CN85102834B - Photo-method for abstraction of main component of image - Google Patents

Abstract

The present invention relates to an optical method for extracting a principal component image to realize K-L transformation. A simple optical system is used to measure the mean value and the integral mean value of a multiband remote sensing image to obtain a covariance matrix; a first principal component image capable of concentrating the characteristic of the multiband remote sensing image is obtained on the optical system by using an intensity weighting method or a time weighting method. The present invention replaces a method for extracting the principal component image by an image processing system of a large-scale computer, and the method for extracting the principal component image is convenient to widely use.

Description

Extract the optical means of principal component image

The invention belongs to the optical processing of image.

The multiple sensor of space flight and airborne remote sensing provides information data with the form of multispectral image, and multispectral image is carried out Karhunen-Loeve transformation, and extracting principal component image is effective feature extraction and information compressing method in the image processing.Because this transformation relation is to the secondary statistic of image, therefore extracting principal component image relates to great calculated amount and memory space.Before the present invention made, this work must use the large-scale computer image disposal system just can finish, and for example adopted to overbalance 1,000,000 dollars 101 image processing systems or similar system, thereby had limited being extensive use of of this method.The present invention is at this problem, has proposed the realization Karhunen-Loeve transformation, extracts the easy optical means of principal component image.

The two dimension, the real-time and parallel processing capability that the objective of the invention is to utilize optical means to have, on simple optical system, measure the average of single wave band image and the long-pending average of two wave band images, thereby obtain covariance matrix, realize concentrating first principal component image of multispectral image principal character then with optical system.

If the wave band number is K, every image comprises MN pixel, and the transmitance of the corresponding pixel of each wave band image constitutes a wave band vector X who is made up of K element, X=(x ₁, x ₂... x _k) ^TThe covariance matrix of X vector is

C _x＝E｛（X-M _x）（X-M _x） ^T｝ （1）

M in the formula _xBe mean vector, E is an expected value operator, and T is the matrix transpose symbol, makes e _iAnd λ _i(i=1,2 ..., K) be C _xProper vector and characteristic of correspondence value, and the supposition eigenwert arranges by subtracting preface, proper vector constitutes the Karhunen-Loeve transformation matrix A, by transform

Y=AX （2）

Finish Karhunen-Loeve transformation and produce new wave band vector Y, constitute K new wave band image, i.e. principal component image by MN vectorial Y.The character of Karhunen-Loeve transformation makes the covariance matrix diagonalization of Y vector.Diagonal entry is represented the variance of principal component image, and equals C _xEigenwert.The importance of this character is to have eliminated between each principal component image correlativity, and the pairing principal component image of bigger eigenwert has bigger variance, thereby comprised more information, so extraction principal component image, especially first principal component image just becomes the important process that remote sensing image is handled.

Because (1) formula can be expressed as following matrix form

（3）

σ wherein &lt;math><msup><mi></mi><msub><mi>2</mi></msup><mi>ij</mi></msub></math> =E｛(x _i- $m_{x_i}$ )(x _j- $m_{x_j}$ )｝

=1/MN $\underset{\mathrm{L=1}}{\overset{\mathrm{NN}}{\mathrm{\&Sigma;}}}{x}_{\mathrm{iL}}{\mathrm{·x}}_{\mathrm{jL}}$ -1/MN $\underset{\mathrm{L=1}}{\overset{\mathrm{MN}}{\mathrm{\&Sigma;}}}{x}_{\mathrm{iL}}$ ·1/MN $\underset{\mathrm{L=1}}{\overset{\mathrm{MN}}{\mathrm{\&Sigma;}}}{x}_{\mathrm{jL}}$

Brief note is

σ &lt;math><msup><mi></mi><msub><mi>2</mi></msup><mi>ij</mi></msub></math> ＝T（ij）-T（i）T（j） （4）

Here i, j=1,2 ..., K, expression band number, T(i in the formula) and T(j) average of expression single band image, T(ij) the long-pending average of two wave band images of expression.

Accompanying drawing 1 is to measure the average of image and the optical system synoptic diagram of long-pending average.

Accompanying drawing 2 is the optical system synoptic diagram that extract principal component image with the intensity weighted method.

Accompanying drawing 3 is the optical system synoptic diagram that extract principal component image with the time method of weighting.

In the optical system shown in the accompanying drawing 1, i wave band in K wave band image image and j wave band image are placed on respectively on the input plane O, throw light on uniform beam S, the transmitted light scioptics L of image is focused on the back focal plane, be positioned at the measured value of the photoelectric detector D on the back focal plane, obtain this two single band image average T(i separately after the measured value normalization during with the nothing image) and T(j).Then i wave band and j wave band image are coincided and be placed on the input plane O, the measured value of photoelectric detector D obtains the long-pending average T(ij of these two wave band images after normalization), by long-pending average T(ij) deduct the product T(i of two averages) T(j), obtain matrix element σ

For three wave band images, only need 9 measurements just can determine C _xBy C _xFinding the solution eigenwert and proper vector can be by simply calculating.

