240820000062
Figure FDA0003030240820000063
Figure FDA0003030240820000064
Figure FDA0003030240820000065
Figure FDA0003030240820000066
Figure FDA0003030240820000067
Figure FDA0003030240820000068
Figure FDA0003030240820000069
Figure FDA00030302408200000610
Figure FDA00030302408200000611
Figure FDA00030302408200000612
Figure FDA00030302408200000613
Figure FDA00030302408200000614
Figure FDA00030302408200000615
Figure FDA0003030240820000071
wherein the content of the first and second substances,
Figure FDA0003030240820000072
is a matrix close to 0 and is,
Figure FDA0003030240820000073
Figure FDA0003030240820000074
reconstructed images representing red, green and blue components of the multi-view color image at view angles 1 to 5 respectively,
Figure FDA0003030240820000075
are respectively Anm，Bnm，Cnm，…，QnmThe reconstruction matrix of (a) is constructed,
Figure FDA0003030240820000076
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