【图像融合】基于matlab curvelet变换图像融合【含Matlab源码 776期】

一、简介

1 curvelet变换的提出


2 curvelet变换的研究进展及现状


3 第一代curvelet变换








4 实现过程


5 第二代 curvelet变换


6 连续的curvelet变换







7 离散的curvelet变换

二、部分源代码

function x = ifdct_wrapping(C, is_real, M, N)

% ifdct_wrapping.m - Inverse Fast Discrete Curvelet Transform via wedge wrapping - Version 1.0
% This is in fact the adjoint, also the pseudo-inverse
%
% Inputs
%   C           Cell array containing curvelet coefficients (see
%               description in fdct_wrapping.m)
%   is_real     As used in fdct_wrapping.m
%   M, N        Size of the image to be recovered (not necessary if finest
%               = 2)
%
% Outputs
%   x           M-by-N matrix
%
% See also fdct_wrapping.m
%
% By Laurent Demanet, 2004

% Initialization
nbscales = length(C);
nbangles_coarse = length(C{2});
nbangles = [1, nbangles_coarse .* 2.^(ceil((nbscales-(nbscales:-1:2))/2))];
if length(C{end}) == 1, finest = 2; else finest = 1; end;
if finest == 2, nbangles(nbscales) = 1; end;
if nargin < 2, is_real = 0; end;
if nargin < 4,
    if finest == 1, error('Syntax: IFCT_wrapping(C,M,N) where the matrix to be recovered is M-by-N'); end;
    [N1,N2] = size(C{end}{1});
else
    N1 = M;
    N2 = N;
end;

M1 = N1/3;
M2 = N2/3;

if finest == 1;
    
    bigN1 = 2*floor(2*M1)+1;
    bigN2 = 2*floor(2*M2)+1;
    X = zeros(bigN1,bigN2);

    % Initialization: preparing the lowpass filter at finest scale
    window_length_1 = floor(2*M1) - floor(M1) - 1 - (mod(N1,3)==0);
    window_length_2 = floor(2*M2) - floor(M2) - 1 - (mod(N2,3)==0);
    coord_1 = 0:(1/window_length_1):1;
    coord_2 = 0:(1/window_length_2):1;
    [wl_1,wr_1] = fdct_wrapping_window(coord_1);
    [wl_2,wr_2] = fdct_wrapping_window(coord_2);
    lowpass_1 = [wl_1, ones(1,2*floor(M1)+1), wr_1];
    if mod(N1,3)==0, lowpass_1 = [0, lowpass_1, 0]; end;
    lowpass_2 = [wl_2, ones(1,2*floor(M2)+1), wr_2];
    if mod(N2,3)==0, lowpass_2 = [0, lowpass_2, 0]; end;
    lowpass = lowpass_1'*lowpass_2;

    scales = nbscales:-1:2;
   
else

    M1 = M1/2;
    M2 = M2/2;
    
    bigN1 = 2*floor(2*M1)+1;
    bigN2 = 2*floor(2*M2)+1;
    X = zeros(bigN1,bigN2);
    
    window_length_1 = floor(2*M1) - floor(M1) - 1;
    window_length_2 = floor(2*M2) - floor(M2) - 1;
    coord_1 = 0:(1/window_length_1):1;
    coord_2 = 0:(1/window_length_2):1;
    [wl_1,wr_1] = fdct_wrapping_window(coord_1);
    [wl_2,wr_2] = fdct_wrapping_window(coord_2);
    lowpass_1 = [wl_1, ones(1,2*floor(M1)+1), wr_1];
    lowpass_2 = [wl_2, ones(1,2*floor(M2)+1), wr_2];
    lowpass = lowpass_1'*lowpass_2;
    hipass_finest = sqrt(1 - lowpass.^2);
    
    scales = (nbscales-1):-1:2;
    
end;

% Loop: pyramidal reconstruction

Xj_topleft_1 = 1;
Xj_topleft_2 = 1;
for j = scales,

    M1 = M1/2;
    M2 = M2/2;
    window_length_1 = floor(2*M1) - floor(M1) - 1;
    window_length_2 = floor(2*M2) - floor(M2) - 1;
    coord_1 = 0:(1/window_length_1):1;
    coord_2 = 0:(1/window_length_2):1;
    [wl_1,wr_1] = fdct_wrapping_window(coord_1);
    [wl_2,wr_2] = fdct_wrapping_window(coord_2);
    lowpass_1 = [wl_1, ones(1,2*floor(M1)+1), wr_1];
    lowpass_2 = [wl_2, ones(1,2*floor(M2)+1), wr_2];
    lowpass_next = lowpass_1'*lowpass_2;
    hipass = sqrt(1 - lowpass_next.^2);
    Xj = zeros(2*floor(4*M1)+1,2*floor(4*M2)+1);
    
