CN104766092B - A kind of hyperspectral image classification method of combination potential function - Google Patents

A kind of hyperspectral image classification method of combination potential function Download PDF

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CN104766092B
CN104766092B CN201510136242.8A CN201510136242A CN104766092B CN 104766092 B CN104766092 B CN 104766092B CN 201510136242 A CN201510136242 A CN 201510136242A CN 104766092 B CN104766092 B CN 104766092B
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goal pels
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CN104766092A (en
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郭宝峰
陈春种
陈华杰
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Kaihang Jiace Wuhu Information Technology Co ltd
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Hangzhou Dianzi University
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Abstract

The invention discloses a kind of hyperspectral image classification method of combination potential function.Conventional method often only utilizes spectrum domain information, and less consideration spatial-domain information.The present invention is classified first on the basis of spectrum domain information using traditional SVMs to high spectrum image;Then, point pixel by mistake is removed by extracting the method for connected region;Finally, classification results are optimized with reference to the neighborhood information and the potential function that newly defines of spatial domain.The present invention improves the purpose of classification accuracy;The performance of whole algorithm is further lifted by the concept for introducing potential function, while accuracy rate can be improved while reducing classification results false alarm rate.

Description

A kind of hyperspectral image classification method of combination potential function
Technical field
The invention belongs to areas of information technology, it is related to pattern-recognition, image processing techniques, is specifically related to a kind of combination The hyperspectral image classification method of potential function.
Background technology
Classification hyperspectral imagery is always one of research emphasis of remote sensing image process field.It is same under standard environment The uniqueness of object spectrum curve assumes to be always a Main Basiss in classification hyperspectral imagery.Believed according to this spectrum Cease, traditional sorting technique such as neutral net, SVMs is successively used for the classification of high spectrum image.In fact, high Spectral remote sensing image can tie up two different angles and terrestrial object information is described from space dimension, spectrum.Conventional method is frequent only Using spectrum domain information, and less consideration spatial-domain information.Spatial-domain information is introduced in the Hyperspectral imaging of collection of illustrative plates integration Help can be provided to the raising of classification accuracy.According to this principle, it is proposed that a kind of that classification hyperspectral imagery result is carried out The method of optimization.High spectrum image is classified using traditional SVMs first on the basis of spectrum domain information; Then, point pixel by mistake is removed by extracting the method for connected region;Finally, with reference to the neighborhood information and the gesture that newly defines of spatial domain Function pair classification results are optimized.Institute's extracting method is verified by measured data, as a result shows that the method proposed exists Accuracy rate can be improved while reduction classification results false alarm rate.
The classification hyperspectral imagery result based on SVM SVMs can be optimized according to this principle.
The content of the invention
There is provided a kind of high spectrum image of combination potential function point aiming at the deficiencies in the prior art for the purpose of the present invention Class method.This method compensate for traditional mode sorting technique and the information of space dimension ignored in hyperspectral classification problem not Foot.In order to which the result that classification is tieed up to spectrum is optimized, present invention introduces space dimension information, free space neighborhood information and construction Potential function realize.
