CN103632348A - Nonlinear image multi-scale geometric representation method - Google Patents

Nonlinear image multi-scale geometric representation method Download PDF

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CN103632348A
CN103632348A CN201310625611.0A CN201310625611A CN103632348A CN 103632348 A CN103632348 A CN 103632348A CN 201310625611 A CN201310625611 A CN 201310625611A CN 103632348 A CN103632348 A CN 103632348A
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雷琳
周石琳
刘俊良
邹焕新
计科峰
李智勇
孙浩
侯毅
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National University of Defense Technology
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Abstract

The invention provides a nonlinear image multi-scale geometric representation method. The technical scheme comprises the following steps of 1, filtering an image by using an FIR medium value mixed filter; 2, performing 2-reducing sampling on the filtered image according to an interlacing inter-row mode to obtain a lower sampling image; step 3, performing medium value-based 2-increasing interpolation filtering on the lower sampling image to obtain an interpolation estimating image; step 4, subtracting the original image by the interpolation estimating image to obtain multiple scale layer nonlinear pyramid decomposing images; step 5, performing Shear directional filtering on each scale layer nonlinear pyramid decomposing image to obtain a sub-band image. The nonlinear image multi-scale geometric representation method belongs to an image nonlinear multi-scale geometric representation method with excellent performance, is less in operand, and has higher application values in aspects such as image compressing, edge extracting, grain retrieving.

Description

A kind of multiple dimensioned geometric representation method of nonlinear images
Technical field
The present invention relates to computer vision and digital image processing field, more particularly, relate to a kind of nonlinear images multi-scale geometric analysis method.
Background technology
Along with the development of computer vision and digital image processing techniques, many new image representations and handling implement have been there is in recent years.Wherein multi-scale geometric analysis is owing to having the characteristics such as multiresolution, Time-Frequency Localization, multidirectional, become the representative theoretical frame in image understanding field, make to extract different object construction features and become possibility in the details of image different resolution, greatly promoted the performance that various images are processed application.In addition, the support Interval of multi-scale geometric analysis basis function shows as has " anisotropy " characteristic that length breadth ratio changes with yardstick, can the rarefaction representation of more effective realization to image.
In Image Multiscale geometric analysis method, representational have Ridgelet, Curvelet, Bandelet, Contourlet and a Shearlet conversion etc.The linear multiple dimensioned decomposition strategy of the many employings of these conversion, realizes simply, and structure is ripe, but they deposit deficiency both ways: the coefficient degree of rarefication of (1) transform domain is not enough, and the dependence between different sub-band coefficient is larger; (2) line sampling and interpolation easily cause edge fog, and image detail loss is many.
Research shows that nonlinear filter has unique advantage in Image Information Processing, because it can remove a large amount of garbages and can reduce edge fog effect again from sampled images.Given this, strengthening the non-linearization research of Image Multiscale geometric representation method is the core place that solves traditional multiple dimensioned geometric representation method deficiency.Yet the wave filter of non-linear Multiresolution Decompositions Approach selects to have diversity, and also relative complex of the building mode of non-linear multi-Scale Data structure, make the non-linear multiple dimensioned geometric representation problem of image never in depth be studied and solve.Given this, the research multiple dimensioned geometric representation method of image non-linear effective, that be simple and easy to realization is all very valuable for the development of the application systems such as compression of images, image retrieval, image co-registration.
Summary of the invention
The present invention, for the efficient solution multiple dimensioned geometric representation problem of linear image by no means, has proposed a kind of multiple dimensioned geometric representation method of nonlinear images.Degree of rarefication and image detail hold facility that this method has obviously improved multiple dimensioned geometric transformation domain coefficient are strong, realize more simply with respect to other nonlinear filtering simultaneously, and operand is little.
