CN115019189A - Hyperspectral image change detection method based on NSST hidden Markov forest model - Google Patents

Hyperspectral image change detection method based on NSST hidden Markov forest model Download PDF

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CN115019189A
CN115019189A CN202210364346.4A CN202210364346A CN115019189A CN 115019189 A CN115019189 A CN 115019189A CN 202210364346 A CN202210364346 A CN 202210364346A CN 115019189 A CN115019189 A CN 115019189A
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CN115019189B (en
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王相海
穆振华
宋若曦
宋传鸣
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Liaoning Normal University
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Abstract

The invention discloses a hyperspectral image change detection method based on an NSST hidden Markov forest model, wherein the proposed three-dimensional hidden Markov forest model makes full use of the multidirectional correlation of HS images and improves the precision of the model; the accurate description of the space-spectrum information among the HS coefficients is realized by establishing a mixed Gaussian model, the strong correlation among the HS wave bands is fully utilized, the low-frequency sub-band space change information is referred to, the correlation between the high-frequency space sub-bands and the spectrum wave bands is combined, the transfer relation of the multi-time-phase hyperspectral image is further defined, the transfer relation and the correlation of the hidden state among time items are fully considered, the change condition of the ground features can be more accurately judged, and more precise ground surface change information is obtained.

Description

Hyperspectral image change detection method based on NSST hidden Markov forest model
Technical Field
The invention relates to the field of hyperspectral remote sensing image processing, in particular to a hyperspectral image change detection method based on a NSST (Nonsubsampled shear wave Transform, NSST) Hidden Markov Forest model (HMF).
Background
In recent years, with the rapid development of Hyperspectral (HS) remote sensing technology and the continuous improvement of the demand for fine detection of surface changes, change detection technology based on Hyperspectral images is gradually emphasized and urgently needed for practical application. The multi-temporal hyperspectral image statistical model based on statistical modeling realizes the mining of the variation attribute by statistically modeling the pixel amplitude of the hyperspectral image or the difference image amplitude of the hyperspectral image. In the method, how to obtain a proper difference image, how to determine an accurate probability density statistical model and estimate parameters thereof, and how to improve the accuracy of change detection by using the correlation between pixels, the transfer characteristics and the like have yet to be deeply researched.
The traditional remote sensing spectrum image change detection method based on the statistical modeling theory is to determine the amplitude of a difference image by analyzing difference information among multi-temporal remote sensing images and further determine a proper threshold value to determine a change area. For example, the polar coordinate-based change vector analysis algorithm is to fit a difference image change region and a constant region respectively by using gaussian distributions with larger variance and smaller variance in mixed gaussian distributions, and then to determine the change region by applying bayesian theory. Rayleigh-Rice (RR) change detection algorithm theoretically analyzes probability distribution functions of a change region and a non-change region of the multi-temporal multispectral image difference image, RR distribution is adopted to fit the change region and the non-change region, and on the basis, the change detection process is realized by estimating model parameters by using an EM algorithm. At present, remote sensing image change detection methods based on statistical theory mostly aim at multispectral images, and probability density distribution of the multispectral images is used as prior distribution.
The hyperspectral image has more precise spectrum description and higher sparsity, so that statistical characteristics different from those of the multispectral image can be presented generally, meanwhile, strong correlation exists between multi-time-phase hyperspectral image spectrums in time, and researches on pixel distribution characteristics, difference image distribution characteristics and coefficient distribution characteristics under a transform domain are few. The existing method only analyzes the statistical characteristics of the pixel amplitude value generally, ignores the correlation of the generalized neighborhood, and is a very significant problem how to fully mine the correlation characteristics of the hyperspectral image and apply the correlation characteristics to the change detection of the hyperspectral image, so that the detection accuracy is improved and the algorithm efficiency is high.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides a hyperspectral image change detection method based on an NSST hidden Markov forest model.
The technical solution of the invention is as follows: a hyperspectral image change detection method based on an NSST hidden Markov forest model is carried out according to the following steps:
step 1, inputting a hyperspectral image H of T1 and T2 time phases T1 And H T2 The size is M × N × B, where M × N is the spatial size of each band image, and B is the number of bands;
step 2, for H T1 And H T2 Each wave band image
Figure BDA0003586408510000021
And
Figure BDA0003586408510000022
performing non-down sampling shear wave transformation of Q scale with K directional sub-bands in each scale to obtain
Figure BDA0003586408510000023
Of the low frequency sub-band
Figure BDA0003586408510000024
And high frequency sub-bands
Figure BDA0003586408510000025
Of the low frequency sub-band
Figure BDA0003586408510000026
And high frequency sub-bands
Figure BDA00035864085100000218
The k is as{1，2，…，K}；
Step 3, obtaining a low-frequency sub-band change detection graph CD by using a change vector analysis method L
Step 3.1 according to the formula (1), calculating a two-time phase hyperspectral image H T1 And H T2 Difference in total gray level of low frequency information | | Δ X therebetween L ||：
Figure BDA0003586408510000028
The i belongs to {1, 2, 3, …, M }, the j belongs to {1, 2, 3, …, N }, and the delta X belongs to {1, 2, 3, …, M }, the j belongs to {1, 2, 3, …, N }, the value of the delta X belongs to the field of the communication technology L (i, j) represents a two-time phase low frequency subband information gray scale difference value at the coordinate (i, j),
Figure BDA0003586408510000029
and
Figure BDA00035864085100000210
coefficient values representing the low frequency subbands at the band b of the hyperspectral images T1 and T2 at coordinates (i, j), respectively;
step 3.2 according to formula (2), utilize total gray level difference | | Δ X L I and beta L Calculating to obtain a low-frequency sub-band transformation detection graph CD L ：
Figure BDA00035864085100000211
Beta is the same as L Indicating the threshold, CD, determined by Otsu method L (i, j) is a low frequency subband change detection result value located at the coordinate (i, j);
step 4, constructing T1 and T2 time-phase high-frequency direction sub-bands
