【图像融合】基于非下采样剪切波变换(NSST)实现红外图像和可见光图像融合ma

1 简介

2 部分代码

function [h0,h1,g0,g1] = atrousfilters(fname);
% ATROUSFILTERS Generate pyramid 2D filters
%
% [h0, h1, g0, g1] = atrousfilters(fname, type)
%
% Input:
% fname: Filter name. Available 'fname' are:
% '9-7': Filters obtained from 9-7 1-D prototypes
% 'maxflat': Filters derived from 1-D using maximally flat mapping function with 4 vanishing moments
% 'pyr': Filters derived from 1-D using maximally flat mapping function with 2 vanishing moments
% 'pyrexc': Same as pyr but exchanging two highpass filters
% Output:
% h0, h1, g0, g1: pyramid filters for 2-D nonsubsampled filter bank (lowpass and highpass)
% To test those filters (for the PR condition for the FIR case), verify that:
% conv2(h0,g0) + conv2(g1, h1) = 1
% (replace + with - for even size filters)
% the filters have horizontal/vertical/diagonal symetry and can be implemented with
% symetric extension.
% filters designed by A. Cunha, May 2004 (see Tech Report, University of Illinois, Set 2004, av. upon req.)
% SEE ALSO: dfilters, nsscdec
switch fname
case '9-7'
% Filters derived from 9-7 prototypes, frame bounds A=0.91, B=1.101
h0 = [0.00010448733363597687 0.000835898669087815 0.0029256453418073525 0.005851290683614705 0.007314113354518382 ...
0.005851290683614705 0.0029256453418073525 0.000835898669087815 0.00010448733363597687;
0.000835898669087815 0.003080092825681339 0.001762583572331734 -0.007296122436400075 ...
-0.013629023704276572 -0.007296122436400075 0.001762583572331734 0.003080092825681339 0.000835898669087815 ;
0.0029256453418073525 0.001762583572331734 -0.01306636838062783 -0.02131840020457929 -0.018830187186854155 ...
-0.02131840020457929 -0.01306636838062783 0.001762583572331734 0.0029256453418073525;
0.005851290683614705 -0.007296122436400075 -0.02131840020457929 0.0740121520471188 0.16436627826336664 ...
0.0740121520471188 -0.02131840020457929 -0.007296122436400075 0.005851290683614705;
0.007314113354518382 -0.013629023704276572 -0.018830187186854155 0.16436627826336664 0.3245066567828517 0.16436627826336664 ...
-0.018830187186854155 -0.013629023704276572 0.007314113354518382;
0.005851290683614705 -0.007296122436400075 -0.02131840020457929 0.0740121520471188 0.16436627826336664 ...
0.0740121520471188 -0.02131840020457929 -0.007296122436400075 0.005851290683614705;
0.0029256453418073525 0.001762583572331734 -0.01306636838062783 -0.02131840020457929 -0.018830187186854155 ...
-0.02131840020457929 -0.01306636838062783 0.001762583572331734 0.0029256453418073525;
0.000835898669087815 0.003080092825681339 0.001762583572331734 ...
-0.007296122436400075 -0.013629023704276572 -0.007296122436400075 0.001762583572331734 0.003080092825681339 0.000835898669087815;
0.00010448733363597687 0.000835898669087815 0.0029256453418073525 ...
0.005851290683614705 0.007314113354518382 0.005851290683614705 0.0029256453418073525 0.000835898669087815 0.00010448733363597687];
h1= [0.0014261212986601578 0.008556727791960947 0.021391819479902367 0.028522425973203154 ...
0.021391819479902367 0.008556727791960947 0.0014261212986601578;
0.008556727791960947 0.01351698519464063 -0.022942609349085995 ...
-0.055805733503531366 -0.022942609349085995 0.01351698519464063 0.008556727791960947;
0.021391819479902367 -0.022942609349085995 -0.1692097602584649 -0.24975066285895303 -0.1692097602584649 ...