The calculating process of the Karhunen-Loeve transformation of formula (2) expression, need carry out computing one by one to MN vectorial X, but on the organic conception that obtains principal component image, its essence is with the various element of proper vector each wave band image weighting sued for peace that first principal component image is the various element e with first proper vector ₁₁, e ₁₂..., e _1KFor former each wave band image weighting of weight and, this process can adopt intensity weighted method or time weight method to realize.The intensity weighted method as shown in Figure 2, when K equals 3.Three wave band image A, B, C are used three element e of three light-beam source intensity and first proper vector respectively ₁₁, e ₁₂, e ₁₃The directional light S that is directly proportional ₁, S ₂, S ₃Illumination, visual A, B, C are respectively through lens L ₁, L ₂, L ₃Imaging overlaps three institute's imaging contrapositions on output plane I, then obtains first principal component image on output plane I; When K greater than 3 the time, corresponding increase image light paths, the intensity of light source of each passage is directly proportional with each element value of first proper vector, the time weight method as shown in Figure 3, when K equals 3, three wave band image A, B, C are sent on the input plane O successively, with parallel beam S illumination, through lens L imaging on output plane I, the time shutter of visual A, B, C respectively with three element e of first proper vector ₁₁, e ₁₂, e ₁₃Be directly proportional, then be positioned at first principal component image under the Film Recording at output plane I place; When K greater than 3 the time, still as stated above each wave band image order is successively sent into plane O, each visual time shutter is directly proportional with each element value of first proper vector respectively.

By the optical means that the present invention proposes, to China somewhere satellite photo MSS4,5,6 tribands image extracts first principal component image, and the optical system shown in the employing accompanying drawing 1 records average and long-pending average is

×10 -2

T(4)7.45

T(5)6.70

T(6)9.36

T(44)0.809

T(45)0.830

T(46)0.755

T(55)1.020

T(56)0.713

T(66)0.979

The covariance matrix C that obtains thus _x, eigenvalue and first proper vector e are respectively

λ ₁＝0.00795 λ ₂＝0.000876 λ ₃＝0.000453

e ₁＝（0.527 0.837 0.148） ^T

Then in the optical system shown in the accompanying drawing 3,4,5,6 three wave band images are sent on the input plane O successively, throw light on parallel beam S, through lens L imaging on output plane I, the time shutter of three images respectively with three elements 0.527,0.837 of first proper vector, 0.148 is directly proportional, be positioned at first principal component image under the Film Recording at output plane I place, this image collection has suffered 86% of original 4,5,6 three wave band picture information total amounts.The professional shows that to the visual interpretation of first principal component image this image collection has suffered the main information of former three wave band images.

The present invention realizes easily, is convenient to be extensive use of, and makes the extraction principal component image that must just can be finished by the large-scale computer image disposal system over, can be realized by simple optical system.

Claims (3)

1, a kind of method of extracting multiband remote sensing image principal component image, it is characterized in that image of the i wave band in K the wave band image and i wave band image are placed on respectively on the input plane of optical system, throw light on uniform beam, the transmitted light scioptics of image are focused on the back focal plane, the measured value normalization of the measured value that is positioned at the photoelectric detector on the back focal plane when not having image, obtain these two wave band images average separately, then i wave band and j wave band image congruencing are placed on the input plane, the measured value of photoelectric detector obtains the long-pending average of these two wave band images after normalization, deduct the product of two averages by long-pending average, obtain covariance matrix unit, the value of i and j from 1 to K, find the solution eigenwert and proper vector by covariance matrix again, various element with first proper vector is a weight, and each wave band image in K the wave band image is adopted synthetic first principal component image of realizing of weighting.

2, in accordance with the method for claim 1, it is characterized in that it is to adopt intensity weighted to realize first principal component image that said weighting is synthesized, when K equals 3, with three wave band images respectively with three the parallel lights that element be directly proportional of three light-beam source intensity with first proper vector, these three images respectively through three lens imagings on output plane, make three institute's imaging contrapositions overlapping, on output plane, obtain first principal component image, when K greater than 3 the time, corresponding increase image light paths, the intensity of light source of each passage are directly proportional with each element value of first proper vector respectively.

3, in accordance with the method for claim 1, it is characterized in that it is to adopt time weight to realize first principal component image that said weighting is synthesized, when K equals 3, three wave band images are sent on the input plane of optical system successively, throw light on parallel beam, through lens imaging on output plane, the time shutter of three images is directly proportional with three elements of first proper vector respectively, be positioned at first principal component image under the Film Recording of output plane, when K greater than 3 the time, corresponding with each wave band image successively the order send into input plane, each visual time shutter is directly proportional with each element value of first proper vector respectively.

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