1. The hyperspectral image eigen decomposition method based on the assistance of a digital surface model is characterized by comprising the following steps of:

s1, inputting the hyperspectral image and the digital surface model data, and calculating to obtain a geometric component;

s2, calculating to obtain a local prior matrix;

s3, calculating to obtain a non-local prior matrix;

and S4, performing eigen decomposition according to the geometric component, the local prior matrix and the non-local prior matrix, and outputting the high spectral reflectivity and the environment illumination.

2. The method for eigen decomposition of hyperspectral images aided based on a digital surface model according to claim 1, wherein the specific method for obtaining geometric components by calculation of S1 comprises:

inputting a hyperspectral image

Inputting digital surface model elevation data

Wherein h is_k＝[h_k(λ₁),h_k(λ₂),…,h_k(λ_d)]^TK 1, 2.. u denotes a spectral feature of each pixel, k 1, 2.. u denotes an index of each pixel, λ denotes a wavelength, d denotes the number of bands, u denotes the number of hyperspectral image pixels, z denotes a spectral feature of each pixel, and₁,z₂,…,z_uthe elevation corresponding to each pixel is represented,a representation domain;

calculating the normal of each pixel to obtain the normal characteristic:

wherein the content of the first and second substances,represents the projection of the normal on the x, y and z space coordinate axes;

and calculating to obtain a geometric component J: j ═ J₁,J₂,…,J_u]^T；

Wherein the content of the first and second substances,

c₁、c₂、c₃、c₄、c₅is five constants.

3. The method for eigen decomposition of hyperspectral image aided based on a digital surface model according to claim 2, wherein c is₁、c₂The method comprises the following steps:

c₁＝0.429,c₂＝0.512。

4. the method for eigen decomposition of hyperspectral image aided based on a digital surface model according to claim 2, wherein c is₃The method comprises the following steps:

c₃＝0.743。

5. the method for eigen decomposition of hyperspectral image aided based on a digital surface model according to claim 2, wherein c is₄The method comprises the following steps:

c₄＝0.886。

6. the method for eigen decomposition of hyperspectral image aided based on a digital surface model according to claim 2, wherein c is₅The method comprises the following steps:

c₅＝0.248。

7. the method for eigen decomposition of hyperspectral images based on the assistance of a digital surface model according to claim 2, wherein the specific method for obtaining the local prior matrix by calculation of S2 comprises:

and traversing the index k of each pixel to be 1,2_k＝[h₁,…,h_k-1,h_k+1,…,h_u,I_d]；

Wherein, I_dRepresenting a d-dimensional identity matrix;

h is calculated according to_kIn dictionary D_kSparse representation coefficient α in (1):

min_α‖α‖₁ subject to h_k＝D_kα；

each element W of the local prior matrix W_kjIs obtained by the following formula:

W_kjan element representing the kth row and jth column of W;

α_jsparse representation coefficient, alpha, representing the j-th column_j-1The sparse representation coefficients representing the j-1 th column.

8. The method for eigen decomposition of hyperspectral images based on the assistance of a digital surface model according to claim 7, wherein the specific method for obtaining the non-local prior matrix by calculation of S3 comprises:

the spectral characteristic h of each pixel of the hyperspectral image_kAnd digital surface model elevation data z_kAnd stacking, namely establishing a d + 1-dimensional vector space: [ h ] of_k ^T,z_k],k＝1,2,...,u；

Searching the adjacent points of each pixel in the d + 1-dimensional vector space, and establishing a set Q of the adjacent points_k；

Each element T of the non-local prior matrix T_kjIs obtained by the following formula:

T_kjthe element representing the kth row and the jth column of T.

9. The method for eigen decomposition of hyperspectral images based on assistance of a digital surface model according to claim 8, wherein the specific method for performing eigen decomposition according to geometric components, local prior matrices and non-local prior matrices to output hyperspectral reflectivity and ambient illumination at S4 comprises:

high spectral reflectance

Wherein r is_k＝[r_k(λ₁),r_k(λ₂),...,r_k(λ_d)]^TK 1, 2.. u denotes the reflectance of each pixel; lambda [ alpha ]₁、λ₂、...、λ_dRespectively representing the wavelengths corresponding to the 1 st, 2 nd, … th and d th image channels;

the ambient light is L ═ L₁,L₂,...,L₉]^T；

L₁、L₂、...、L₉Coefficients representing the nine-dimensional spherical harmonic illumination, respectively;

the total cost function of the eigen decomposition is:

σ_rweights, σ, representing local prior cost terms_zWeights representing non-local prior cost terms;

calculating partial derivatives to obtain:

wherein the intermediate variable G ═ I_u+σ_r(I_u-W^T)(I_u-W)+σ_z(I_u-T^T)(I_u-T)；

Wherein 1 is_dRepresenting a full 1-column vector, I, of size dX 1_uRepresents a u × u identity matrix;

order toAnd obtaining a linear equation set related to R and L, and solving to obtain the hyperspectral image reflectivity R and the ambient illumination L.

