CN113077381B - Color image description method based on ternary number continuous orthogonal moment - Google Patents

Abstract

The invention provides a color image description method based on ternary number continuous orthogonal moments, which comprises the following steps: a. representing a sub-polar color image f (r, theta)Is a set of pure ternary numbers; b. constructing three-element continuous orthogonal moment of the color image f (r, theta); c. using a finite number of ternary continuous orthogonal moments (with the highest order being n)_maxThe maximum repetition degree is l_max) The original image f (r, θ) is approximately reconstructed. The invention describes the color image by constructing the ternary number continuous orthogonal moment, not only fully utilizes the relation among all channels, but also avoids information redundancy and reduces the calculation cost.

Description

Color image description method based on ternary number continuous orthogonal moment

Technical Field

The invention relates to the technical field of image processing, in particular to an image description method, and specifically relates to a color image description method based on ternary continuous orthogonal moments.

Background

The concept of moments originally appeared in the research field of statistics and classical mechanics, and Hu proposed Hu invariant moment for the first time in 1962, introduced into the image processing field, and proposed the image moment theory for describing image features. Image moments, which are a invariant feature describing an image, find wide application in many fields of image processing, such as object recognition, image retrieval, and image watermarking. However, the definition of the continuous orthogonal moments of the image is for grayscale images. As color images can provide more information, how to calculate the continuous orthogonal moments of color images attracts great attention.

In order to apply image continuous orthogonal moments to color images, there are generally two processing methods: one is to convert the color image into a gray image and then calculate the continuous orthogonal moment; the other is to calculate the successive orthogonal moments of the three channels of the color image separately and then simply combine them. Obviously, the two methods cannot capture the correlation between channels, lose image information and influence the calculation accuracy of moments.

For this reason, the quaternion theory is applied to the continuous orthogonal moments of the color image, and the internal relation between color image channels is fully preserved. Quaternion continuous orthogonal moments preserve the relationship between the three channels of the color image, but the fourth dimension of quaternions creates information redundancy when processing color images and is computationally expensive.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides the color image description method based on the ternary number continuous orthogonal moment, which makes full use of the relationship among all channels, avoids information redundancy and reduces the calculation cost.

The continuous orthogonal moment of the image is the projection of the image function on the continuous basis function, is a stable image characteristic, and has strong image description capability and geometric invariance. Continuous orthogonal moment M of image with order n of repetition degree l of polar coordinate image f (r, theta)_nlIs defined as:

wherein C is a constant, and C is a constant,

denotes the conjugated complex number, P_n(r) is a radial basis function, theta is a polar angle, the value range of theta is more than or equal to 0 and less than or equal to 2 pi, and the range of r is more than or equal to 0 and less than or equal to 1.

As can be seen from the theory of the orthogonal integral function system, the original image function f (r, θ) can be approximately reconstructed by using a finite number of moment-weighted superposition, and the greater the number of moments used, the higher the degree of approximation:

and a ternary number is an extension of a complex number, defined as μ ═ a + ib + jc, μ is a ternary number, where a, b, and c are real numbers, and i and j are operators that satisfy the following rules:

i²＝j,ij＝ji＝-1,j²＝-i

the three basic elements {1, i, j } of a ternary number form an abelian group, where 1 is the multiplicative unit bit and μ is a pure ternary number when a is 0.

The ternary number μ ═ a + ib + jc can be written as follows:

μ＝|μ|(cos(φ)+μsin(φ))

wherein the content of the first and second substances,

is the magnitude of the ternary number, and when | μ | ═ 1, μ is the unit ternary number.

Mu.s of₁＝a₁+ib₁+jc₁And mu₂＝a₂+ib₂+jc₂Is two ternary numbers, then μ is defined₁And mu₂Satisfy addition and multiplication of

μ₁+μ₂＝(a₁+a₂)+i(b₁+b₂)+j(c₁+c₂)

μ₁μ₂＝(a₁a₂-b₁c₂-c₁b₂)+i(a₁b₂+b₁a₂-c₁c₂)+j(a₁c₂+b₁b₂+c₁a₂)

Unlike quaternions, quaternions are interchangeable under both addition and multiplication:

μ₁+μ₂＝μ₂+μ₁

μ₁μ₂＝μ₂μ₁

note that the ternary numbers are not reversible.