The technical solution adopted for the present invention to solve the technical problems specifically includes following steps:
Step 1, the classification of EO-1 hyperion spectral domain;
Normalized is done to high-spectral data first;
Secondly according to priori, in each atural object category regions, 30% training sample composing training is randomly selected Sample set;
Then the training of grader is carried out using training sample set, the grader used is trained for SVMs;
The test of high-spectral data is finally carried out with the grader trained, so as to obtain spectral domain classification results matrix;
Described priori includes previously known all kinds of target locations;
Step 2, to spectral domain classification results matrix extract connected region;
The essence for extracting connected region is exactly that the pixel in the close spectral domain classification results matrix in space is classified as a class, most Leave out the connected region that pixel number is less than 10 afterwards;Comprise the following steps that:
2-1. is begun stepping through from first pixel in spectral domain classification results matrix, finds first aim pixel as first Initial point, and initial point is defined as number of regions n=1;
2-2. judges to whether there is goal pels in initial vertex neighborhood, using template p1With the region centered on initial point Seek common ground;
If 2-2-1. does not occur simultaneously, n, n=n+1 are updated, continues to travel through and finds next target picture without attributed region Member, n is entered as by the number of regions of the goal pels without attributed region;
2-2-2. then illustrates initial vertex neighborhood internal memory in goal pels, by the number of regions of goal pels if occuring simultaneously It is set to n;
2-3. regard the goal pels newly increased as initial point, repeat step 2-2, until having traveled through all pixels;
Described template p1It is specific as follows:
2-4. calculates the pixel number of each connected region, will be deleted less than the connected region of 10 pixels, i.e. assignment 0, it is classified as backdrop pels;
Step 3, with reference to potential function the connected region of extraction is optimized;
The spectrum average of pixel in the connected region of all extractions of 3-1. calculating
Wherein, N is the number of category goal pels, fiFor the curve of spectrum, i is natural number;
3-2. selectes goal pels x to be optimizedI, j, it is desirable to (5 × 5 template) has goal pels in its 24 neighborhood;Using template p1With with goal pels x to be optimizedI, jCentered on region seek common ground;
3-3. judges goal pels number in 24 neighborhoods, and calculates the spectrum average of goal pels in neighborhoodIf 24 is adjacent Goal pels number is more than 14 in domain, then shows that goal pels are to surround goal pels x to be optimized in neighborhoodI, j, satisfaction is determined The condition of the potential function of justice, goes to step 3-4 and calculates potential function;If less than 14, goal pels x to be optimized is calculated respectivelyI, jWith The spectrum average of pixel in connected regionThe spectrum average of goal pels in neighborhoodDistance, if the condition that meets (3) It is classified as target point;
Wherein fI, jIt is pixel x to be optimizedI, jThe curve of spectrum, T1、T2It is two given threshold values, the selection of threshold value is root Depending on specific high-spectral data;Described is less than T1Show goal pels x to be optimizedI, jWith the goal pels phase in neighborhood Seemingly;Less than T2Show goal pels x to be optimizedI, jIt is also integrally similar to such target;
3-4. calculates potential function;For the goal pels x to be optimized surrounded by goal pels in neighborhoodI, j, using template q1、q2The local derviation R in X, Y-direction is calculated respectivelyx、Ry
Described template q1、q2It is specific as follows:
Using template q1With with goal pels x to be optimizedI, jCentered on region seek local derviation Rx
Using template q2With with goal pels x to be optimizedI, jCentered on region seek local derviation Ry
Calculate goal pels x to be optimizedI, jThe direction θ of the gesture optimized:
θ=arctan (Ry/Rx) (6)
It is 8 intervals by 2 π points, each interval size is π/4, according to distributions of the obtained θ on interval graph, treats excellent Change goal pels xI, j24 neighborhoods carry out 8 kinds of directions optimization.
3-5. calls formula (3) to judge whether that this is optimized for goal pels.
The present invention has the beneficial effect that:
The present invention is according to spatial-domain information, it is proposed that a kind of hyperspectral image classification method of combination potential function:Traditional The sorting technique that sky-spectrum is combined is added to spatial-domain information in traditional sorting technique, to improve the accuracy rate of classification;And Method proposed by the present invention is believed after being handled with conventional method SVM (SVMs) classification, then using the neighborhood of spatial domain Breath is optimized to classification results:On the one hand, this continuously distributed sky is spatially typically into according to the pixel of same atural object Between domain information, it is believed that in classification results isolate distribution pixel be under the conditions of maximum probability by mistake branch, so as to be deleted Divided by reduction false alarm rate;On the other hand, according to spatially adjacent, while the high pixel of spectrum similarity is under the conditions of maximum probability It is the neighborhood information of this similar spatial domain, can be by partly unidentified pixel out recognizes into target again in the first stage Pixel, so as to reach the purpose for improving classification accuracy;Finally, the performance of whole algorithm is entered by introducing the concept of potential function The further lifting of row.