10. The method for eigen decomposition of a hyperspectral image assisted based on a digital surface model according to claim 9, wherein the ambient illumination L is a nine-dimensional spherical harmonic illumination coefficient.

Background

The hyperspectral image has abundant spectral information, but the high-dimensional spectral space also causes high redundancy of information, which is not beneficial to the processing and interpretation of the information. Various methods of feature extraction have been devised for better mining of information, but these methods of information extraction have substantial drawbacks. When imaging conditions such as ambient light change, the spectrum obtained by imaging also changes, which causes the obtained spectrum to have high uncertainty, and the uncertainty is reflected in the extracted features, so that the information expressed by the features is unreliable. In order to solve the problem, the research of the intrinsic decomposition method based on the physical imaging model has great significance. Intrinsic decomposition aims at studying the physical imaging process, recovering the reflectivity reflecting the properties of the ground objects themselves, and also reversing the environmental imaging elements, such as illumination. The difficulty of eigen-decomposition is that eigen-decomposition is an underdetermined problem and challenges exist in model solution.

Disclosure of Invention

The invention aims to solve the problem of low intrinsic decomposition precision of the existing hyperspectral image and provides a digital surface model-assisted hyperspectral image intrinsic decomposition method.

The invention relates to a hyperspectral image intrinsic decomposition method based on assistance of a digital surface model, which comprises the following steps of:

s1, inputting the hyperspectral image and the digital surface model data, and calculating to obtain a geometric component;

s2, calculating to obtain a local prior matrix;

s3, calculating to obtain a non-local prior matrix;

and S4, performing eigen decomposition according to the geometric component, the local prior matrix and the non-local prior matrix, and outputting the high spectral reflectivity and the environment illumination.

Preferably, the specific method for obtaining the geometric component by calculation in S1 includes:

inputting a hyperspectral image

Inputting digital surface model elevation data

Wherein h is_k＝[h_k(λ₁),h_k(λ₂),…,h_k(λ_d)]^TK 1, 2.. u denotes a spectral feature of each pixel, k 1, 2.. u denotes an index of each pixel, λ denotes a wavelength, d denotes the number of bands, u denotes the number of hyperspectral image pixels, z denotes a spectral feature of each pixel, and₁,z₂,…,z_uthe elevation corresponding to each pixel is represented,a representation domain;

calculating the normal of each pixel to obtain the normal characteristic:

wherein the content of the first and second substances,represents the projection of the normal on the x, y and z space coordinate axes;

and calculating to obtain a geometric component J: j ═ J₁,J₂,…,J_u]^ú；

Wherein the content of the first and second substances,

c₁、c₂、c₃、c₄、c₅is five constants.

Preferably, said c₁、c₂、c₃、c₄、c₅The method comprises the following steps:

c₁＝0.429,c₂＝0.512,c₃＝0.743,c₄＝0.886,c₅＝0.248。

preferably, the specific method for obtaining the local prior matrix by calculation in S2 includes:

and traversing the index k of each pixel to be 1,2_k＝[h₁,…,h_k-1,h_k+1,…,h_u,I_d]；

Wherein, I_dRepresenting a d-dimensional identity matrix;

h is calculated according to_kIn dictionary D_kSparse representation coefficient α in (1):

min_α‖α‖₁subject to h_k＝D_kα；

each element W of the local prior matrix W_kjIs obtained by the following formula:

W_kjan element representing the kth row and jth column of W;

α_jsparse representation coefficient, alpha, representing the j-th column_j-1The sparse representation coefficients representing the j-1 th column.

Preferably, the specific method for obtaining the non-local prior matrix by calculation in S3 includes:

the spectral characteristic h of each pixel of the hyperspectral image_kAnd digital surface model elevation data z_kAnd stacking, namely establishing a d + 1-dimensional vector space: [ h ] of_k ^ú,z_k],k＝1,2,...,u；

Searching the adjacent points of each pixel in the d + 1-dimensional vector space, and establishing a set Q of the adjacent points_k；

Each element T of the non-local prior matrix T_kjIs obtained by the following formula:

T_kjthe element representing the kth row and the jth column of T.