The invention describes the color image by constructing the ternary number continuous orthogonal moment, not only fully utilizes the relation among all channels, but also avoids information redundancy and reduces the calculation cost.

The invention is realized by the following technical scheme, and provides a color image description method based on ternary continuous orthogonal moments, which comprises the following steps:

a. a polar color image f (r, theta) is represented as a set of pure ternary numbers,

f(r,θ)＝R(r,θ)+G(r,θ)i+B(r,θ)k

wherein, R (R, θ), G (R, θ) and B (R, θ) represent the red, green and blue three channel components of the color image f (R, θ), respectively;

b. constructing three-element continuous orthogonal moments of the color image f (r, theta),

wherein, mu₁＝β₁i+γ₁j is any unit of pure ternary number,

and is

P_n(r) is a radial basis function;

c. using a finite number of ternary continuous orthogonal moments (with the highest order being n)_maxThe maximum repetition degree is l_max) Approximate reconstructed original image function f (r, θ):

wherein mu₂＝α₂+β₂i+γ₂j is a ternary number consisting of₁μ₂Is given as-1

Further, the calculation process of the three-element continuous orthogonal moment of the color image f (r, θ) in step b is as follows:

wherein the content of the first and second substances,

wherein, M_nl(R)、M_nl(G) And M_nl(B) The successive orthogonal moments of the three channels R (R, θ), G (R, θ) and B (R, θ), Re (·) and Im (·) of the color image f (R, θ), respectively, represent the real and imaginary parts, respectively, of the complex number.

Further, the calculation process of the reconstructed color image f (r, θ) according to the three-element continuous orthogonal moments in the step c is as follows:

where R '(R, θ), G' (R, θ) and B '(R, θ) are the three red, green and blue channels of the reconstructed color image f' (R, θ), respectively, and are derived by the following equation:

R′(r,θ)＝Re(A(r,θ))+α₂Im(A(r,θ))-γ₂Im(D(r,θ))-β₂Im(E(r,θ))

G′(r,θ)＝Re(D(r,θ))+β₂Im(A(r,θ))+α₂Im(D(r,θ))-γ₂Im(E(r,θ))

B′(r,θ)＝Re(E(r,θ))+γ₂Im(A(r,θ))+β₂Im(D(r,θ))+α₂Im(E(r,θ))

wherein A (r, theta), D (r, theta) and E (r, theta) are respectively A_nl、D_nlAnd E_nlThe resulting matrix is reconstructed and the matrix is reconstructed,

in conclusion, the color image is described by constructing the ternary continuous orthogonal moment, so that the relationship among channels is fully utilized, information redundancy is avoided, and the calculation cost is reduced.

Drawings

FIG. 1 is a flow chart of the steps of calculating and reconstructing a color image description method based on three-component continuous orthogonal moments according to 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 specific embodiments.

A color image description method based on ternary number continuous orthogonal moment is characterized by comprising the following steps:

a. a polar color image f (r, theta) is represented as a set of pure ternary numbers,

f(r,θ)＝R(r,θ)+G(r,θ)i+B(r,θ)k

wherein, R (R, θ), G (R, θ) and B (R, θ) represent the red, green and blue three channel components of the color image f (R, θ), respectively;

b. constructing three-element continuous orthogonal moments of the color image f (r, theta),

wherein, mu₁＝β₁i+γ₁j is any unit of pure ternary number,

and is

P_n(r) is a radial basis function;

c. using a finite number of ternary continuous orthogonal moments (with the highest order being n)_maxThe maximum repetition degree is l_max) Approximate reconstructed original image function f (r, θ):

wherein mu₂＝α₂+β₂i+γ₂j is a ternary number consisting of₁μ₂Is given as-1

In this embodiment, the process of calculating the three-element continuous orthogonal moment of the color image f (r, θ) in step b is as follows:

wherein the content of the first and second substances,

A_nl＝Re(M_nl(R))-γ₁Im(M_nl(G))-β₁Im(M_nl(B))

D_nl＝β₁Im(M_nl(R))+Re(M_nl(G))-γ₁Im(M_nl(B))

E_nl＝γ₁Im(M_nl(R))+β₁Im(M_nl(G))+Re(M_nl(B))

wherein, M_nl(R)、M_nl(G) And M_nl(B) The successive orthogonal moments of the three channels R (R, θ), G (R, θ) and B (R, θ), Re (·) and Im (·) of the color image f (R, θ), respectively, represent the real and imaginary parts, respectively, of the complex number.

