Gabor cube feature selection-based classification method and system for hyperspectral remote sensing images
The present invention provides a Gabor cube feature selection-based classification method for hyperspectral remote sensing images, comprising the following steps: generating three-dimensional Gabor filters according to set frequency and direction parameter values; convoluting hyperspectral remote sensing images with the three-dimensional Gabor filters to obtain three-dimensional Gabor features; selecting three-dimensional Gabor features, classification contribution degrees to various classes of which meet preset requirements, from the three-dimensional Gabor features; and classifying the hyperspectral remote sensing images by a multi-task joint sparse representation-based classification means by using the selected three-dimensional Gabor features. The present invention is based on the three-dimensional Gabor features, and the used three-dimensional Gabor features contain rich local change information of a signal and are competent in feature characterizing. Using a Fisher discriminant criterion not only makes full use of high-level semantics hidden among the features, but also eliminates redundant information and reduces the classification time complexity.
1. A Gabor cube feature selection-based classification method for hyperspectral remote sensing images, the classification method for hyperspectral remote sensing images comprising the following steps:
A, generating a number of three-dimensional Gabor filters according to set frequency and direction parameter values;
B, convoluting hyperspectral remote sensing images with the generated three-dimensional Gabor filters to obtain a number of three-dimensional Gabor features;
C, selecting a number of three-dimensional Gabor features, classification contribution degrees to various classes of which meet preset requirements, from the obtained three-dimensional Gabor features; and
D, classifying the hyperspectral remote sensing images by a multi-task joint sparse representation-based classification means by using the selected three-dimensional Gabor features;
wherein R represents the hyperspectral remote sensing images, 52 three-dimensional Gabor features obtained by the hyperspectral remote sensing images R participating in convolution operation are represented by {M t , t=1, . . . , 52}, wherein M 1 represents a t th three-dimensional Gabor feature;
the step C of selecting three-dimensional Gabor features by utilizing a Fisher discriminant criterion, particularly comprising:
C1, dividing each of the three-dimensional Gabor feature into a training set and a test set;
A t represents a training set of the t th three-dimensional Gabor feature M t , G t represents a test set of t th three-dimensional Gabor feature M t , t ∈ {1, . . . , 52}, and therefore all training sets {A t , t=1, . . . , 52} and test sets {G t , t=1, . . . , 52} of the 52 three-dimensional Gabor features are obtained;
step C2, respectively calculating an intra-class spacing and an inter-class spacing of each three-dimensional Gabor feature by using the training set {A t , t=1, . . . , 52};
γ W (A p t ) represents an intra-class spacing of a p t class in the t th three-dimensional Gabor feature, and γ B (A p t ) represents an inter-class spacing of the p th class in the t h three-dimensional Gabor feature, then:
γ
W
(
A
p
t
)
=
∑
α
=
A
p
t
(
α
i
-
m
p
t
)
T
(
α
i
-
m
p
t
)
γ
B
(
A
p
t
)
=
n
p
(
m
p
t
-
m
t
)
T
(
m
p
t
-
m
t
)
;
wherein A p t represents a training set of the p th class of the training sets A t , A t =[A 1 t , . . . , A p t ], α 1 represents one training sample in A p t : n p represents the number of the samples in the p th class p ∈ {1, . . . , P} represents the number of the classes; m t and m p t respectively represent mean vectors
m
t
=
1
n
∑
α
i
∈
A
t
α
i
and
m
p
t
=
1
n
p
∑
α
i
∈
A
p
t
α
i
of
A
t
and
A
p
t
;
step C3, calculating Fisher scores of the classes in the 52 three-dimensional Gabor features by using the intra-class spacing and the inter-class spacing calculated in the step C2:
the Fisher scores of the classes in the 52 three-dimensional Gabor features are stored by using a matrix F (F∈ 52×P , represents a Fisher score of the p th class in the t th three-dimensional Gabor feature. then:
F
p
T
=
γ
B
(
A
p
t
)
/
γ
W
(
A
p
t
)
;
wherein F∈ 52×P , P represents the number of the classes, F p t represents elements in a t th and a p th column of the matrix F;
step C4, selecting V elements with higher scores from each column of the matrix F, and storing indexes of the selected elements in a preliminary index matrix, removing repeated indexes in the preliminary index matrix to obtain a final index matrix, and determining three-dimensional Gabor features to be selected according to the index matrix;
S represents the preliminary index matrix, I represents the final index matrix, the V elements with higher Fisher scores are selected from each column of the matrix F, and the index of the selected elements are stored in the preliminary index matrix S, S∈ V×P ; the repeated indexes in the preliminary index matrix S are removed to obtain finally-selected indexes, the finally-selected indexes are stored in the index martix I, I ∈ K×1 ; and no repeated indexes exist in the indes matrix I, and eah index points to a specific three-dimensional Gabor feature.