-0.022942609349085995 0.021391819479902367;
0.028522425973203154 -0.055805733503531366 -0.24975066285895303 1.669154993235563 -0.24975066285895303 ...
-0.055805733503531366 0.028522425973203154;
0.021391819479902367 -0.022942609349085995 -0.1692097602584649 -0.24975066285895303 ...
-0.1692097602584649 -0.022942609349085995 0.021391819479902367 ;
0.008556727791960947 0.01351698519464063 -0.022942609349085995 -0.055805733503531366 ...
-0.022942609349085995 0.01351698519464063 0.008556727791960947 ;
0.0014261212986601578 0.008556727791960947 0.021391819479902367 0.028522425973203154 ...
0.021391819479902367 0.008556727791960947 0.0014261212986601578 ];
g0= [-0.0014261212986601578 -0.008556727791960947 -0.021391819479902367 -0.028522425973203154 ...
-0.021391819479902367 -0.008556727791960947 -0.0014261212986601578;
-0.008556727791960947 -0.020709925973203154 -0.005829153765164099 0.012648088832156207...
-0.005829153765164099 -0.020709925973203154 -0.008556727791960947;
-0.021391819479902367 -0.005829153765164099 0.1692097602584649 0.3072941890874532 ...
0.1692097602584649 -0.005829153765164099 -0.021391819479902367;
-0.028522425973203154 0.012648088832156207 0.3072941890874532 0.5322473485641878 ...
0.3072941890874532 0.012648088832156207 -0.028522425973203154 ;
-0.021391819479902367 -0.005829153765164099 0.1692097602584649 0.3072941890874532 ...
0.1692097602584649 -0.005829153765164099 -0.021391819479902367 ;
-0.008556727791960947 -0.020709925973203154 -0.005829153765164099 0.012648088832156207 ...
-0.005829153765164099 -0.020709925973203154 -0.008556727791960947;
-0.0014261212986601578 -0.008556727791960947 -0.021391819479902367 -0.028522425973203154...
-0.021391819479902367 -0.008556727791960947 -0.0014261212986601578];
g1= [ 0.00010448733363597687 0.000835898669087815 0.0029256453418073525 0.005851290683614705 0.007314113354518382...
0.005851290683614705 0.0029256453418073525 0.000835898669087815 0.00010448733363597687;
0.000835898669087815 0.0036070965270211808 0.004924605780370786 0.0006089330836975557 -0.0030889496774797283...
0.0006089330836975557 0.004924605780370786 0.0036070965270211808 0.000835898669087815;
0.0029256453418073525 0.004924605780370786 -0.006742323964549725 -0.024480422412618347 -0.03147827601901037...
-0.024480422412618347 -0.006742323964549725 0.004924605780370786 0.0029256453418073525;
0.005851290683614705 0.0006089330836975557 -0.024480422412618347 -0.06732496269441629 -0.09617379576343019 ...
-0.06732496269441629 -0.024480422412618347 0.0006089330836975557 0.005851290683614705 ;
0.007314113354518382 -0.0030889496774797283 -0.03147827601901037 -0.09617379576343019 0.849802834447164 ...
-0.09617379576343019 -0.03147827601901037 -0.0030889496774797283 0.007314113354518382;
0.005851290683614705 0.0006089330836975557 -0.024480422412618347 -0.06732496269441629 -0.09617379576343019...
-0.06732496269441629 -0.024480422412618347 0.0006089330836975557 0.005851290683614705 ;
0.0029256453418073525 0.004924605780370786 -0.006742323964549725 -0.024480422412618347 -0.03147827601901037 ...
-0.024480422412618347 -0.006742323964549725 0.004924605780370786 0.0029256453418073525;
0.000835898669087815 0.0036070965270211808 0.004924605780370786 0.0006089330836975557 -0.0030889496774797283 ...
0.0006089330836975557 0.004924605780370786 0.0036070965270211808 0.000835898669087815;
0.00010448733363597687 0.000835898669087815 0.0029256453418073525 0.005851290683614705 0.007314113354518382...