Brief description of the drawings
Fig. 1 is gradient distribution map.
Fig. 2 is 2 class templates of different directions.
Fig. 3 is the wave band gray-scale map of data the 11st.
Fig. 4 is flow chart of the present invention.
Fig. 5 is result figure before and after present invention optimization.
Embodiment
The invention will be further described with reference to the accompanying drawings and examples.
Step 1, the classification of EO-1 hyperion spectral domain.
Normalized is done to high-spectral data first;
Secondly according to priori, in each atural object category regions, 30% training sample composing training is randomly selected Sample set;
Then the training of grader is carried out using training sample set, the grader used is trained for SVMs;
The test of high-spectral data is finally carried out with the grader trained, so as to obtain spectral domain classification results matrix.
Step 2, to spectral domain classification results matrix extract connected region.
The essence for extracting connected region is exactly that the pixel in the close spectral domain classification results matrix in space is classified as a class, most Leave out the less connected region of pixel number afterwards;Comprise the following steps that:
2-1. is begun stepping through from first pixel in spectral domain classification results matrix, finds first aim pixel as first Initial point, and initial point is defined as number of regions n=1.
2-2. judges to whether there is goal pels in initial vertex neighborhood, using template p1With the region centered on initial point Seek common ground;
If 2-2-1. does not occur simultaneously, n, n=n+1 are updated, continues to travel through and finds next target picture without attributed region Member, n is entered as by the number of regions of the goal pels without attributed region;
2-2-2. then illustrates initial vertex neighborhood internal memory in goal pels, by the number of regions of goal pels if occuring simultaneously It is set to n;
2-3. regard the goal pels newly increased as initial point, repeat step 2-2, until having traveled through all pixels.
Described template p1It is specific as follows:
2-4. calculates the pixel number of each connected region, will be deleted less than the connected region of 10 pixels, i.e. assignment 0, it is classified as backdrop pels.
Step 3, with reference to potential function the connected region of extraction is optimized.
The spectrum average of pixel in the connected region of all extractions of 3-1. calculating
Wherein, N is the number of category goal pels, fiFor the curve of spectrum, i is natural number;
3-2. selectes goal pels x to be optimizedI, j, it is desirable to (5 × 5 template) has goal pels in its 24 neighborhood;Using template p1With with goal pels x to be optimizedI, jCentered on region seek common ground;
3-3. judges goal pels number in 24 neighborhoods, and calculates the spectrum average of goal pels in neighborhoodIf 24 is adjacent Goal pels number is more than 14 in domain, then shows that goal pels are to surround goal pels x to be optimized in neighborhoodI, j, satisfaction is determined The condition of the potential function of justice, goes to step 3-4 and calculates potential function;If less than 14, goal pels x to be optimized is calculated respectivelyI, jWith The spectrum average of pixel in connected regionThe spectrum average of goal pels in neighborhoodDistance, if meeting condition (3) Then it is classified as target point;
Wherein fI, jIt is pixel x to be optimizedI, jThe curve of spectrum, T1、T2It is two given threshold values, the selection of threshold value is root Depending on specific high-spectral data.Less than T1Show goal pels x to be optimizedI, jIt is similar to the goal pels in neighborhood;It is less than T2Show goal pels x to be optimizedI, jIt is also integrally similar to such target.Finally, goal pels x to be optimizedI, jBoth with sky Between the goal pels spectrum that closes on it is similar and similar with target overall spectrum, thus it is considered that the pixel should be target.