2. The classification method for hyperspectral remote sensing images according to claim 1 , wherein the step A particularly comprises:
step A 1 , generating 64 three-dimensional Gabor filters according to the set frequency and direction parameter values;
f t represents a frequency, {φ k ,θ j } represents a direction, then the frequency is set as follows: f t =[0.5,0.25,0.125,0.0625], 16 directions are set as follows: {φ k ,θ j }=[0,π/4,π/2,3π/4], and then the 64 three-dimensional Gabor filters are generated according to a formula
Ψ
f
φ
,
θ
(
x
,
y
,
λ
)
=
1
(
2
π
)
2
/
3
σ
3
exp
(
j
2
π
(
xu
+
yv
+
λ
w
)
)
×
exp
(
-
x
2
+
y
2
+
λ
2
2
σ
2
)
,
wherein u=f sin φ cos θ, v=f sin φ sin θ, w=f cos φ; φ represents an included angle between the filter and a ω axis, θ represents an included angle between the filter and a μ−ν plane; φ k represents a k th value of the φ, θ j represents a j th value of the θ; (x, y, λ) respectively represents an x coordinate, a y coordinate and a spectrum coordinate of a pixel; σ represents a width of a Gaussian envelope; and
step A 2 , removing 8 repeated three-dimensional Gabor filters in the 64 three-dimensional Gabor filters, wherein the remaining 52 three-dimensional Gabor filters serve as three-dimensional Gabor filters participating in subsequent convolution operation and are represented by {Ψ i , i=1, . . . , 52}.
3. The classification method for hyperspectral remote sensing images according to claim 1 , wherein there are 52 generated three-dimensional Gabor filters, which are represented by {Ψ i , i=1, . . . , 52}; and the step B particularly comprises:
step B 1 , convoluting hyperspectral remote sensing images with the 52 three-dimensional Gabor filters; and
step B 2 , calculating amplitude from a result of convolution operation to obtain 52 three-dimensional Gabor features of the hyperspectral remote sensing images;
R represents the hyperspectral remote sensing images, and M t represents a generated t th three-dimensional Gabor feature, then the calculating amplitude is represented as M t (x,y,λ)=|(R⊗Ψ t )(x,y,λ)|; the generated 52 three-dimensional Gabor features are represented as {M t , t=1, . . . , 52}, wherein (x,y,λ) respectively represents an x coordinate, a y coordinate and a spectrum coordinate.
4. The classification method for hyperspectral remote sensing images according to claim 1 , wherein indexes of K three-dimensional Gabor features selected in the step C are stored in the index matrix I; and the step D particularly comprises:
step D 1 , dividing each selected three-dimensional Gabor feature into a training set and a test set;
{A I(k) , k=1, . . . , K} represents training sets corresponding to the K three-dimensional Gabor features, and {G I(k) , k=1, . . . , K} represents corresponding test sets;
step D 2 , calculating sparse coding coefficients of three-dimensional Gabor features of test samples on the training sets;
g represents one test sample in the test sets, and the K three-dimensional Gabor features corresponding to it are represented as {g I(k) , k=1, . . . , K}, and if the sparse coding coefficients of the K three-dimensional Gabor features {g I(k) , k=1, . . . , K} of the test sample on the training sets {A k , k=1, . . . , K} are respectively represented as {α k , k=1, . . . , K}, then:
{
α
k
}
=
arg
min
k
=
{
1
,
…
K
}
{
g
I
(
k
)
-
A
I
(
k
)
α
k
2
2
+
η
α
k
1
}
;
wherein α k represents any one vector which is identical to a dimension of α k ; and η represents a coefficient of a L 1 norm;
step D 3 , respectively reconstructing {g I(k) , k=1, . . . , K} according to the preliminary index matrix S by using the sparse coding coefficients {α k , k=1, . . . , K} and the training sets {A I(k) , k=1, . . . , K} to obtain K reconstruction errors and accumulating them, wherein a class with minimal accumulated reconstruction errors serves as the class of the test sample g; and represents a class predicted for the test sample g, then:
Ϛ
=
arg
min
p
∈
{
1
,
…
,
P
}
∑
i
=
S
(
1
,
p
)
S
(
V
,
p
)
g
i
-
A
p
i
α
p
i
2
2
;
wherein α p k represents a coefficient corresponding to the p th class in the sparse coding coefficients α k corresponding to the selected k th three-dimensional Gabor feature g k ; and the index matrix I is obtained by removing the repeated indexes from the preliminary index matrix S, then iϵ{I(k), k=1, . . . , K}.