0.005851290683614705 0.0029256453418073525 0.000835898669087815 0.00010448733363597687 ];
% normalize filters
h0 = h0 ;
h1 = h1./2 ;
g0 = g0./2;
g1 = g1;
case 'maxflat'
% Quasi-tight frame filters, frame bounds A=.97 and B=1
h0=[-7.900496718847182e-07 0. 0.000014220894093924927 0.000025281589500310983 -0.000049773129328737247 -0.00022753430550279883 -0.00033182086219158167;
0 0 0 0 0 0 0;
0.000014220894093924927 0. -0.0002559760936906487 -0.00045506861100559767 0.0008959163279172705 0.004095617499050379 0.00597277551944847;
0.000025281589500310983 0. -0.00045506861100559767 0.0009765625 0.0015927401385195919 -0.0087890625 -0.01795090623402861;
-0.000049773129328737247 0. 0.0008959163279172705 0.0015927401385195919 -0.0031357071477104465 -0.014334661246676327 -0.020904714318069645;
-0.00022753430550279883 0. 0.004095617499050379 -0.0087890625 -0.014334661246676327 0.0791015625 0.16155815610625748;
-0.00033182086219158167 0. 0.00597277551944847 -0.01795090623402861 -0.020904714318069645 0.16155815610625748 0.3177420190660832];
g0=[-6.391587676622346e-010 0. 1.7257286726880333e-08 3.067962084778726e-08 -1.3805829381504267e-07 -5.522331752601707e-07 ...
-3.3747582932565985e-07 1.9328161134105974e-06 5.6949046198705095e-06 7.649452131381623e-06;
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. ;
1.7257286726880333e-08 0. -4.65946741625769e-07 -8.283497628902559e-07 3.727573933006152e-06 0.000014910295732024608 ...
9.111847391792816e-06 -0.000052186035062086126 -0.00015376242473650378 -0.00020653520754730382;
3.067962084778726e-08 0. -8.283497628902559e-07 -1.2809236054493144e-06 6.6267981031220475e-06 0.00002305662489808766 ...
0.000010064497559808503 -0.0000806981871433068 -0.00021814634152337594 -0.00028666046030363884;
-1.3805829381504267e-07 0. 3.727573933006152e-06 6.6267981031220475e-06 -0.000029820591464049215 -0.00011928236585619686 ...
-0.00007289477913434253 0.000417488280496689 0.0012300993978920302 0.0016522816603784306;
-5.522331752601707e-07 0. 0.000014910295732024608 0.00002305662489808766 -0.00011928236585619686 -0.00041501924816557786 ...
-0.00018116095607655303 0.0014525673685795225 0.0039266341474207675 0.005159888285465499;
-3.3747582932565985e-07 0. 9.111847391792816e-06 0.000010064497559808503 -0.00007289477913434253 -0.00018116095607655303 ...
0.001468581806076247 0.0006340633462679356 -0.01181401175635013 -0.021745034491193898;
1.9328161134105974e-06 0. -0.000052186035062086126 -0.0000806981871433068 0.000417488280496689 0.0014525673685795225 ...
0.0006340633462679356 -0.005083985790028328 -0.013743219515972684 -0.018059608999129246;
5.6949046198705095e-06 0. -0.00015376242473650378 -0.00021814634152337594 0.0012300993978920302 0.0039266341474207675 ...
-0.01181401175635013 -0.013743219515972684 0.0826466923977296 0.1638988884584603;
7.649452131381623e-06 0. -0.00020653520754730382 -0.00028666046030363884 0.0016522816603784306 0.005159888285465499 ...