Figure BDA00035864085100000212
And
Figure BDA00035864085100000213
hidden Markov forest model
Figure BDA00035864085100000214
The device is used for carrying out probability state amplitude modulation on the high-frequency subband coefficient;
step 4.1 according to the definition of formula (3), constructing general time phase T high-frequency direction sub-band
Figure BDA00035864085100000215
Set of hidden markov forest model parameters
Figure BDA00035864085100000216
Figure BDA00035864085100000217
The meaning of the parameters is as follows:
m and n are hidden states, the values of the hidden states are 1 or 0, and the hidden states represent changed states and unchanged states respectively;
Figure BDA0003586408510000031
high-frequency direction subband coefficients which are T time phase, b wave band, Q scale and k direction point (i, j) position;
Figure BDA0003586408510000032
is the root coefficient of sub-band in T time phase, b wave band, Q scale and k direction
Figure BDA0003586408510000033
The state probability of (2);
Figure BDA0003586408510000034
coefficient of T time phase, b-1 wave band, Q scale, k direction sub-band (i, j) position
Figure BDA0003586408510000035
Probability of state of (2), said
Figure BDA0003586408510000036
And divided into space dimensional state probabilities
Figure BDA0003586408510000037
And spectral dimension state probability
Figure BDA0003586408510000038
The above-mentioned
Figure BDA0003586408510000039
Is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure BDA00035864085100000310
Is used to determine the spatial dimension parent coefficient
Figure BDA00035864085100000311
Probability of state of (2), said
Figure BDA00035864085100000312
Is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure BDA00035864085100000313
Spectral wiid of
Figure BDA00035864085100000314
The state probability of (2);
Figure BDA00035864085100000315
is a T-phase space dimensional state transition probability, wherein
Figure BDA00035864085100000316
To represent
Figure BDA00035864085100000317
The parent coefficients of the same (j, j) position in the previous dimension,
Figure BDA00035864085100000318
the expression of (c) is:
Figure BDA00035864085100000319
the meaning is that in the k direction sub-band of the b wave band at the T phase, the parent coefficient
Figure BDA00035864085100000320
Hidden state variable of
Figure BDA00035864085100000321
When the value of (c) is equal to m or n, the child coefficient
Figure BDA00035864085100000322
Hidden state variable of (2)
Figure BDA00035864085100000323
A conditional probability equal to m or n;
Figure BDA00035864085100000324
is the spectral dimension state transition probability;
Figure BDA00035864085100000325
and
Figure BDA00035864085100000326
sub-bands in T time phase, b wave band, Q scale and k direction
Figure BDA00035864085100000327
The node space dimension is hidden state
Figure BDA00035864085100000328
Variance and mean of time;
step 4.2, estimating the space dimension parameters in the formula (3) through the EM algorithm of the hidden Markov tree model, and continuously iterating and updating the parameters in the EM model to obtain a local optimal solution to obtain the space dimension parameters
Figure BDA00035864085100000329
Step 4.3 hiding the spectral dimension according to formula (4)
Figure BDA00035864085100000330
And classifying the high-frequency direction subband coefficients:
Figure BDA00035864085100000331
the sigma T，b，Q，k Is the T time phase, b wave band, Q scale, k direction sub-band coefficient standard deviation, T T，b，Q，k Is a given threshold value for the value of the threshold,
Figure BDA00035864085100000332
represents T time phase, b wave band, Q scale and k direction coefficient
Figure BDA00035864085100000333
Hidden states of spectral dimension change and unchanged;
step 4.4 according to the formula (5) and the formula (6), calculating the parent coefficient in the spectrum dimension
Figure BDA00035864085100000423
State probability of
Figure BDA0003586408510000041
Coefficient of sum
Figure BDA0003586408510000042
State transition probability parameter of
Figure BDA0003586408510000043
Figure BDA0003586408510000044
Figure BDA0003586408510000045
The parameters have the following meanings:
y x y is the size of the neighborhood;
Figure BDA0003586408510000046
representing the paternal coefficient
Figure BDA0003586408510000047
The hidden state variable of (a) is,
Figure BDA0003586408510000048
representing child coefficients
Figure BDA0003586408510000049
Hidden state variables of (2);
Figure BDA00035864085100000410
is shown in
Figure BDA00035864085100000411
A set of positions corresponding to state values m within a neighborhood y x y centered at the position,
Figure BDA00035864085100000412
the number of coefficients in the neighborhood of 1;
Figure BDA00035864085100000413
and
Figure BDA00035864085100000414
respectively represent T time phase, b-1 wave band, Q scale and k direction father coefficient
Figure BDA00035864085100000415
A spectral dimension state probability of m and n;
Figure BDA00035864085100000416
shows hidden state variables in T-phase, b-wave band and Q-scale k-direction sub-bands
Figure BDA00035864085100000417
When the value of (b) is equal to m or n, the hidden state variable
Figure BDA00035864085100000418
A conditional probability equal to m or n;
step 4.5 according to the definitions of the formulas (7), (8) and (9), calculating the probability of the state of spatial dimension and spectral dimension change and unchanged
Figure BDA00035864085100000419
And
Figure BDA00035864085100000420
Figure BDA00035864085100000421
Figure BDA00035864085100000422
Figure BDA0003586408510000051
the parameters have the following meanings:
Figure BDA0003586408510000052
is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure BDA0003586408510000053
The state probability of the space dimension of (1) is m or n;
Figure BDA0003586408510000054
is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure BDA0003586408510000055
The state probability of the spectral dimension of (1) is m or n;
ξ T a correlation metric coefficient of a b wave band and a b-1 wave band representing a T phase;
Figure BDA0003586408510000056
and
Figure BDA0003586408510000057
pixel points at the positions of the hyperspectral images b and b-1 wave bands (i, j) respectively,
Figure BDA0003586408510000058
and
Figure BDA0003586408510000059
are respectively as
Figure BDA00035864085100000510
And
Figure BDA00035864085100000511
mean value of (1), namely
Figure BDA00035864085100000512
Step 4.6, according to the construction process of the universal time phase T high-frequency direction sub-band hidden Markov range model in the steps 4.1-4.5, the T1 and T2 time phase high-frequency direction sub-bands shown in the formulas (10) and (11) can be constructed
Figure BDA00035864085100000513
And
Figure BDA00035864085100000514
hidden Markov(s)Forest model
Figure BDA00035864085100000515
Figure BDA00035864085100000516
Figure BDA00035864085100000517
Step 5, according to the definitions of the formulas (12) and (13), calculating the probability of the changed and unchanged state of the current coefficient based on the time phase T1 and T2 space-spectrum dimensional joint correlation
Figure BDA00035864085100000518
And
Figure BDA00035864085100000519
Figure BDA00035864085100000520
Figure BDA0003586408510000061
the parameters have the following meanings:
Figure BDA0003586408510000062
and
Figure BDA0003586408510000063
respectively T1 time phase, b wave band, Q scale, k direction sub-band coefficient
Figure BDA0003586408510000064