Technical scheme of the present invention is: a kind of multiple dimensioned geometric representation method of nonlinear images, specific implementation process comprises the steps:
If FIR intermediate value compound filter is image H (m, n) to the filtering result of input picture i (m, n), concrete filtering is shown below:
Figure BDA0000425522080000021
In above formula, y 1(m, n)=MED{MED[Subset 1(m, n)], i (m, n), MED[Subset 2(m, n)] },
y 2(m,n)=MED{MED[Subset 3(m,n)],i(m,n),MED[Subset 4(m,n)]}，
Subset 1(m,n)={i(m,n+q):q∈[-N,N]\{0}}
Subset 2(m,n)={i(m+q,n):q∈[-N,N]\{0}}
Subset 3(m,n)={i(m+q,n+q):q∈[-N,N]\{0}}
Subset 4(m,n)={i(m-q,n+q):q∈[-N,N]\{0}}
MED is for getting median operation, m ∈ [1, N ir], n ∈ [1, N ic], N irthe line number of image i (m, n), N icbe the columns of image i (m, n), the line number of FIR intermediate value compound filter and columns are all 2N+1 and N ir>2N+1, N ic>2N+1.
For any yardstick j, j=1 ..., M, M is the Scale Decomposition number of plies.Pending image f (m, n) is designated as to original input picture f 1(m, n).Make j=1, then carry out following process:
Step is 1.: utilize FIR intermediate value compound filter to image f j(m, n) carries out filtering, obtains image H j(m, n);
Step is 2.: to image H j(m, n) falls 2 samplings by interlacing every row mode, obtains down-sampled images
Figure BDA0000425522080000022
Step is 3.: to down-sampled images
Figure BDA0000425522080000023
by following formula, carry out liter 2 filtering interpolations based on intermediate value, obtain Interpolate estimation image
H 2 j ( 2 m - 1,2 n - 1 ) = H 1 j ( m , n ) H 2 j ( 2 m - 1,2 n ) = [ H 1 j ( m , n ) + H 1 j ( m , n + 1 ) ] / 2 H 2 j ( 2 m , 2 n - 1 ) = [ H 1 j ( m + 1 , n ) + H 1 j ( m , n ) ] / 2 H 2 j ( 2 m , 2 n ) = MED { H 1 j ( m , n ) , H 1 j ( m , n + 1 ) , H 1 j ( m + 1 , n ) , H 1 j ( m + 1 , n + 1 ) , z }
In above formula, z=MED{z 1, z 2, z 3}
z 1 = [ H 1 j ( m , n ) + H 1 j ( m + 1 , n + 1 ) ] / 2 , z 2 = [ H 1 j ( m , n + 1 ) + H 1 j ( m + 1 , n ) ] / 2 z 3 = [ H 1 j ( m , n ) + H 1 j ( m + 1 , n + 1 ) + H 1 j ( m , n + 1 ) + H 1 j ( m + 1 , n ) ] / 4
Step is 4.: by image f j(m, n) and Interpolate estimation image
Figure BDA0000425522080000032
subtract each other to obtain the non-linear pyramid decomposition image of j yardstick layer
Step is 5.: by f j+1(m, n) is updated to down-sampled images make j=j+1, return to step 1..
Repeat M step 1. to after 5., obtain the non-linear pyramid decomposition image sequence of M layer
Figure BDA0000425522080000034
To any yardstick j, j=1 ..., M, by the non-linear pyramid decomposition image of j yardstick layer
Figure BDA0000425522080000035
by following formula, carry out Shear trend pass filtering and obtain sub-band images f j,l(m, n):
f j , l ( m , n ) = f d j ( m , n ) * w j , l s ( m , n )
In above formula,
Figure BDA0000425522080000037
L=1 ..., D is direction numbering, D is trend pass filtering number; the discrete Fourier transformation of representative δ function in pseudo-polar coordinate system; for Meyer wavelet frequency domain window function, and meet
Figure BDA00004255220800000310
Figure BDA00004255220800000311
mapping function for the conversion from pseudo-polar coordinate system to cartesian coordinate system.N rfor
Figure BDA00004255220800000312
line number, N cfor
Figure BDA00004255220800000313
columns.N rvalue be less than or equal to image
Figure BDA00004255220800000314
line number, N cvalue be less than or equal to image
Figure BDA00004255220800000315
columns.