-0.021745034491193898 -0.018059608999129246 0.1638988884584603 0.31358726209239235];
g1=[-7.900496718847182e-07 0. 0.000014220894093924927 0.000025281589500310983 -0.000049773129328737247 -0.00022753430550279883 -0.00033182086219158167;
0 0 0 0 0 0 0 ;
0.000014220894093924927 0. -0.0002559760936906487 -0.00045506861100559767 0.0008959163279172705 0.004095617499050379 0.00597277551944847 ;
0.000025281589500310983 0. -0.00045506861100559767 -0.0009765625 0.0015927401385195919 0.0087890625 0.01329909376597139 ;
-0.000049773129328737247 0. 0.0008959163279172705 0.0015927401385195919 -0.0031357071477104465 -0.014334661246676327 -0.020904714318069645 ;
-0.00022753430550279883 0. 0.004095617499050379 0.0087890625 -0.014334661246676327 -0.0791015625 -0.1196918438937425 ;
-0.00033182086219158167 0. 0.00597277551944847 0.01329909376597139 -0.020904714318069645 -0.1196918438937425 0.8177420190660831 ];
h1=[6.391587676622346e-010 0. -1.7257286726880333e-08 -3.067962084778726e-08 1.3805829381504267e-07 5.522331752601707e-07 ...
3.3747582932565985e-07 -1.9328161134105974e-06 -5.6949046198705095e-06 -7.649452131381623e-06;
0. 0. 0. 0. 0. 0. 0. 0. 0. 0.;
-1.7257286726880333e-08 0. 4.65946741625769e-07 8.283497628902559e-07 -3.727573933006152e-06 -0.000014910295732024608 ...
-9.111847391792816e-06 0.000052186035062086126 0.00015376242473650378 0.00020653520754730382;
-3.067962084778726e-08 0. 8.283497628902559e-07 -2.9917573832012203e-07 -6.6267981031220475e-06 5.3851632897621965e-06 ...
0.00004049868144081346 -0.00001884807151416769 -0.00023692226948222173 -0.0003769812640795245;
1.3805829381504267e-07 0. -3.727573933006152e-06 -6.6267981031220475e-06 0.000029820591464049215 0.00011928236585619686 ...
0.00007289477913434253 -0.000417488280496689 -0.0012300993978920302 -0.0016522816603784306;
5.522331752601707e-07 0. -0.000014910295732024608 5.3851632897621965e-06 0.00011928236585619686 -0.00009693293921571956 ...
-0.0007289762659346422 0.00033926528725501844 0.004264600850679991 0.006785662753431441;
3.3747582932565985e-07 0. -9.111847391792816e-06 0.00004049868144081346 0.00007289477913434253 -0.0007289762659346422 ...
-0.001468581806076247 0.002551416930771248 0.01181401175635013 0.017093222023136675;
-1.9328161134105974e-06 0. 0.000052186035062086126 -0.00001884807151416769 -0.000417488280496689 0.00033926528725501844 ...
0.002551416930771248 -0.0011874285053925643 -0.01492610297737997 -0.023749819637010044;
-5.6949046198705095e-06 0. 0.00015376242473650378 -0.00023692226948222173 -0.0012300993978920302 0.004264600850679991 ...
0.01181401175635013 -0.01492610297737997 -0.0826466923977296 -0.12203257624594532;
-7.649452131381623e-06 0. 0.00020653520754730382 -0.0003769812640795245 -0.0016522816603784306 0.006785662753431441 ...