State probabilities of change 1 and no change 0 of the spatial-spectral dimensional joint correlation;
Figure BDA0003586408510000065
and
Figure BDA0003586408510000066
respectively T2 time phase, b wave band, Q scale and k direction sub-band coefficient
Figure BDA0003586408510000067
The state probability of change 1 and no change 0 of the spatial-spectral dimension joint correlation;
ξ T1 and xi T2 Correlation metric coefficients of b-band and b-1 band at the time phases T1 and T2, respectively;
step 6, calculating the time phase coefficient of T1 according to the definitions of the formula (14) and the formula (15)
Figure BDA0003586408510000068
Gaussian probability edge density function value of
Figure BDA0003586408510000069
And coefficient of
Figure BDA00035864085100000610
Expected probability of being a changing state
Figure BDA00035864085100000611
Figure BDA00035864085100000612
Figure BDA00035864085100000613
Step 7, calculating the time phase coefficient of T2 according to the definitions of the formula (16) and the formula (17)
Figure BDA00035864085100000614
Edge density function value of
Figure BDA00035864085100000615
And coefficient of
Figure BDA00035864085100000616
Expected probability of being a changing state
Figure BDA00035864085100000617
Figure BDA00035864085100000618
Figure BDA00035864085100000619
Step 8, calculating the time phase direction templates D of T1 and T2 according to the definitions of the formula (18) and the formula (19) r Probability of region change state coefficient occupying change state coefficient in whole region
Figure BDA0003586408510000071
Figure BDA0003586408510000072
Figure BDA0003586408510000073
The parameters have the following meanings:
D r a 3 × 3 directional template;
Figure BDA0003586408510000074
is the time phase T1 to
Figure BDA0003586408510000075
Coefficient-centered D r The expected probability of the state with the coefficient m equal to 1 in the region, i.e. theThe probability that the m-1 state coefficient occupies the whole direction area is equal to the probability of the 1 state coefficient;
Figure BDA0003586408510000076
is the time phase T2 to
Figure BDA0003586408510000077
Coefficient-centered D r The state expectation probability of the in-region coefficient m being 1, that is, the probability that the in-region m being 1 state coefficient occupies the m being 1 state coefficient in the whole direction region;
step 9. high frequency subband coefficient for T1 and T2 phases according to the definitions of equations (20) and (21)
Figure BDA0003586408510000078
And
Figure BDA0003586408510000079
carrying out probability state amplitude modulation:
Figure BDA00035864085100000710
Figure BDA00035864085100000711
the parameters have the following meanings:
Figure BDA00035864085100000712
representing the coefficient of
Figure BDA00035864085100000713
Passing probability
Figure BDA00035864085100000714
The adjusted sub-band coefficient of the position in the k direction (i, j) of the Q scale of the phase b wave band at T1;
Figure BDA00035864085100000715
represents the coefficient of
Figure BDA00035864085100000716
Passing probability
Figure BDA00035864085100000717
The adjusted sub-band coefficient of the position in the k direction (i, j) of the Q scale of the phase b wave band at T2;
step 10, according to the definitions of the formula (22) and the formula (23), calculating the directional region energy of the T1 and the T2 based on the directional region
Figure BDA00035864085100000718
Figure BDA00035864085100000719
Figure BDA00035864085100000720
The parameters have the following meanings:
Figure BDA00035864085100000721
representation based on orientation template D r The direction region energy of the position coefficient in the k direction (i, j) of the Q scale of the phase b wave band at the internal T1;
Figure BDA0003586408510000081
representation based on orientation template D r The direction region energy of the position coefficient in the k direction (i, j) of the Q scale of the phase b wave band at the internal T2;
(u, v) is a 3X 3-directional template D centered on (i, j) r An inner position coordinate;
step 11, according to the definitions of the formula (22) and the formula (23), calculating the direction region entropy of the T1 and the T2 based on the direction region
Figure BDA0003586408510000082
Figure BDA0003586408510000083
Figure BDA0003586408510000084
The parameters have the following meanings:
Figure BDA0003586408510000085
representation based on orientation template D r The direction regional entropy of the position coefficient in the k direction (i, j) of the Q scale of the phase b wave band at the internal T1;
Figure BDA0003586408510000086
representation based on orientation template D r The direction regional entropy of the position coefficient in the k direction (i, j) of the Q scale of the b wave band at the internal T2 phase;
step 12, according to the definitions of the formula (24) and the formula (25), calculating the directional local correlation of the T1 and the T2 based on the region energy and the region entropy
Figure BDA0003586408510000087
Figure BDA0003586408510000088
Figure BDA0003586408510000089
The parameters have the following meanings:
Figure BDA00035864085100000810
and
Figure BDA00035864085100000811
respectively representing orientation-based templates D r The direction local correlation of the b-waveband Q-scale k direction (i, j) position coefficients of the inner T1 time phase and the T2 time phase based on the region energy and the region entropy;
Figure BDA00035864085100000812
and
Figure BDA00035864085100000813
respectively representing the mean values of the directional energy graphs of the b wave band Q scale k direction of the T1 time phase and the T2 time phase;
Figure BDA00035864085100000814
and
Figure BDA00035864085100000815
respectively representing direction entropy diagram mean values of b wave band Q scale k directions at the time phase T1 and the time phase T2;
step 13, calculating T1 and T2 high frequency direction sub-band change detection maps CD according to the definitions of the formula (26) and the formula (27) H_Q，k，T1 、CD H_Q，k，T2 ；
Figure BDA0003586408510000091
Figure BDA0003586408510000092
The parameters have the following meanings:
CD H_Q，k，T1 (i, j) and CD H_Q，k，T2 (i, j) respectively representing the detection coefficients of the high-frequency sub-bands in the Q scale k direction of the b wave band at the time phase of T1 and the high-frequency sub-bands at the time phase of T2 at the coordinates (i, j);
β H_Q，k，T1 and beta H_Q，k，T2 Respectively representing the high-frequency sub-bands in the Q scale k direction of the b wave band at the time phase of T1 and the time phase of T2 determined based on Otsu's methodA threshold value;
step 14, calculating the final high-frequency subband variation detection merging graph CD according to the definition of the formula (28) H ：
CD H (i，j)＝CD H_Q，k，T1 (i，j)+CD H_Q，k，T2 (i，j) (28)
The CD H (i, j) represents the coefficient at (i, j) in the two-time-phase high-frequency subband variation detection combined graph;
step 15, according to the definition of the formula (29), detecting the graph CD by using the low-frequency sub-band transform of the formula (2) L And (28) the high-frequency subband transform detection combined graph CD H Obtaining a final change detection map CD F ：
Figure BDA0003586408510000093
The CD F (i, j) represents the final change detection graph CD F The element at (i, j) in (a) has a value of 1 indicating that a change has occurred, and a value of 0 indicating that no change has occurred.