The non-linear pyramid decomposition image sequence of M layer carried out respectively to the Shear trend pass filtering of D direction, the sub-band images sequence f obtaining 1,1(m, n), f 1,2(m, n) ..., f 1, D(m, n) ..., f m, 1(m, n), f m, 2(m, n) ... f m,D(m, n) is exactly the non-linear multiple dimensioned geometric representation result of pending image f provided by the invention (m, n).
The invention has the beneficial effects as follows: utilize FIR intermediate value compound filter to carry out non-linear pyramid decomposition to image and can remove a large amount of garbage of image and can reduce edge fog effect again; Shear anisotropic filter has multi-direction anisotropy geometric analysis and optimum non-linear approximation capability, and implementation is quick; In conjunction with FIR intermediate value compound filter and Shear anisotropic filter, the multiple dimensioned geometric representation method of nonlinear images that the present invention proposes, not only can improve the degree of rarefication of sub-band images coefficient, reduces the dependence between coefficient; Can also improve edge details and catch and hold facility, be conducive to successive image feature extraction, be a kind of multiple dimensioned geometric representation method of image non-linear of function admirable.In addition, the discrete Shearlet conversion based on FIR intermediate value mixed filtering only relates to some simple arithmetical operations (intermediate value, convolution etc.), and operand is few, at aspects such as compression of images, edge extracting, Texture Retrievals, has higher using value.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of the multiple dimensioned geometric representation method of nonlinear images provided by the invention;
Fig. 2 is the multiple dimensioned geometric representation result of method provided by the invention to experimental image Lena;
Fig. 3 carries out the result comparison diagram of edge extracting again after utilizing method provided by the invention and conventional discrete Shearlet transform method to represent experimental image House.
Embodiment
Below in conjunction with accompanying drawing, the multiple dimensioned geometric representation method of nonlinear images provided by the invention is elaborated.
Fig. 1 is the process flow diagram of the multiple dimensioned geometric representation method of nonlinear images provided by the invention.
The first step of this process flow diagram is to build FIR intermediate value compound filter, by obtaining the sampling subset Subset of four direction subfilter to image 1(m, n), Subset 2(m, n), Subset 3(m, n) and Subset 4the intermediate value of (m, n) calculating sampling subset realizes.Each subfilter is designed to retain the detailed information of a direction, and the edge details information of image all directions can be caught and retain to FIR intermediate value compound filter, in conjunction with the subfilter of multiple directions, well.In addition the sample mode that subfilter is different can construct different FIR intermediate value compound filters.
Second step is image non-linear pyramid decomposition, corresponding to the step of summary of the invention 1. to 5..For j=1 ..., M, M is the Scale Decomposition number of plies.First to image f j(m, n) carries out FIR intermediate value mixed filtering and obtains H j(m, n), then to H j(m, n) interlacing is fallen 2 every row and is sampled
Figure BDA0000425522080000041
secondly right
Figure BDA0000425522080000042
liter 2 filtering interpolations that carry out based on intermediate value obtain
Figure BDA0000425522080000043
finally by f j(m, n) with
Figure BDA0000425522080000044
subtract each other to obtain the non-linear pyramid decomposition image of j yardstick layer
Figure BDA0000425522080000045
When j=1, f 1(m, n) is pending image.When j>1, f j(m, n) uses the down-sampled images of last layer
Figure BDA0000425522080000046
replace, repeat just to obtain the non-linear pyramid decomposition sequence of M tomographic image after said process M time
Figure BDA0000425522080000051
the value of M is according to practical application and Image Multiscale geometric representation determine precision, and general span is [2,4].M is larger, and the number of times that carries out non-linear pyramid decomposition is more, and calculated amount is also larger.
The 3rd step is the Shear trend pass filtering of non-linear pyramid decomposition image.Utilize the non-linear pyramid diagram picture of Shear anisotropic filter to any yardstick layer j
Figure BDA0000425522080000052
carry out D trend pass filtering, obtain sub-band images sequence f j, 1(m, n) ..., f j,D(m, n).The value of D is according to practical application and Image Multiscale geometric representation determine precision, the power side that general value is 2, and as 4,8,16 etc.