0.017093222023136675 -0.023749819637010044 -0.12203257624594532 0.821896776039774];
g0 = [g0 fliplr(g0(:,1:end-1))];
g0 = [g0 ; flipud(g0(1:end-1,:))];
h0 = [h0 fliplr(h0(:,1:end-1))];
h0 = [h0 ; flipud(h0(1:end-1,:))];
g1 = [g1 fliplr(g1(:,1:end-1))];
g1 = [g1 ; flipud(g1(1:end-1,:))];
h1 = [h1 fliplr(h1(:,1:end-1))];
h1 = [h1 ; flipud(h1(1:end-1,:))];
case 'pyr'
% these filters are very short and very close tight
h0 = [-0.003236043456039806 -0.012944173824159223 -0.019416260736238835;
-0.012944173824159223 0.0625 0.15088834764831843 ;
-0.019416260736238835 0.15088834764831843 0.3406092167691145];
g1 = [-0.003236043456039806 -0.012944173824159223 -0.019416260736238835;
-0.012944173824159223 -0.0625 -0.09911165235168155 ;
-0.019416260736238835 -0.09911165235168155 0.8406092167691145];
g0 = [ -0.00016755163599004882 -0.001005309815940293 -0.002513274539850732 -0.003351032719800976;
-0.001005309815940293 -0.005246663087920392 -0.01193886400821893 -0.015395021472477663;
-0.002513274539850732 -0.01193886400821893 0.06769410071569153 0.15423938036811946 ;
-0.003351032719800976 -0.015395021472477663 0.15423938036811946 0.3325667382415921];
h1 = [ 0.00016755163599004882 0.001005309815940293 0.002513274539850732 0.003351032719800976;
0.001005309815940293 -0.0012254238241592198 -0.013949483640099517 -0.023437500000000007;
0.002513274539850732 -0.013949483640099517 -0.06769410071569153 -0.10246268507148255;
0.003351032719800976 -0.023437500000000007 -0.10246268507148255 0.8486516952966369];
g0 = [g0 fliplr(g0(:,1:end-1))];
g0 = [g0 ; flipud(g0(1:end-1,:))];
h0 = [h0 fliplr(h0(:,1:end-1))];
h0 = [h0 ; flipud(h0(1:end-1,:))];
g1 = [g1 fliplr(g1(:,1:end-1))];
g1 = [g1 ; flipud(g1(1:end-1,:))];
h1 = [h1 fliplr(h1(:,1:end-1))];
h1 = [h1 ; flipud(h1(1:end-1,:))];
case 'pyrexc'
% these filters are very short and very close tight
h0 = [-0.003236043456039806 -0.012944173824159223 -0.019416260736238835;
-0.012944173824159223 0.0625 0.15088834764831843 ;
-0.019416260736238835 0.15088834764831843 0.3406092167691145];
h1 = [-0.003236043456039806 -0.012944173824159223 -0.019416260736238835;
-0.012944173824159223 -0.0625 -0.09911165235168155 ;
-0.019416260736238835 -0.09911165235168155 0.8406092167691145];
g0 = [ -0.00016755163599004882 -0.001005309815940293 -0.002513274539850732 -0.003351032719800976;
-0.001005309815940293 -0.005246663087920392 -0.01193886400821893 -0.015395021472477663;
-0.002513274539850732 -0.01193886400821893 0.06769410071569153 0.15423938036811946 ;
-0.003351032719800976 -0.015395021472477663 0.15423938036811946 0.3325667382415921];
g1 = [ 0.00016755163599004882 0.001005309815940293 0.002513274539850732 0.003351032719800976;
0.001005309815940293 -0.0012254238241592198 -0.013949483640099517 -0.023437500000000007;
0.002513274539850732 -0.013949483640099517 -0.06769410071569153 -0.10246268507148255;
0.003351032719800976 -0.023437500000000007 -0.10246268507148255 0.8486516952966369];
g0 = [g0 fliplr(g0(:,1:end-1))];
g0 = [g0 ; flipud(g0(1:end-1,:))];
h0 = [h0 fliplr(h0(:,1:end-1))];
h0 = [h0 ; flipud(h0(1:end-1,:))];
g1 = [g1 fliplr(g1(:,1:end-1))];
g1 = [g1 ; flipud(g1(1:end-1,:))];
h1 = [h1 fliplr(h1(:,1:end-1))];
h1 = [h1 ; flipud(h1(1:end-1,:))];
end

3 仿真结果

4 参考文献

[1]王昭、杜庆治、董安勇、苏斌、赵文博. 基于非下采样剪切波变换的红外与可见光图像融合[J]. 光电子．激光, 2020, 31(10):12.

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