Compared with the prior art, the invention has the following advantages: firstly, compared with an image processing method of a hidden Markov tree model based on multi-scale transformation, the hidden Markov tree model can simultaneously describe the edge statistical characteristics and the joint statistical characteristics of a multi-scale geometric analysis sub-band, and can only describe the transmission relationship of a two-dimensional image through a tree structure, but the three-dimensional hidden Markov forest model provided by the invention fully utilizes the multi-direction correlation of HS images, and improves the precision of the model; secondly, compared with other traditional change detection methods, the NSST-HMF method provided by the invention realizes accurate description of space-spectrum information among HS coefficients by establishing a mixed Gaussian model, makes full use of strong correlation among HS wave bands, not only refers to low-frequency subband space change information, but also combines the correlation between high-frequency space subbands and spectrum wave bands, further defines the transfer relation of multi-time-phase hyperspectral images, fully considers the transfer relation and correlation of a hidden state among time items, can more accurately distinguish ground feature change conditions, and obtains more precise ground surface change information.
Drawings
FIG. 1 is a schematic diagram of an overall detection process according to an embodiment of the present invention.
FIG. 2 is a graph comparing the results of the Wetland Agricultural Area change test according to the present invention and the prior art.
Detailed Description
The invention discloses a hyperspectral image change detection method based on an NSST hidden Markov forest model, which is shown in figure 1 and is carried out according to the following steps:
step 1, inputting a hyperspectral image H of T1 and T2 two time phases T1 And H T2 The size is M × N × B, where M × N is the spatial size of each band image, and B is the number of bands;
step 2, for H T1 And H T2 Each wave band image
Figure BDA0003586408510000101
And
Figure BDA0003586408510000102
performing non-subsampled shear wave transform (NSST) of Q scale with K directional sub-bands per scale to obtain
Figure BDA0003586408510000103
Of the low frequency sub-band
Figure BDA0003586408510000104
And high frequency sub-bands
Figure BDA0003586408510000105
Of the low frequency sub-band
Figure BDA0003586408510000106
And high frequency sub-bands
Figure BDA0003586408510000107
The K belongs to {1, 2, …, K };
step 3, obtaining a low-frequency sub-band change detection graph CD by using a change vector analysis method L
Step 3.1 according to the formula (1), calculating a two-time phase hyperspectral image H T1 And H T2 Difference in total gray level of low frequency information | | Δ X therebetween L ||：
Figure BDA0003586408510000108
The i belongs to {1, 2, 3, …, M }, the j belongs to {1, 2, 3, …, N }, and the delta X belongs to {1, 2, 3, …, M }, the j belongs to {1, 2, 3, …, N }, the value of the delta X belongs to the field of the communication technology L (i, j) represents a two-time phase low frequency subband information gray scale difference value at the coordinate (i, j),
Figure BDA0003586408510000109
and
Figure BDA00035864085100001010
coefficient values representing the low frequency subbands at the band b of the hyperspectral images T1 and T2 at coordinates (i, j), respectively;
step 3.2 according to formula (2), utilize total gray level difference | | Δ X L | | and β L Calculating to obtain a low-frequency sub-band transformation detection graph CD L ：
Figure BDA00035864085100001011
Beta is the same as L Indicating the threshold, CD, determined by Otsu method L (i, j) is a low frequency subband change detection result value located at the coordinate (i, j);
step 4, constructing T1 and T2 time-phase high-frequency direction sub-bands
Figure BDA00035864085100001012
And
Figure BDA00035864085100001013
hidden Markov forest model
Figure BDA0003586408510000111
For performing probability state amplitude on high-frequency subband coefficientsValue modulation;
step 4.1 according to the definition of formula (3), constructing general time phase T high-frequency direction sub-band
Figure BDA0003586408510000112
Set of hidden markov forest model (HMF) parameters
Figure BDA0003586408510000113
Figure BDA0003586408510000114
The meaning of the parameters is as follows:
m and n are hidden states, the values of the m and n are 1 or 0, and the m and n respectively represent changed states and unchanged states;
Figure BDA0003586408510000115
high-frequency direction subband coefficients which are T time phase, b wave band, Q scale and k direction point (i, j) position;
Figure BDA0003586408510000116
is the root coefficient of sub-band in T time phase, b wave band, Q scale and k direction
Figure BDA0003586408510000117
The state probability of (2);
Figure BDA0003586408510000118
coefficient of T time phase, b-1 wave band, Q scale, k direction sub-band (i, j) position
Figure BDA0003586408510000119
Probability of state of (2), said
Figure BDA00035864085100001110
And is divided into spatial dimension state probability
Figure BDA00035864085100001111
And spectral dimensional state probability
Figure BDA00035864085100001112
The above-mentioned
Figure BDA00035864085100001113
Is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure BDA00035864085100001114
Is used to determine the spatial dimension parent coefficient
Figure BDA00035864085100001115
Probability of state of (2), said
Figure BDA00035864085100001116
Is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure BDA00035864085100001117
Spectral wiid of
Figure BDA00035864085100001118
The state probability of (2);
Figure BDA00035864085100001119
is a T-phase space dimension state transition probability, wherein
Figure BDA00035864085100001120
To represent
Figure BDA00035864085100001121
The parent coefficients of the same (i, j) position in the previous dimension,
Figure BDA00035864085100001122
the expression of (a) is:
Figure BDA00035864085100001123
the meaning is that in the k direction sub-band of the b wave band at the T phase, the parent coefficient
Figure BDA00035864085100001124
Hidden state variable of (2)
Figure BDA00035864085100001125
When the value of (d) is equal to m or n, the child coefficient
Figure BDA00035864085100001126
Hidden state variable of
Figure BDA00035864085100001127
A conditional probability equal to m or n;
Figure BDA00035864085100001128
is the spectral dimension state transition probability;
Figure BDA00035864085100001129
and
Figure BDA00035864085100001130
sub-bands in T time phase, b wave band, Q scale and k direction
Figure BDA00035864085100001131
The node space dimension is hidden state
Figure BDA00035864085100001132
Variance and mean of time;
step 4.2, estimating the space dimension parameters in the formula (3) through an EM algorithm of a hidden Markov tree model (HMF), and continuously iteratively updating the parameters in the EM model to obtain a local optimal solution and obtain the space dimension parameters
Figure BDA00035864085100001133
Step 4.3 hiding the spectral dimension state according to formula (4)
Figure BDA00035864085100001134
And classifying the high-frequency direction subband coefficients:
Figure BDA0003586408510000121