Fig. 2 is the multiple dimensioned geometric representation result of method provided by the invention to experimental image Lena.For simplicity, make M=2, D=4, carries out the Shear trend pass filtering of 2 layers of non-linear pyramid decomposition and 4 directions to image.Wherein, subgraph (a) is experimental image Lena, subgraph (b) be respectively from left to right the 2nd yardstick layer 0, the sub-band images of π/4, pi/2, these 4 directions of 3 π/4, subgraph (c) be respectively from left to right the 1st yardstick layer 0, π/4, pi/2, these 4 directional subband images of 3 π/4.
Can find out, the coefficient amplitude at sub-band images edge details place is all larger, clear contour structure information of having portrayed image.Usage factor mutual information is weighed dependent size between coefficient, and specific algorithm can be with reference to the Elements of Information Theory of T.M.Cover.By calculating the coefficient mutual information of the sub-band images sequence of many group experimental image (as Lena etc.), can obtain, the sub-band images sequence of utilizing method provided by the invention to obtain, its coefficient mutual information has on average reduced by 0.1 left and right than conventional discrete Shearlet conversion, thereby verified that the method for carrying with the present invention carries out multiple dimensioned geometric representation to image, between the coefficient of sub-band images sequence, dependence is lower, i.e. few this advantage of amount of redundant information between coefficient.By calculating entropy and the nonzero coefficient ratio of many group experimental image (as Lena etc.) sub-band images sequence, can obtain, the sub-band images sequence of utilizing method provided by the invention to obtain, its entropy has on average reduced by 0.071 left and right with respect to conventional discrete Shearlet conversion, nonzero coefficient ratio has reduced by 0.04 left and right, thereby verified that the method for carrying with the present invention carries out multiple dimensioned geometric representation to image, high this advantage of coefficient degree of rarefication of sub-band images sequence.
Fig. 3 carries out the result comparison diagram of edge extracting again after utilizing method provided by the present invention and conventional discrete Shearlet transform method to represent experimental image House.In specific implementation, the M=3 Scale Decomposition number of plies is all 3 layers.Wherein, subgraph (a) is experimental image House, subgraph (b) is respectively 1 to the 3 layer of edge extracting image obtaining after conventional discrete Shearlet conversion represents from left to right, and subgraph (c) is respectively 1 to 3 layer of edge extracting image based on obtaining after method representation provided by the invention from left to right.
Poor by the known image detail capturing ability of subgraph (b), can only catch some obvious contour edge information, lost a lot of important information.By contrast, the edge extracting result of subgraph (c) is more complete, and location, edge is relatively more accurate, embodies method for expressing provided by the present invention image detail is caught and the strong advantage of hold facility.
Above-described embodiment of the present invention, does not form limiting the scope of the present invention, any modification of doing within the present invention spirit and principle, is equal to replacement and improvement etc., within all should being included in claim protection domain of the present invention.