5. A Gabor cube feature selection-based classification system for hyperspectral remote sensing images, wherein the classification system for hyperspectral remote sensing images comprises:
a generation unit, which is configured to generate a number of three-dimensional Gabor filters according to set frequency and direction parameter values;
a calculation unit, which is configured to convolute hyperspectral remote sensing images with the generated three-dimensional Gabor filters to obtain a number of three-dimensional Gabor features;
a selection unit, which is configured to select a number of three-dimensional Gabor features, classification contribution degrees to various classes of which meet preset requirements, from the obtained three-dimensional Gabor features; and
a classification unit, which is configured to classify the hyperspectral remote sensing images by a multi-task joint sparse representation-based classification means by using the selected three-dimensional Gabor features;
wherein the generation unit is particulary configured to:
firstly, set frequency and direction parameter values, and then generate 64 three-dimensional Gabor filters according to the set values;
f t represents a frequency, {φ k , θ j } represents a direction, then the frequency is set as follows:
f t =[0.5, 0.25, 0.125, 0.0625], 16 directions are set as follows: {φ k , θ j }=[0, π/4, π/2,3π/4], and the 64 three-dimensional Gabor filters are generated according to a formula
Ψ
f
,
ϕ
,
θ
(
x
,
y
,
λ
)
=
1
(
2
π
)
2
/
3
σ
3
exp
(
j
2
π
(
x
u
+
y
v
-
λ
w
)
)
×
exp
(
-
x
2
+
y
2
+
λ
2
2
σ
2
)
,
wherein u=f sin φcos θ, v=f sin φsin θ, w=f cos φ; φrepresents an included angle between a filter and a ω axis, φ represents an included angle between the filter and a u−v plane; φ k represents a k th value of the φ, θ j represents a j th value of the θ; (x,y,λ) respectively represents an x coordinate, a y coordinate and a spectrum coordinate of a pixel; σ represents a width of a Gaussian envelope; and
finally, remove 8 repeated three-dimensional Gabor filters in the 64 three-dimensional Gabor filters, wherein the remaining 52 three-dimensional Gabor filters serve as three-dimensional Gabor filters participating in subsequent convolution operation and are represented by {Ψ t ,i=1, . . . , 52}.
6. The classification system for hyperspectral remote sensing images according to claim 5 , wherein there are 52 three-dimensional Gabor filters, which are represented by {Ψ i , i=1, . . . , 52};
the calculation unit is particularly configured to:
firstly, convolute hyperspectral remote sensing images with the generated 52 three-dimensional Gabor filters; and
then calculate amplitude from a result of convolution operation to obtain 52 three-dimensional Gabor features of the hyperspectral remote sensing images;
R represents the hyperspectral remote sensing images, and M t represents the generated t th three-dimensional Gabor feature, then:
the calculating amplitude is represented as M t (x,y,λ)=|(R⊗Ψ t )(x,y,λ)|; the generated 52 three-dimensional Gabor features are represented as {M t , t=1, . . . , 52}, wherein (x,y,λ) respectively represents an x coordinate, a y coordinate and a spectrum coordinate.