the sigma T，b，Q，k Is the T time phase, b wave band, Q scale, k direction sub-band coefficient standard deviation, T T，b，Q，k Is a given threshold value for the value of the threshold,
Figure BDA0003586408510000122
represents T time phase, b wave band, Q scale and k direction coefficient
Figure BDA0003586408510000123
A hidden state of spectral dimension change and no change;
step 4.4 according to the formula (5) and the formula (6), calculating the parent coefficient in the spectrum dimension
Figure BDA0003586408510000124
State probability of
Figure BDA0003586408510000125
Coefficient of sum
Figure BDA0003586408510000126
State transition probability parameter of
Figure BDA0003586408510000127
Figure BDA0003586408510000128
Figure BDA0003586408510000129
The parameters have the following meanings:
y x y is the size of the neighborhood;
Figure BDA00035864085100001210
representing the paternal coefficient
Figure BDA00035864085100001211
The hidden state variable of (a) is,
Figure BDA00035864085100001212
representing child coefficients
Figure BDA00035864085100001213
A hidden state variable of (a);
Figure BDA00035864085100001214
is shown in
Figure BDA00035864085100001215
A set of positions corresponding to state values m within a neighborhood y x y centered at the position,
Figure BDA00035864085100001216
the number of coefficients in the neighborhood of 1;
Figure BDA00035864085100001217
and
Figure BDA00035864085100001218
respectively represent T time phase, b-1 wave band, Q scale and k direction father coefficient
Figure BDA00035864085100001219
Spectral dimension state probabilities of m and n;
Figure BDA00035864085100001220
expressed in the T time phase, b wave band and Q scale k powerInto subbands, hidden state variables
Figure BDA00035864085100001221
When the value of (d) is equal to m or n, the hidden state variable
Figure BDA00035864085100001222
A conditional probability equal to m or n;
step 4.5 according to the definitions of the formulas (7), (8) and (9), calculating the probability of the state of spatial dimension and spectral dimension change and unchanged
Figure BDA00035864085100001223
And
Figure BDA00035864085100001224
(Note: these two state probabilities are collectively referred to as state probabilities in the HMF parameter set model
Figure BDA00035864085100001225
)：
Figure BDA0003586408510000131
Figure BDA0003586408510000132
Figure BDA0003586408510000133
The parameters have the following meanings:
Figure BDA0003586408510000134
is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure BDA0003586408510000135
The state probability of the space dimension of (1) is m or n;
Figure BDA0003586408510000136
is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure BDA0003586408510000137
The state probability of the spectral dimension of (1) is m or n;
ξ T a correlation metric coefficient of a b wave band and a b-1 wave band representing a T phase;
Figure BDA0003586408510000138
and
Figure BDA0003586408510000139
pixel points at the positions of the hyperspectral images b and b-1 wave bands (i, j) respectively,
Figure BDA00035864085100001310
and
Figure BDA00035864085100001311
are respectively as
Figure BDA00035864085100001312
And
Figure BDA00035864085100001313
mean value of (i) i.e. having
Figure BDA00035864085100001314
Step 4.6, according to the construction process of the hidden Markov process model of the universal time phase T high-frequency direction sub-band in the steps 4.1-4.5, the T1 and T2 time phase high-frequency direction sub-bands shown in the formulas (10) and (11) can be constructed
Figure BDA00035864085100001315
And
Figure BDA00035864085100001316
hidden Markov forest model
Figure BDA00035864085100001317
Figure BDA00035864085100001318
Figure BDA00035864085100001319
Step 5, according to the definitions of the formulas (12) and (13), calculating the probability of the changed and unchanged state of the current coefficient based on the time phase T1 and T2 space-spectrum dimensional joint correlation
Figure BDA00035864085100001320
And
Figure BDA0003586408510000141
Figure BDA0003586408510000142
Figure BDA0003586408510000143
the parameters have the following meanings:
Figure BDA0003586408510000144
and
Figure BDA0003586408510000145
respectively T1 time phase, b wave band, Q scale and k direction sub-band coefficient
Figure BDA0003586408510000146
Of joint correlations in the space-spectral dimensionState probability of 1 change, 0 no change;
Figure BDA0003586408510000147
and
Figure BDA0003586408510000148
respectively T2 time phase, b wave band, Q scale, k direction sub-band coefficient
Figure BDA0003586408510000149
The state probability of change 1 and no change 0 of the spatial-spectral dimension joint correlation;
ξ T1 and xi T2 Correlation metric coefficients of b-band and b-1 band at T1 and T2 phases, respectively (see equation (8));
step 6, calculating the time phase coefficient of T1 according to the definitions of the formula (14) and the formula (15)
Figure BDA00035864085100001410
Gaussian probability edge density function value of
Figure BDA00035864085100001411
And coefficient of
Figure BDA00035864085100001412
Expected probability of being a changing state
Figure BDA00035864085100001413
Figure BDA00035864085100001414
Figure BDA00035864085100001415
Step 7, calculating the time phase coefficient of T2 according to the definitions of the formula (16) and the formula (17)
Figure BDA00035864085100001416
Edge density function value of
Figure BDA00035864085100001417
And coefficient of
Figure BDA00035864085100001418
Expected probability of being a changing state
Figure BDA00035864085100001419
Figure BDA0003586408510000151
Figure BDA0003586408510000152
Step 8, calculating the time phase direction templates D of T1 and T2 according to the definitions of the formula (18) and the formula (19) r Probability of region change state coefficient occupying change state coefficient in whole region
Figure BDA0003586408510000153
Figure BDA0003586408510000154
Figure BDA0003586408510000155
The parameters have the following meanings:
D r representing a 3 × 3 directional template in size;
Figure BDA0003586408510000156
is the time phase T1 to
Figure BDA0003586408510000157
Coefficient-centered D r The state expectation probability of the coefficient m ═ 1 in the region, that is, the probability that the state coefficient m ═ 1 in the region occupies the state coefficient m ═ 1 in the whole direction region;
Figure BDA0003586408510000158
is the time phase T2 to
Figure BDA0003586408510000159
Coefficient-centered D r The state expectation probability of the in-region coefficient m being 1, that is, the probability that the in-region m being 1 state coefficient occupies the m being 1 state coefficient in the whole direction region;
step 9. high frequency subband coefficient for T1 and T2 phases according to the definitions of equations (20) and (21)
Figure BDA00035864085100001510
And
Figure BDA00035864085100001511
carrying out probability state amplitude modulation:
Figure BDA00035864085100001512
Figure BDA00035864085100001513
the parameters have the following meanings:
Figure BDA00035864085100001514
represents the coefficient of
Figure BDA00035864085100001515
Passing probability
Figure BDA00035864085100001516
The adjusted T1 phase b band Q-dimension k-direction (i,j) subband coefficients of a position;
Figure BDA00035864085100001517
representing the coefficient of
Figure BDA00035864085100001518
Passing probability
Figure BDA00035864085100001519
The adjusted sub-band coefficient of the position in the k direction (i, j) of the Q scale of the phase b wave band at T2;