3-4. calculates potential function;For the goal pels x to be optimized surrounded by goal pels in neighborhoodI, j, using template q1、q2The local derviation R in X, Y-direction is calculated respectivelyx、Ry
Described template q1、q2It is specific as follows:
Using template q1With with goal pels x to be optimizedI, jCentered on region seek local derviation Rx
Using template q2With with goal pels x to be optimizedI, jCentered on region seek local derviation Ry
Calculate goal pels x to be optimizedI, jThe direction θ of the gesture optimized:
θ=arctan (Ry/Rx) (6)
If being 8 intervals by 2 π points, each interval size is π/4, as shown in Figure 1.Can be according to obtained θ in interval graph On distribution, the optimization in 8 kinds of directions is carried out to the neighborhood of initial point 24, wherein interval excellent in-π/8~π/8 and π/8~3 π/8 two Shown in change mode such as Fig. 2 (a) (b):
Other 6 directions are this 2 kinds rotations.Judge whether that this is optimized for goal pels finally according to formula (3).
Embodiment
1) overview of the data
International Publication data AVIRIS-92AV3C on internet is derived from for the data set of verification algorithm performance, In June, 1992 Indiana, USA India pine tree forest land is photographed on, the spatial resolution of data is 20m, and spectrum model is provided altogether Enclose 220 wave bands for 0.2~2.4 μm, size is 145x145 pixels, include soybean, clover, no-tillage milpa, small 16 kinds of different classes of objects such as wheat, meadow.11st wave band gray-scale map is as shown in Figure 3.
The inventive method flow chart is as shown in Figure 4.
2) experiment flow
The spectral domain classification of the first step uses SVM, selects to pasture (target 1), hay (target 2), no-tillage soybean (target 3) this 3 class atural object is classified, the backdrop pels of random selection 5%, 30% target 1, target 2, the pixel institute in the region of target 3 The curve of spectrum composition training sample set answered;Combination of two trains 6 graders, wherein, select Gauss radial direction kernel function, parameter C and γ passes through grid data service optimizing (c is that penalty factor, γ are kernel functional parameter);Finally with the grader trained to figure As being classified.Shown in first classification results such as Fig. 5 (a) based on SVMs, what red was represented is the pasture of target 1;Green What is represented is the hay of target 2;What blueness was represented is the no-tillage soybean of target 3.Fig. 5 (b) is shown after the inventive method optimization As a result, threshold value T in experiment1、T2Value be respectively chosen as 2500 and 1500.The target newly increased after optimization is shown in Fig. 5 (c) Pixel.
3) result and analysis
Contrasted before and after the AVIRIS-92AV3C of table 1 optimizations
Two classification targets detection pixel number before and after optimization, the contrast of accuracy rate and false alarm rate is as shown in table 1.Target 1 Classification accuracy brings up to 87.95% from 80.72%, and the classification accuracy of target 2 brings up to 96.3%, target 3 from 84.46% Classification accuracy bring up to 89.36% from 83.01%, the overall accuracy rate of target increases;On the other hand, target 1 False alarm rate is reduced to 0.08% from 0.76%, and the false alarm rate of target 2 is reduced to 0.12% from 0.15%, and the classification of target 3 is accurate Rate is reduced to 0.13% from 0.64%, and the overall false alarm rate of target has obvious reduction.
Experiment shows:On the one hand algorithm proposed by the present invention can eliminate more misclassification picture when extracting connected region Member, remains the correct pixel of target classification;On the other hand, in the case of effectively reduction false alarm rate, algorithm can make accurately Rate has a certain upgrade.