The calculation process of the reconstructed color image f (r, theta) according to the ternary number continuous orthogonal moment in the step c is as follows:

where R '(R, θ), G' (R, θ) and B '(R, θ) are the three red, green and blue channels of the reconstructed color image f' (R, θ), respectively, and are derived by the following equation:

R′(r,θ)＝Re(A(r,θ))+α₂Im(A(r,θ))-γ₂Im(D(r,θ))-β₂Im(E(r,θ))

G′(r,θ)＝Re(D(r,θ))+β₂Im(A(r,θ))+α₂Im(D(r,θ))-γ₂Im(E(r,θ))

B′(r,θ)＝Re(E(r,θ))+γ₂Im(A(r,θ))+β₂Im(D(r,θ))+α₂Im(E(r,θ))

wherein A (r, theta), D (r, theta) and E (r, theta) are respectively A_nl、D_nlAnd E_nlThe resulting matrix is reconstructed and the matrix is reconstructed,

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; the above embodiments and drawings are only for illustrating the technical solutions of the present invention and not for limiting the present invention, and the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that changes, modifications, additions or substitutions within the spirit and scope of the present invention may be made by those skilled in the art without departing from the spirit of the present invention, and shall also fall within the scope of the claims of the present invention.

Claims (1)

1. A color image description method based on ternary continuous orthogonal moments is characterized by comprising the following steps:

a. a polar color image f (r, theta) is represented as a set of pure ternary numbers,

f(r,θ)＝R(r,θ)+G(r,θ)i+B(r,θ)k

wherein, R (R, theta), G (R, theta) and B (R, theta) respectively represent red, green and blue channel components of the color image f (R, theta), theta is a polar angle and has a value range of 0-2 pi, and R has a value range of 0-1R;

b. constructing three-element continuous orthogonal moments of the color image f (r, theta),

wherein, mu₁＝β₁i+γ₁j is any unit pure ternary number, beta₁ ²+γ₁ ²1 and

P_n(r) is a radial basis function;

c. reconstructing the original image f (r, θ) using a finite number of successive orthogonal moments approximations:

wherein mu₂＝α₂+β₂i+γ₂j is a ternary number consisting of₁μ₂Is given as-1

The calculation process of the three-element continuous orthogonal moment of the color image f (r, theta) in the step b is as follows:

wherein the content of the first and second substances,

A_nl＝Re(M_nl(R))-γ₁Im(M_nl(G))-β₁Im(M_nl(B))

D_nl＝β₁Im(M_nl(R))+Re(M_nl(G))-γ₁Im(M_nl(B))

E_nl＝γ₁Im(M_nl(R))+β₁Im(M_nl(G))+Re(M_nl(B))

wherein M is_nl(R)、M_nl(G) And M_nl(B) The successive orthogonal moments of the three channels R (R, θ), G (R, θ) and B (R, θ), Re (·) and Im (·) of the color image f (R, θ), respectively, represent the real and imaginary parts, respectively, of the complex number.

The calculation process of the reconstructed color image f (r, theta) according to the three-element continuous orthogonal moment in the step c is as follows:

where R '(R, θ), G' (R, θ) and B '(R, θ) are the three red, green and blue channels of the reconstructed color image f' (R, θ), respectively, and are derived by the following equation:

R′(r,θ)＝Re(A(r,θ))+α₂Im(A(r,θ))-γ₂Im(D(r,θ))-β₂Im(E(r,θ))

G′(r,θ)＝Re(D(r,θ))+β₂Im(A(r,θ))+α₂Im(D(r,θ))-γ₂Im(E(r,θ))

B′(r,θ)＝Re(E(r,θ))+γ₂Im(A(r,θ))+β₂Im(D(r,θ))+α₂Im(E(r,θ))

wherein A (r, θ), D (r, θ) and E (r, θ) are each A_nl、D_nlAnd E_nlThe resulting matrix is reconstructed and the matrix is reconstructed,

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