step 10, according to the definitions of the formula (22) and the formula (23), calculating the directional region energy of the T1 and the T2 based on the directional region
Figure BDA0003586408510000161
Figure BDA0003586408510000162
Figure BDA0003586408510000163
The parameters have the following meanings:
Figure BDA0003586408510000164
representation based on orientation template D r The direction region energy of the position coefficient in the k direction (i, j) of the Q scale of the phase b wave band at the internal T1;
Figure BDA0003586408510000165
representation based on orientation template D r The direction region energy of the position coefficient in the k direction (i, j) of the Q scale of the phase b wave band at the internal T2;
(u, v) is a 3X 3-directional template D centered on (i, j) r An inner position coordinate;
step 11. according to the formula (22) and the formula (23)Defining, calculating orientation region entropy for T1 and T2 based on orientation regions
Figure BDA0003586408510000166
Figure BDA0003586408510000167
Figure BDA0003586408510000168
The parameters have the following meanings:
Figure BDA0003586408510000169
representation based on orientation template D r The direction regional entropy of the position coefficient in the k direction (i, j) of the Q scale of the phase b wave band at the internal T1;
Figure BDA00035864085100001610
representation based on orientation template D r The direction regional entropy of the position coefficient in the k direction (i, j) of the Q scale of the b wave band at the internal T2 phase;
step 12, according to the definitions of the formula (24) and the formula (25), calculating the directional local correlation of the T1 and the T2 based on the region energy and the region entropy
Figure BDA00035864085100001611
Figure BDA00035864085100001612
Figure BDA00035864085100001613
The parameters have the following meanings:
Figure BDA0003586408510000171
and
Figure BDA0003586408510000172
respectively representing orientation-based templates D r The direction local correlation of the b-waveband Q-scale k direction (i, j) position coefficients of the inner T1 time phase and the T2 time phase based on the region energy and the region entropy;
Figure BDA0003586408510000173
and
Figure BDA0003586408510000174
respectively representing the mean values of the directional energy maps in the Q-scale k direction of the b wave band of the T1 time phase and the T2 time phase;
Figure BDA0003586408510000175
and
Figure BDA0003586408510000176
respectively representing direction entropy diagram mean values of b wave band Q scale k directions at the time phase T1 and the time phase T2;
step 13, calculating T1 and T2 high frequency direction sub-band change detection maps CD according to the definitions of the formula (26) and the formula (27) H_Q，k，T1 、CD H_Q，k，T2 ；
Figure BDA0003586408510000177
Figure BDA0003586408510000178
The parameters have the following meanings:
CD H_Q，k，T1 (i, j) and CD H_Q，k，T2 (i, j) respectively representing the detection coefficients of the high-frequency sub-bands in the Q scale k direction of the b wave band at the time phase of T1 and the high-frequency sub-bands at the time phase of T2 at the coordinates (i, j);
β H_Q，k，T1 and beta H_Q，k，T2 Respectively representing the thresholds determined by Otsu method based on the high-frequency sub-band in the b wave band Q scale k direction of the T1 time phase and the T2 time phase;
step 14, calculating the final high-frequency subband variation detection merging graph CD according to the definition of the formula (28) H ：
CD H (i，j)＝CD H_Q，k，T1 (i，j)+CD H_Q，k，T2 (i，j) (28)
The CD H (i, j) represents the coefficient at (i, j) in the two-time phase high frequency subband change detection combination graph;
step 15, according to the definition of formula (29), detecting the graph CD by using the low frequency subband transform of formula (2) L And (28) the high-frequency subband transform detection combined graph CD H Obtaining a final change detection map CD F ：
Figure BDA0003586408510000179
The CD F (i, j) represents the final change detection graph CD F The element in (i, j) in (a) has a value of 1 indicating that the element is changed, and a value of 0 indicating that the element is not changed.
FIG. 2 shows a comparison of the results of the Wetland Agricultural Area change test in the present embodiment with those in the prior art, and NSST-HMF is an embodiment of the present invention.
The objective evaluation index pair table is shown below for the Wetland Agricultural Area change test.
Methods OA_CHG OA_UN OA Kappa
MAD 0.864 0.076 0.618 -0.071
ED 0.611 0.867 0.787 0.492
CVA 0.617 0.868 0.790 0.499
PCDA 0.788 0.796 0.793 0.548
NSST-HMF 0.828 0.938 0.879 0.759
From the above comparison, it can be seen that the overall performance index of the inventive example (NSST-HMF) is superior to that of the prior art.

Claims (1)

1. A hyperspectral image change detection method based on an NSST hidden Markov forest model is characterized by comprising the following steps:
step 1, inputting a hyperspectral image H of T1 and T2 two time phases T1 And H T2 The size is M × N × B, where M × N is the spatial size of each band image, and B is the number of bands;
step 2, for H T1 And H T2 Each wave band image of
Figure FDA0003586408500000011
And
Figure FDA0003586408500000012
b belongs to {1, 2, …, B }, and non-down sampling shear wave transformation of Q scale with K direction sub-bands in each scale is obtained
Figure FDA0003586408500000013
Of the low frequency sub-band
Figure FDA0003586408500000014
And high frequency sub-bands
Figure FDA0003586408500000015
Of the low frequency sub-band
Figure FDA0003586408500000016
And high frequency sub-bands
Figure FDA0003586408500000017
The K belongs to {1, 2, …, K };
step 3, obtaining a low-frequency subband change detection graph CD by using a change vector analysis method L
Step 3.1 according to the formula (1), calculating a two-time phase hyperspectral image H T1 And H T2 Difference in total gray level of low frequency information | | Δ X therebetween L ||：
Figure FDA0003586408500000018
The i belongs to {1, 2, 3, …, M }, i belongs to {1, 2, 3, …, N }, and delta X belongs to L (i, j) represents a two-time phase low frequency subband information gray scale difference value at the coordinate (i, j),
Figure FDA0003586408500000019
and
Figure FDA00035864085000000110
coefficient values representing the low frequency subbands at the band b of the hyperspectral images T1 and T2 at coordinates (i, j), respectively;
step 3.2 according to formula (2), utilize total gray level difference | | Δ X L I and beta L Calculating to obtain a low-frequency sub-band transformation detection graph CD L ：
Figure FDA00035864085000000111
Beta is the same as L Indicating the threshold, CD, determined by Otsu method L (i, j) is the low frequency subband variation detection result value located at coordinate (i, j);
step 4, constructing T1 and T2 time-phase high-frequency direction sub-bands
Figure FDA00035864085000000112
And
Figure FDA00035864085000000113
hidden Markov forest model of K e {1, 2, …, K }
Figure FDA00035864085000000114
The device is used for carrying out probability state amplitude modulation on the high-frequency subband coefficient;
step 4.1 according to the definition of formula (3), constructing general time phase T high-frequency direction sub-band