Preferably, the specific method for performing eigen decomposition according to the geometric component, the local prior matrix and the non-local prior matrix to output the high spectral reflectance and the ambient illumination in S4 includes:

high spectral reflectance

Wherein r is_k＝[r_k(λ₁),r_k(λ₂),...,r_k(λ_d)]^TK 1, 2.. u denotes the reflectance of each pixel; lambda [ alpha ]₁、λ₂、...、λ_dRespectively representing the wavelengths corresponding to the 1 st, 2 nd, … th and d th image channels;

the ambient light is L ═ L₁,L₂,...,L₉]^ú；

L₁、L₂、...、L₉Coefficients representing the nine-dimensional spherical harmonic illumination, respectively;

the total cost function of the eigen decomposition is:

σ_rweights, σ, representing local prior cost terms_zWeights representing non-local prior cost terms;

calculating partial derivatives to obtain:

wherein the intermediate variable G ═ I_u+σ_r(I_u-W)(I_u-W)+σ_z(I_u-T)(I_u-T)；

Wherein 1 is_dRepresenting a full 1-column vector, I, of size dX 1_uRepresents a u × u identity matrix;

order toAnd obtaining a linear equation set related to R and L, and solving to obtain the hyperspectral image reflectivity R and the ambient illumination L.

Preferably, the ambient illumination L is a nine-dimensional spherical harmonic illumination coefficient.

The invention has the advantages that: in order to solve the problem of low intrinsic decomposition precision of the hyperspectral image, the invention introduces elevation information of DSM (Digital Surface Model) data as guidance, and can greatly improve the intrinsic decomposition precision. The method can perform high-precision hyperspectral image eigen decomposition under the guidance of DSM data elevation information, generate hyperspectral reflectivity and environmental illumination, and is simple, high in calculation efficiency and easy to implement. The hyperspectral image intrinsic decomposition method provided by the invention establishes a hyperspectral imaging physical model, combines the spectral information of the hyperspectral image and the elevation information of DSM data from the signal perspective, and eliminates the spectrum uncertainty of the hyperspectral image caused by the spectral information degradation caused by illumination.

Drawings

FIG. 1 is a schematic block diagram of a digital surface model-based aided hyperspectral image eigen decomposition method;

FIG. 2 is a schematic illustration of an input hyperspectral image;

FIG. 3 is a schematic illustration of input digital surface model data;

FIG. 4 is a graphical illustration of the output hyperspectral reflectance;

FIG. 5 is a schematic illustration of output ambient lighting;

FIG. 6 is a comparison of errors of the hyperspectral reflectances obtained by the eigen-decomposition method of the invention with those obtained by other methods, where a represents the hyperspectral reflectance error obtained by the hyperspectral image eigen-decomposition method assisted by the digital surface model of the invention, b represents the hyperspectral reflectance error obtained by the hyperspectral eigen-decomposition method based on sparse graph coding, c represents the hyperspectral reflectance error obtained by the hyperspectral eigen-decomposition method based on feature extraction, and d represents the hyperspectral reflectance error obtained by the hyperspectral eigen-decomposition method based on texture structure separation.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.

The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.

The first embodiment is as follows: the following describes an embodiment with reference to fig. 1, where the method for eigen-decomposition of a hyperspectral image based on assistance of a digital surface model in the embodiment includes:

s1, inputting the hyperspectral image and the digital surface model data, and calculating to obtain a geometric component;

s2, calculating to obtain a local prior matrix;

s3, calculating to obtain a non-local prior matrix;

and S4, performing eigen decomposition according to the geometric component, the local prior matrix and the non-local prior matrix, and outputting the high spectral reflectivity and the environment illumination.

The second embodiment is as follows: in this embodiment, to further explain the first embodiment, the specific method for obtaining the geometric component by calculation in S1 includes:

inputting a hyperspectral image

Inputting digital surface model elevation data

Wherein h is_k＝[h_k(λ₁),h_k(λ₂),…,h_k(λ_d)]^TK 1, 2.. u denotes a spectral feature of each pixel, k 1, 2.. u denotes an index of each pixel, λ denotes a wavelength, d denotes the number of bands, u denotes the number of hyperspectral image pixels, z denotes a spectral feature of each pixel, and₁,z₂,…,z_uthe elevation corresponding to each pixel is represented,a representation domain;

calculating the normal of each pixel to obtain the normal characteristic:

wherein the content of the first and second substances,represents the projection of the normal on the x, y and z space coordinate axes;

and calculating to obtain a geometric component J: j ═ J₁,J₂,…,J_u]^ú；

Wherein the content of the first and second substances,

c₁、c₂、c₃、c₄、c₅is five constants.