Claims (2)

1. the multiple dimensioned geometric representation method of nonlinear images, is characterized in that, comprises the steps:
If FIR intermediate value compound filter is image H (m, n) to the filtering result of input picture i (m, n), concrete filtering is shown below:
Figure FDA0000425522070000011
In above formula, y 1(m, n)=MED{MED[Subset 1(m, n)], i (m, n), MED[Subset 2(m, n)] },
y 2(m,n)=MED{MED[Subset 3(m,n)],i(m,n),MED[Subset 4(m,n)]}，
Subset 1(m,n)={i(m,n+q):q∈[-N,N]\{0}}
Subset 2(m,n)={i(m+q,n):q∈[-N,N]\{0}}
Subset 3(m,n)={i(m+q,n+q):q∈[-N,N]\{0}}，
Subset 4(m,n)={i(m-q,n+q):q∈[-N,N]\{0}}
MED is for getting median operation, m ∈ [1, N ir], n ∈ [1, N ic], N irthe line number of image i (m, n), N icbe the columns of image i (m, n), the line number of FIR intermediate value compound filter and columns are all 2N+1 and N ir>2N+1, N ic>2N+1;
For any yardstick j, j=1 ..., M, M is the Scale Decomposition number of plies; Pending image f (m, n) is designated as to original input picture f 1(m, n); Make j=1, then carry out following process:
Step is 1.: utilize FIR intermediate value compound filter to image f j(m, n) carries out filtering, obtains image H j(m, n);
Step is 2.: to image H j(m, n) falls 2 samplings by interlacing every row mode, obtains down-sampled images
Figure FDA0000425522070000012
Step is 3.: to down-sampled images
Figure FDA0000425522070000013
carry out liter 2 filtering interpolations based on intermediate value, obtain Interpolate estimation image
Figure FDA0000425522070000014
Step is 4.: by image f j(m, n) and Interpolate estimation image subtract each other to obtain the non-linear pyramid decomposition image of j yardstick layer
Step is 5.: by f j+1(m, n) is updated to down-sampled images
Figure FDA0000425522070000017
make j=j+1, return to step 1.;
Repeat M step 1. to after 5., obtain the non-linear pyramid decomposition image sequence of M layer
Figure FDA0000425522070000018
To any yardstick j, by the non-linear pyramid decomposition image of j yardstick layer
Figure FDA0000425522070000019
by following formula, carry out Shear trend pass filtering and obtain sub-band images f j,l(m, n):
f j , l ( m , n ) = f d j ( m , n ) * w j , l s ( m , n )
In above formula,
Figure FDA0000425522070000022
L=1 ..., D is direction numbering, D is trend pass filtering number;
Figure FDA0000425522070000023
the discrete Fourier transformation of representative δ function in pseudo-polar coordinate system;
Figure FDA0000425522070000024
for Meyer wavelet frequency domain window function, and meet
Figure FDA0000425522070000025
Figure FDA0000425522070000026
mapping function for the conversion from pseudo-polar coordinate system to cartesian coordinate system; N rfor
Figure FDA0000425522070000027
line number, N cfor
Figure FDA0000425522070000028
columns; N rvalue be less than or equal to image
Figure FDA0000425522070000029
line number, N cvalue be less than or equal to image
Figure FDA00004255220700000210
columns;
The non-linear pyramid decomposition image sequence of M layer carried out respectively to the Shear trend pass filtering of D direction, the sub-band images sequence f obtaining 1,1(m, n), f 1,2(m, n) ..., f 1, D(m, n) ..., f m, 1(m, n), f m, 2(m, n) ... f m,D(m, n) is exactly the non-linear multiple dimensioned geometric representation result of pending image f (m, n).
2. the multiple dimensioned geometric representation method of nonlinear images according to claim 1, is characterized in that, to down-sampled images
Figure FDA00004255220700000214
by following formula, carry out liter 2 filtering interpolations based on intermediate value, obtain Interpolate estimation image
H 2 j ( 2 m - 1,2 n - 1 ) = H 1 j ( m , n ) H 2 j ( 2 m - 1,2 n ) = [ H 1 j ( m , n ) + H 1 j ( m , n + 1 ) ] / 2 H 2 j ( 2 m , 2 n - 1 ) = [ H 1 j ( m + 1 , n ) + H 1 j ( m , n ) ] / 2 H 2 j ( 2 m , 2 n ) = MED { H 1 j ( m , n ) , H 1 j ( m , n + 1 ) , H 1 j ( m + 1 , n ) , H 1 j ( m + 1 , n + 1 ) , z }
In above formula, z=MED{z 1, z 2, z 3}
z 1 = [ H 1 j ( m , n ) + H 1 j ( m + 1 , n + 1 ) ] / 2 , z 2 = [ H 1 j ( m , n + 1 ) + H 1 j ( m + 1 , n ) ] / 2 z 3 = [ H 1 j ( m , n ) + H 1 j ( m + 1 , n + 1 ) + H 1 j ( m , n + 1 ) + H 1 j ( m + 1 , n ) ] / 4 .
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