Claims (1)

1. a kind of hyperspectral image classification method of combination potential function, its feature is comprising the following steps:
Step 1, the classification of EO-1 hyperion spectral domain;
Normalized is done to high-spectral data first;
Secondly according to priori, in each atural object category regions, 30% training sample composing training sample is randomly selected Collection;
Then the training of grader is carried out using training sample set, the grader used is trained for SVMs;
The test of high-spectral data is finally carried out with the grader trained, so as to obtain spectral domain classification results matrix;
Described priori includes previously known all kinds of target locations;
Step 2, to spectral domain classification results matrix extract connected region;
The essence for extracting connected region is exactly that the pixel in the close spectral domain classification results matrix in space is classified as a class, is finally deleted Pixel number is gone to be less than 10 connected region;Comprise the following steps that:
2-1. is begun stepping through from first pixel in spectral domain classification results matrix, finds first aim pixel as initial Point, and initial point is defined as number of regions n=1;
2-2. judges to whether there is goal pels in initial vertex neighborhood, using template p1Friendship is asked with the region centered on initial point Collection;
If 2-2-1. does not occur simultaneously, n, n=n+1 are updated, continues to travel through and finds next goal pels without attributed region, will The number of regions for not having the goal pels of attributed region is entered as n;
2-2-2. then illustrates that initial vertex neighborhood internal memory, in goal pels, the number of regions of goal pels is also set to if occuring simultaneously n;
2-3. regard the goal pels newly increased as initial point, repeat step 2-2, until having traveled through all pixels;
Described template p1It is specific as follows:
<mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
2-4. calculates the pixel number of each connected region, will delete, i.e. assignment 0, returns less than the connected region of 10 pixels For backdrop pels;
Step 3, with reference to potential function the connected region of extraction is optimized;
The spectrum average of pixel in the connected region of all extractions of 3-1. calculating
<mrow> <msub> <mover> <mi>F</mi> <mo>~</mo> </mover> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>f</mi> <mi>i</mi> </msub> </mrow> <mi>N</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein, N is the number of category goal pels, fiFor the curve of spectrum, i is natural number;
3-2. selectes goal pels x to be optimizedi,j, it is desirable to having in its 24 neighborhood in goal pels, i.e. 5 × 5 templates has target picture Member,;Using template p1With with goal pels x to be optimizedi,jCentered on region seek common ground;
3-3. judges goal pels number in 24 neighborhoods, and calculates the spectrum average of goal pels in neighborhoodIf mesh in 24 neighborhoods Mark pixel number and be more than 14, then show that goal pels are to surround goal pels x to be optimized in neighborhoodi,j, meet defined gesture The condition of function, goes to step 3-4 and calculates potential function;If less than 14, goal pels x to be optimized is calculated respectivelyi,jWith connected region The spectrum average of pixel in domainThe spectrum average of goal pels in neighborhoodDistance, returned if the condition that meets (3) For target point;
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>F</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>|</mo> <mo>|</mo> <mo>&lt;</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>f</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>F</mi> <mo>~</mo> </mover> <mn>0</mn> </msub> <mo>|</mo> <mo>|</mo> <mo>&lt;</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Wherein fi,jIt is pixel x to be optimizedi,jThe curve of spectrum, T1、T2It is two given threshold values, the selection of threshold value is according to tool Depending on body high-spectral data;Described is less than T1Show goal pels x to be optimizedi,jIt is similar to the goal pels in neighborhood;It is small In T2Show goal pels x to be optimizedi,jIt is also integrally similar to such target;
3-4. calculates potential function;For the goal pels x to be optimized surrounded by goal pels in neighborhoodi,j, using template q1、q2Point The local derviation R in X, Y-direction is not calculatedx、Ry
Described template q1、q2It is specific as follows:
<mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>q</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Using template q1With with goal pels x to be optimizedi,jCentered on region seek local derviation Rx
Using template q2With with goal pels x to be optimizedi,jCentered on region seek local derviation Ry
Calculate goal pels x to be optimizedi,jThe direction θ of the gesture optimized:
θ=arctan (Ry/Rx) (6)
It is 8 intervals by 2 π points, each interval size is π/4, according to distributions of the obtained θ on interval graph, to mesh to be optimized Mark pixel xi,j24 neighborhoods carry out 8 kinds of directions optimization;
3-5. calls formula (3) to judge whether that this is optimized for goal pels.
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