Further, said c₁、c₂、c₃、c₄、c₅The method comprises the following steps:

c₁＝0.429,c₂＝0.512,c₃＝0.743,c₄＝0.886,c₅＝0.248。

the third concrete implementation mode: in this embodiment, further describing the second embodiment, the specific method for obtaining the local prior matrix by calculation in S2 includes:

and traversing the index k of each pixel to be 1,2_k＝[h₁,…,h_k-1,h_k+1,…,h_u,I_d]；

Wherein, I_dRepresenting a d-dimensional identity matrix;

h is calculated according to_kIn dictionary D_kSparse representation coefficient α in (1):

min_α‖α‖₁subject to h_k＝D_kα；

each element W of the local prior matrix W_kjIs obtained by the following formula:

W_kjan element representing the kth row and jth column of W;

α_jsparse representation coefficient, alpha, representing the j-th column_j-1The sparse representation coefficients representing the j-1 th column.

The fourth concrete implementation mode: in this embodiment, a third embodiment is further described, and the specific method for obtaining the non-local prior matrix by calculation in S3 includes:

the spectral characteristic h of each pixel of the hyperspectral image_kAnd digital surface model elevation data z_kAnd stacking, namely establishing a d + 1-dimensional vector space: [ h ] of_k ^ú,z_k],k＝1,2,...,u；

Searching the adjacent points of each pixel in the d + 1-dimensional vector space, and establishing a set Q of the adjacent points_k；

Each element T of the non-local prior matrix T_kjIs obtained by the following formula:

T_kjthe element representing the kth row and the jth column of T.

The fifth concrete implementation mode: in this embodiment, further describing the fourth embodiment, the specific method for performing eigen decomposition according to the geometric component, the local prior matrix, and the non-local prior matrix to output the high spectral reflectance and the ambient illumination in S4 includes:

high spectral reflectance

Wherein r is_k＝[r_k(λ₁),r_k(λ₂),...,r_k(λ_d)]^TK 1, 2.. u denotes the reflectance of each pixel; lambda [ alpha ]₁、λ₂、...、λ_dRespectively representing the wavelengths corresponding to the 1 st, 2 nd, … th and d th image channels;

the ambient light is L ═ L₁,L₂,...,L₉]^ú；

L₁、L₂、...、L₉Coefficients representing the nine-dimensional spherical harmonic illumination, respectively;

the total cost function of the eigen decomposition is:

σ_rweights, σ, representing local prior cost terms_zWeights representing non-local prior cost terms;

calculating partial derivatives to obtain:

wherein the intermediate variable G ═ I_u+σ_r(I_u-W)(I_u-W)+σ_z(I_u-T)(I_u-T)；

Wherein 1 is_dRepresenting a full 1-column vector, I, of size dX 1_uRepresents a u × u identity matrix;

order toAnd obtaining a linear equation set related to R and L, and solving to obtain the hyperspectral image reflectivity R and the ambient illumination L.

Further, the ambient illumination L is a nine-dimensional spherical harmonic illumination coefficient.

In the invention, the hyperspectral image and DSM elevation data have complementarity and isomerism, more specifically, the hyperspectral image has rich spectral information, but the spatial information is the degradation of a three-dimensional image to a two-dimensional image; DSM can acquire accurate three-dimensional spatial information, but the spectral information is relatively poor.

In order to verify the performance of the hyperspectral image intrinsic decomposition method provided by the invention, a group of actually photographed hyperspectral images and DSM data are verified, as shown in FIG. 2, input hyperspectral images are shown, as shown in FIG. 3, input DSM data are shown, as shown in FIG. 4, the hyperspectral reflectivity obtained by the hyperspectral image intrinsic decomposition method provided by the invention is shown, as shown in FIG. 5, environment illumination obtained by the hyperspectral image intrinsic decomposition method provided by the invention is shown, as shown in FIG. 6, errors of the hyperspectral reflectivity obtained by the intrinsic decomposition method provided by the invention and the hyperspectral reflectivity obtained by other methods are compared, as shown in FIG. 6, the effectiveness of the hyperspectral image intrinsic decomposition method provided by the invention is shown, and as shown in FIG. 6, the hyperspectral reflectivity error recovered by the hyperspectral image intrinsic decomposition method provided by the invention is the minimum.

Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.