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 f^S(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):

f^S(r,θ)＝f_r1(r,θ)e₁+f_g1(r,θ)e₂+f_b1(r,θ)e₃+f_r2(r,θ)e₄+f_g2(r,θ)e₅+f_b2(r,θ)e₆+f_r3(r,θ)e₇+f_g3(r,θ)e₈+f_b3(r,θ)e₉+f_r4(r,θ)e₁₀+f_g4(r,θ)e₁₁+f_b4(r,θ)e₁₂+f_r5(r,θ)e₁₃+f_g5(r,θ)e₁₄+f_b5(r,θ)e₁₅

wherein f is_r1(r,θ)，f_g1(r,θ)，f_b1(r,θ)，…，f_r5(r,θ)，f_g5(r,θ)，f_b5(r, theta) each represents f^SRed, 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),

whereinRepresenting the right SPHFMs, and is,representing the left SPHFMs, N (N belongs to N) is the order, m (m belongs to Z) is the repetition degree, T_n(r) is the radial basis function of the polar harmonic-Fourier moments of the sixteen elements, μ is the unit pure sixteen element:

same multi-view color image f^SThe relationship of the right and left SPHFMs of (r, θ) is as follows:

because f is^S(r, θ) is a pure sixteen-element number matrix, soTherefore:

c. using the right sixteen-element order harmonic-Fourier momentOr the order sixty-digit harmonic-Fourier momentCan approximately reconstruct the image f^S(r, θ), the formula is as follows:

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 moments^S(r, theta) ofRight sixteen-element order harmonic-Fourier momentThe calculation process is as follows:

wherein:

wherein P is_nm(f_r1)，P_nm(f_g1)，P_nm(f_b1)，…，P_nm(f_r5)，P_nm(f_g5)，P_nm(f_b5) Each represents f^SRed, 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 moments^SThe detailed image reconstruction process of (r, θ) is as follows:

wherein:

wherein the content of the first and second substances,is a matrix close to 0 and is, reconstructed images representing red, green and blue components of the multi-view color image at view angles 1 to 5 respectively,are respectively A_nm，B_nm，C_nm，…，Q_nmThe reconstruction matrix of (a) is constructed,

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:

the norm of the sixteen element number is:

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:

wherein P is_nmIs 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, T_n(r) is the radial basis function:

T_n(r) is orthogonal within the range of r is more than or equal to 0 and less than or equal to 1:

wherein delta_noIs the kronecker function.

From the nature of the angular Fourier factor, the basis function H_nk(r,θ)＝T_n(r) exp (jk θ) is orthogonal within the unit circle:

whereinIs H_ol(r, theta) conjugate, where r is 0-1, theta is 0-2 pi,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:

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 f^S(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):

f^S(r,θ)＝f_r1(r,θ)e₁+f_g1(r,θ)e₂+f_b1(r,θ)e₃+f_r2(r,θ)e₄+f_g2(r,θ)e₅+f_b2(r,θ)e₆+ f_r3(r,θ)e₇+f_g3(r,θ)e₈+f_b3(r,θ)e₉+f_r4(r,θ)e₁₀+f_g4(r,θ)e₁₁+f_b4(r,θ)e₁₂+ f_r5(r,θ)e₁₃+f_g5(r,θ)e₁₄+f_b5(r,θ)e₁₅

wherein f is_r1(r,θ)，f_g1(r,θ)，f_b1(r,θ)，…，f_r5(r,θ)，f_g5(r,θ)，f_b5(r, theta) each represents f^SRed, 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),

whereinRepresenting the right SPHFMs, and is,represents the left SPHFMs, T_n(r) is the radial basis function of the polar harmonic-Fourier moments of the sixteen elements, μ is the unit pure sixteen element:

same multi-view color image f^SThe relationship of the right and left SPHFMs of (r, θ) is as follows:

because f is^S(r, θ) is a pure sixteen-element number matrix, soTherefore:

c. using the right sixteen-element order harmonic-Fourier momentOr the order sixty-digit harmonic-Fourier momentCan approximately reconstruct the image f^S(r, θ), the formula is as follows:

further, the harmonic-Fourier moments of the right sixteen elementsFor example, in step b, the multi-view color image f^SRight sixty-digit harmonic-Fourier moment of (r, theta)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:

wherein:

wherein P is_nm(f_r1)，P_nm(f_g1)，P_nm(f_b1)，…，P_nm(f_r5)，P_nm(f_g5)，P_nm(f_b5) Each represents f^SPolar 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 c^SThe detailed image reconstruction process of (r, θ) is as follows:

wherein:

wherein the content of the first and second substances,is a matrix close to 0 and is, reconstructed images representing red, green and blue components of the multi-view color image at view angles 1 to 5 respectively,are respectively A_nm，B_nm，C_nm，…，Q_nmThe reconstruction matrix of (a) is constructed,

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 f^S(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):

f^S(r,θ)＝f_r1(r,θ)e₁+f_g1(r,θ)e₂+f_b1(r,θ)e₃+f_r2(r,θ)e₄+f_g2(r,θ)e₅+f_b2(r,θ)e₆+ f_r3(r,θ)e₇+f_g3(r,θ)e₈+f_b3(r,θ)e₉+f_r4(r,θ)e₁₀+f_g4(r,θ)e₁₁+f_b4(r,θ)e₁₂+ f_r5(r,θ)e₁₃+f_g5(r,θ)e₁₄+f_b5(r,θ)e₁₅

wherein f is_r1(r,θ)，f_g1(r,θ)，f_b1(r,θ)，…，f_r5(r,θ)，f_g5(r,θ)，f_b5(r, theta) each represents f^SRed, 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),

whereinRepresenting the right SPHFMs, and is,represents the left SPHFMs, T_n(r) is the radial basis function of the polar harmonic-Fourier moments of the sixteen elements, μ is the unit pure sixteen element:

same multi-view color image f^SThe relationship of the right and left SPHFMs of (r, θ) is as follows:

because f is^S(r, θ) is a pure sixteen-element number matrix, soTherefore:

c. using the right sixteen-element order harmonic-Fourier momentOr the order sixty-digit harmonic-Fourier momentCan approximately reconstruct the image f^S(r, θ), the formula is as follows:

further, the harmonic-Fourier moments of the right sixteen elementsFor example, in step b, the multi-view color image f^SRight sixty-digit harmonic-Fourier moment of (r, theta)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:

wherein:

wherein P is_nm(f_r1)，P_nm(f_g1)，P_nm(f_b1)，…，P_nm(f_r5)，P_nm(f_g5)，P_nm(f_b5) Each represents f^SPolar 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 c^SThe detailed image reconstruction process of (r, θ) is as follows:

wherein:

wherein the content of the first and second substances,is a matrix close to 0 and is, reconstructed images representing red, green and blue components of the multi-view color image at view angles 1 to 5 respectively,are respectively A_nm，B_nm，C_nm，…，Q_nmThe reconstruction matrix of (a) is constructed,

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

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

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

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

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

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 selected_max10,20, …,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.