Figure FDA00035864085000000115
Set of hidden markov forest model parameters
Figure FDA00035864085000000116
Figure FDA00035864085000000117
The meaning of the parameters is as follows:
m and n are hidden states, the values of the m and n are 1 or 0, and the m and n respectively represent changed states and unchanged states;
Figure FDA0003586408500000021
high-frequency direction subband coefficients which are T time phase, b wave band, Q scale and k direction point (i, j) position;
Figure FDA0003586408500000022
is the sub-band root coefficient of T time phase, b wave band, Q scale and k direction
Figure FDA0003586408500000023
State probability of (2);
Figure FDA0003586408500000024
coefficient of T time phase, b-1 wave band, Q scale, k direction sub-band (i, j) position
Figure FDA0003586408500000025
State probability of (2), said
Figure FDA0003586408500000026
And divided into space dimensional state probabilities
Figure FDA0003586408500000027
And spectral dimension state probability
Figure FDA0003586408500000028
The above-mentioned
Figure FDA0003586408500000029
Is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure FDA00035864085000000210
Is used to determine the spatial dimension parent coefficient
Figure FDA00035864085000000211
Probability of state of (2), said
Figure FDA00035864085000000212
Is the sub-band coefficient of T time phase, b wave band, Q scale and k direction
Figure FDA00035864085000000213
Spectral wiid of
Figure FDA00035864085000000214
The state probability of (2);
Figure FDA00035864085000000215
is a T-phase space dimensional state transition probability, wherein
Figure FDA00035864085000000216
To represent
Figure FDA00035864085000000217
The parent coefficients of the same (i, j) position in the previous dimension,
Figure FDA00035864085000000218
the expression of (c) is:
Figure FDA00035864085000000219
the meaning is that in the b wave band k direction sub-band in T time phase, the father coefficient
Figure FDA00035864085000000220
Hidden state variable of
Figure FDA00035864085000000221
When the value of (d) is equal to m or n, the child coefficient
Figure FDA00035864085000000222
Hidden state variable of
Figure FDA00035864085000000223
A conditional probability equal to m or n;
Figure FDA00035864085000000224
is the spectral dimension state transition probability;
Figure FDA00035864085000000225
and
Figure FDA00035864085000000226
respectively a T time phase, a b wave band, a Q scale and a k direction sub-band
Figure FDA00035864085000000227
The node space dimension is hidden state
Figure FDA00035864085000000228
Variance and mean of time;
step 4.2 estimating the space dimension parameter in the formula (3) by the EM algorithm of the hidden Markov tree model, and continuously iteratingThe parameters in the EM model are updated to obtain the local optimal solution and the space dimension parameters
Figure FDA00035864085000000229
Step 4.3 hiding the spectral dimension according to formula (4)
Figure FDA00035864085000000230
And (3) classifying the high-frequency direction subband coefficients:
Figure FDA00035864085000000231
the sigma T，b，Q，k Is the T time phase, b wave band, Q scale, k direction sub-band coefficient standard deviation, T T，b，Q，k Is a given threshold value for the value of the threshold,
Figure FDA00035864085000000232
represents T time phase, b wave band, Q scale and k direction coefficient
Figure FDA00035864085000000233
Hidden states of spectral dimension change and unchanged;
step 4.4 according to the formula (5) and the formula (6), calculating the parent coefficient in the spectrum dimension
Figure FDA0003586408500000031
State probability of
Figure FDA0003586408500000032
Sum coefficient
Figure FDA0003586408500000033
State transition probability parameter of
Figure FDA0003586408500000034
Figure FDA0003586408500000035
Figure FDA0003586408500000036
The parameters have the following meanings:
y x y is the size of the neighborhood;
Figure FDA0003586408500000037
representing the paternal coefficient
Figure FDA0003586408500000038
The hidden state variable of (a) is,
Figure FDA0003586408500000039
representing child coefficients
Figure FDA00035864085000000310
Hidden state variables of (2);
Figure FDA00035864085000000311
is shown in
Figure FDA00035864085000000312
A set of positions corresponding to state values m within a neighborhood y x y centered at the position,
Figure FDA00035864085000000313
the number of coefficients in the neighborhood of 1;
Figure FDA00035864085000000314
and
Figure FDA00035864085000000315
respectively represent T time phase, b-1 wave band, Q scale and k direction father coefficient
Figure FDA00035864085000000316
Spectral dimension state probabilities of m and n;
Figure FDA00035864085000000317
shows hidden state variables in T-phase, b-wave band and Q-scale k-direction sub-bands
Figure FDA00035864085000000318
When the value of (d) is equal to m or n, the hidden state variable
Figure FDA00035864085000000319
A conditional probability equal to m or n;
step 4.5 according to the definitions of the formulas (7), (8) and (9), calculating the probability of the state of space dimension and spectrum dimension change and no change
Figure FDA00035864085000000320
And
Figure FDA00035864085000000321
Figure FDA00035864085000000322
Figure FDA00035864085000000323
Figure FDA00035864085000000324
the parameters have the following meanings:
Figure FDA0003586408500000041
is T time phase, b wave band, Q scale, k direction sub-band coefficient
Figure FDA0003586408500000042
The state probability of the space dimension of (1) is m or n;
Figure FDA0003586408500000043
is T time phase, b wave band, Q scale, k direction sub-band coefficient
Figure FDA0003586408500000044
The state probability of the spectral dimension of (1) is m or n;
ξ T a correlation metric coefficient of a b wave band and a b-1 wave band representing a T phase;
Figure FDA0003586408500000045
and
Figure FDA0003586408500000046
respectively the pixel points at the positions of the hyperspectral images b and b-1 wave bands (i, j),
Figure FDA0003586408500000047
and
Figure FDA0003586408500000048
are respectively as
Figure FDA0003586408500000049
And
Figure FDA00035864085000000410
mean value of (i) i.e. having
Figure FDA00035864085000000411
Step 4.6, according to the construction process of the universal time phase T high-frequency direction sub-band hidden Markov range model in the steps 4.1-4.5, the T1 and T2 time phase high-frequency direction sub-bands shown in the formulas (10) and (11) can be constructed
Figure FDA00035864085000000412
And
Figure FDA00035864085000000413
hidden Markov forest model of K e {1, 2, …, K }
Figure FDA00035864085000000414
Figure FDA00035864085000000415
Figure FDA00035864085000000416
Step 5, according to the definitions of the formulas (12) and (13), calculating the probability of the changed and unchanged state of the current coefficient based on the time phase T1 and T2 space-spectrum dimensional joint correlation
Figure FDA00035864085000000417
And
Figure FDA00035864085000000418
Figure FDA00035864085000000419
Figure FDA00035864085000000420
the parameters have the following meanings:
Figure FDA0003586408500000051
and
Figure FDA0003586408500000052
respectively T1 time phase, b wave band, Q scale and k direction sub-band coefficient
Figure FDA0003586408500000053
State probabilities of change 1 and no change 0 of the spatial-spectral dimensional joint correlation;
Figure FDA0003586408500000054
and
Figure FDA0003586408500000055