7. The classification system for hyperspectral remote sensing images according to claim 5 , wherein R represents the hyperspectral remote sensing images, 52 three-dimensional Gabor features obtained by the hyperspectral remote sensing images R participating in convolution operation are represented by {M t , t=1, . . . , 52}, wherein M t represents a t th three-dimensional Gabor feature;
the selection unit selects three-dimensional Gabor features by utilizing a Fisher discriminant criterion, with particular steps as follows:
firstly, dividing each of the three-dimensional Gabor feature into a training set and a test set;
A t represents a training set of the t th three-dimensional Gabor feature M t , G t represents a test set of the t th three-dimensional Gabor feature M t , tϵ{1, . . . , 52}, and therefore all training sets {A t , t=1, . . . , 52} and test sets {G t , t=1, . . . , 52} of the 52 three-dimensional Gabor features are obtained;
then, respectively calculating an intra-class spacing and an inter-class spacing of each three-dimensional Gabor feature by using the training set {A t , t=1, . . . , 52};
γ W (A p t ) represents an intra-class spacing of a p th class in the t th three-dimensional Gabor feature, and γ B (A p t ) represents an inter-class spacing of the p th class in the t th three-dimensional Gabor feature, then:
γ
W
(
A
p
t
)
=
∑
α
i
∈
A
p
t
(
α
i
-
m
p
t
)
T
(
α
i
-
m
p
t
)
γ
B
(
A
p
t
)
=
n
p
(
m
p
t
-
m
t
)
T
(
m
p
t
-
m
t
)
;
wherein A p t represents a training set of the p th class of the training sets A t , A t =[A 1 t , . . . , A p t ], α i represents one training sample in A p t ; n p represents the number of the samples in the p th class, pϵ{1, . . . , P}, P represents the number of the classes; m t and m p t respectively represent mean vectors
m
t
=
1
n
∑
α
i
∈
A
t
α
i
and
m
p
t
=
1
n
p
∑
α
i
∈
A
p
t
α
i
of A t and A p t ;
then, calculating Fisher scores of the classes in the 52 three-dimensional Gabor features by using the calculated intra-class spacing and the calculated inter-class spacing;
the Fisher scores of the classes in the 52 three-dimensional Gabor features are stored by using a matrix F (F ϵ 52×P ), F p t represents a Fisher score of the p th class in the t th three-dimensional Gabor feature, then:
F p t =γ B ( A p t )/γ W ( A p t );
wherein F ϵ 52×P , P represents the number of the classes, and F p t represents elements in a t th line and a p th column of the matrix F;
finally, selecting V elements with higher scores from each column of the matrix F, and storing indexes of the selected elements in a preliminary index matrix, removing repeated indexes in the preliminary index matrix to obtain a final index matrix, and determining three-dimensional Gabor features to be selected according to the index matrix;
S represents the preliminary index matrix, I represents a final index matrix, the V elements with higher Fisher scores are selected from each column of the matrix F, and the index of the selected elements are stored in the preliminary index matrix S, Sϵ V×P ; the repeated indexes in the preliminary index matrix S are removed to obtain finally-selected indexes, the finally-selected indexes are stored in the index matrix I, Iϵ K×1 ; and no repeated indexes exist in the index matrix I, and each index points to a specific three-dimensional Gabor feature.
8. The classification system for hyperspectral remote sensing images according to claim 7 , wherein the classification unit is particularly configured to:
firstly, divide each selected three-dimensional Gabor feature into a training set and a test set;
{A I(k) , k=1, . . . , K} represents training sets corresponding to the K three-dimensional Gabor features, and {G I(k) , k=1, . . . , K} represents corresponding test sets;
then, calculate sparse coding coefficients of three-dimensional Gabor features of test samples on the training sets;
g represents one test sample, and the K three-dimensional Gabor features corresponding to it are represented as {g I(k) , k=1, . . . , K}, and if the sparse coding coefficients of the K three-dimensional Gabor features {g I(k) , k=1, . . . , K} of the test sample on the training sets {A k , k=1, . . . , K} are respectively represented as {α k , k=1, . . . , K}, then:
{
α
k
}
=
arg
min
k
=
{
1
,
…
K
}
{
g
I
(
k
)
-
A
I
(
k
)
α
k
2
2
+
η
α
k
1
}
wherein α k represents any one vector which is identical to a dimension of α k ; and η represents a coefficient of a L 1 norm;
finally, respectively reconstruct {g I(k) , k=1, . . . , K} according to the preliminary index matrix S by using the sparse coding coefficients {α k , k=1, . . . , K} and the training sets {A I(k) , k=1, . . . , K} to obtain K reconstruction errors and accumulate them, wherein a class with minimal accumulated reconstruction errors serves as the class of the test sample g; and represents a class predicted for the test sample g, then:
Ϛ
=
arg
min
p
∈
{
1
,
…
,
P
}
∑
i
=
S
(
1
,
p
)
S
(
V
,
p
)
g
i
-
A
p
i
α
p
t
2
2
;
wherein α p k represents a coefficient corresponding to the p th class in the sparse coding coefficients α k corresponding to the selected k th three-dimensional Gabor feature g k ; and the index matrix I is obtained by removing the repeated indexes from the preliminary index matrix S, then iϵ{I(k), k=1, . . . , K}.