respectively T2 time phase, b wave band, Q scale and k direction sub-band coefficient
Figure FDA0003586408500000056
The state probability of change 1 and no change 0 of the spatial-spectral dimension joint correlation;
ξ T1 and xi T2 Correlation metric coefficients of b-band and b-1 band at the time phases T1 and T2, respectively;
step 6, calculating the time phase coefficient of T1 according to the definitions of the formula (14) and the formula (15)
Figure FDA0003586408500000057
Gaussian probability edge density function value of
Figure FDA0003586408500000058
And coefficient of
Figure FDA0003586408500000059
Expected probability of being a changing state
Figure FDA00035864085000000510
Figure FDA00035864085000000511
Figure FDA00035864085000000512
Step 7, calculating the time phase coefficient of T2 according to the definitions of the formula (16) and the formula (17)
Figure FDA00035864085000000513
Edge density function value of
Figure FDA00035864085000000514
And coefficient of
Figure FDA00035864085000000515
Expected probability of being a changing state
Figure FDA00035864085000000516
Figure FDA00035864085000000517
Figure FDA00035864085000000518
Step 8, calculating the time phase direction templates D of T1 and T2 according to the definitions of the formula (18) and the formula (19) r Probability of region change state coefficient occupying change state coefficient in whole region
Figure FDA00035864085000000519
Figure FDA00035864085000000520
Figure FDA0003586408500000061
The parameters have the following meanings:
D r representing a 3 × 3 directional template in size;
Figure FDA0003586408500000062
is the time phase T1 to
Figure FDA0003586408500000063
Coefficient-centered D r The state expectation probability of the in-region coefficient m being 1, that is, the probability that the in-region m being 1 state coefficient occupies the m being 1 state coefficient in the whole direction region;
Figure FDA0003586408500000064
is the time phase T2 to
Figure FDA0003586408500000065
Coefficient-centered D r The state expectation probability of the in-region coefficient m being 1, that is, the probability that the in-region m being 1 state coefficient occupies the m being 1 state coefficient in the whole direction region;
step 9. high frequency subband coefficient for T1 and T2 phases according to the definitions of equations (20) and (21)
Figure FDA0003586408500000066
And
Figure FDA0003586408500000067
carrying out probability state amplitude modulation:
Figure FDA0003586408500000068
Figure FDA0003586408500000069
the parameters have the following meanings:
Figure FDA00035864085000000610
represents the coefficient of
Figure FDA00035864085000000611
Passing probability
Figure FDA00035864085000000612
The adjusted sub-band coefficient of the position in the k direction (i, j) of the Q scale of the phase b wave band at T1;
Figure FDA00035864085000000613
representing the coefficient of
Figure FDA00035864085000000614
Passing probability
Figure FDA00035864085000000615
The adjusted sub-band coefficient of the position in the k direction (i, j) of the Q scale of the phase b wave band at T2;
step 10, according to the definitions of the formula (22) and the formula (23), calculating the directional region energy of the T1 and the T2 based on the directional region
Figure FDA00035864085000000616
Figure FDA00035864085000000617
Figure FDA00035864085000000618
The parameters have the following meanings:
Figure FDA00035864085000000619
representation based on orientation template D r The direction region energy of the position coefficient in the k direction (i, j) of the Q scale of the phase b wave band at the internal T1;
Figure FDA00035864085000000620
representation based on orientation template D r The direction region energy of the position coefficient in the k direction (i, j) of the Q scale of the phase b wave band at the internal T2;
(u, v) is a 3X 3-directional template D centered on (i, j) r An inner position coordinate;
step 11, according to the definitions of the formula (22) and the formula (23), calculating the direction region entropy of the T1 and the T2 based on the direction region
Figure FDA0003586408500000071
Figure FDA0003586408500000072
Figure FDA0003586408500000073
The parameters have the following meanings:
Figure FDA0003586408500000074
representation based on orientation template D r The direction regional entropy of the position coefficient in the k direction (i, j) of the Q scale of the b wave band at the internal T1 phase;
Figure FDA0003586408500000075
representation based on orientation template D r The direction regional entropy of the position coefficient in the k direction (i, j) of the Q scale of the b wave band at the internal T2 phase;
step 12, according to the definitions of the formula (24) and the formula (25), calculating the directional local correlation of the T1 and the T2 based on the region energy and the region entropy
Figure FDA0003586408500000076
Figure FDA0003586408500000077
Figure FDA0003586408500000078
The parameters have the following meanings:
Figure FDA0003586408500000079
and
Figure FDA00035864085000000710
respectively representing orientation-based templates D r The direction local correlation of the b-waveband Q-scale k direction (i, j) position coefficients of the inner T1 time phase and the T2 time phase based on the region energy and the region entropy;
Figure FDA00035864085000000711
and
Figure FDA00035864085000000712
respectively representing the mean values of the directional energy graphs of the b wave band Q scale k direction of the T1 time phase and the T2 time phase;
Figure FDA00035864085000000713
and
Figure FDA00035864085000000714
respectively representing direction entropy diagram mean values of b wave band Q scale k directions at the time phase T1 and the time phase T2;
step 13, calculating T1 and T2 high frequency direction sub-band change detection maps CD according to the definitions of the formula (26) and the formula (27) H_Q，k，T1 、CD H_Q，k，T2 ；
Figure FDA00035864085000000715
Figure FDA0003586408500000081
The parameters have the following meanings:
CD H_Q，k，T1 (i, j) and CD H_Q，k，T2 (i, j) respectively representing the detection coefficients of the high-frequency sub-bands in the Q scale k direction of the b wave band at the time phase of T1 and the high-frequency sub-bands at the time phase of T2 at the coordinates (i, j);
β H_Q，k，T1 and beta H_Q，k，T2 Respectively representing the threshold values of the b wave band Q scale k direction high-frequency sub-band determined by the Otsu method in the T1 time phase and the T2 time phase;
step 14, calculating the final high-frequency subband variation detection merging graph CD according to the definition of the formula (28) H ：
CD H (i，j)＝CD H_Q，k，T1 (i，j)+CD H_Q，k，T2 (i，j) (28)
The CD H (i, j) represents the coefficient at (i, j) in the two-time-phase high-frequency subband variation detection combined graph;
step 15 according to formula (29)By definition, the detection of the graph CD is performed using the low frequency subband transform of equation (2) L And (28) the high-frequency subband transform detection combined graph CD H Obtaining a final change detection map CD F ：
Figure FDA0003586408500000082
The CD F (i, j) represents the final change detection graph CD F The element at (i, j) in (a) has a value of 1 indicating that a change has occurred, and a value of 0 indicating that no change has occurred.
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