    % Loop: angles
    l = 0;
    nbquadrants = 2 + 2*(~is_real);
    nbangles_perquad = nbangles(j)/4;
    for quadrant = 1:nbquadrants
        
        M_horiz = M2 * (mod(quadrant,2)==1) + M1 * (mod(quadrant,2)==0);
        M_vert = M1 * (mod(quadrant,2)==1) + M2 * (mod(quadrant,2)==0);
        if mod(nbangles_perquad,2),
            wedge_ticks_left = round((0:(1/(2*nbangles_perquad)):.5)*2*floor(4*M_horiz) + 1);
            wedge_ticks_right = 2*floor(4*M_horiz) + 2 - wedge_ticks_left;
            wedge_ticks = [wedge_ticks_left, wedge_ticks_right(end:-1:1)];
        else
            wedge_ticks_left = round((0:(1/(2*nbangles_perquad)):.5)*2*floor(4*M_horiz) + 1);
            wedge_ticks_right = 2*floor(4*M_horiz) + 2 - wedge_ticks_left;
            wedge_ticks = [wedge_ticks_left, wedge_ticks_right((end-1):-1:1)];
        end;
        wedge_endpoints = wedge_ticks(2:2:(end-1));         % integers
        wedge_midpoints = (wedge_endpoints(1:(end-1)) + wedge_endpoints(2:end))/2;
        
        % Left corner wedge
        
        l = l+1;
        first_wedge_endpoint_vert = round(2*floor(4*M_vert)/(2*nbangles_perquad) + 1);
        length_corner_wedge = floor(4*M_vert) - floor(M_vert) + ceil(first_wedge_endpoint_vert/4);
        Y_corner = 1:length_corner_wedge;
        [XX,YY] = meshgrid(1:(2*floor(4*M_horiz)+1),Y_corner);
        width_wedge = wedge_endpoints(2) + wedge_endpoints(1) - 1;
        slope_wedge = (floor(4*M_horiz) + 1 - wedge_endpoints(1))/floor(4*M_vert);
        left_line = round(2 - wedge_endpoints(1) + slope_wedge*(Y_corner - 1));
        [wrapped_XX, wrapped_YY] = deal(zeros(length_corner_wedge,width_wedge));
        first_row = floor(4*M_vert)+2-ceil((length_corner_wedge+1)/2)+...
            mod(length_corner_wedge+1,2)*(quadrant-2 == mod(quadrant-2,2));
        first_col = floor(4*M_horiz)+2-ceil((width_wedge+1)/2)+...
            mod(width_wedge+1,2)*(quadrant-3 == mod(quadrant-3,2));
        
        for row = Y_corner
            cols = left_line(row) + mod((0:(width_wedge-1))-(left_line(row)-first_col),width_wedge);
            new_row = 1 + mod(row - first_row, length_corner_wedge);
            admissible_cols = round(1/2*(cols+1+abs(cols-1)));
            wrapped_XX(new_row,:) = XX(row,admissible_cols);
            wrapped_YY(new_row,:) = YY(row,admissible_cols);
        end;

        slope_wedge_right = (floor(4*M_horiz)+1 - wedge_midpoints(1))/floor(4*M_vert);
        mid_line_right = wedge_midpoints(1) + slope_wedge_right*(wrapped_YY - 1);
                                                            % not integers
                                                            % in general
        coord_right = 1/2 + floor(4*M_vert)/(wedge_endpoints(2) - wedge_endpoints(1)) * ...
            (wrapped_XX - mid_line_right)./(floor(4*M_vert)+1 - wrapped_YY);
        C2 = 1/(1/(2*(floor(4*M_horiz))/(wedge_endpoints(1) - 1) - 1) + 1/(2*(floor(4*M_vert))/(first_wedge_endpoint_vert - 1) - 1));
        C1 = C2 / (2*(floor(4*M_vert))/(first_wedge_endpoint_vert - 1) - 1);
        wrapped_XX((wrapped_XX - 1)/floor(4*M_horiz) + (wrapped_YY-1)/floor(4*M_vert) == 2) = ...
            wrapped_XX((wrapped_XX - 1)/floor(4*M_horiz) + (wrapped_YY-1)/floor(4*M_vert) == 2) + 1;
        coord_corner = C1 + C2 * ((wrapped_XX - 1)/(floor(4*M_horiz)) - (wrapped_YY - 1)/(floor(4*M_vert))) ./ ...
            (2-((wrapped_XX - 1)/(floor(4*M_horiz)) + (wrapped_YY - 1)/(floor(4*M_vert))));
        wl_left = fdct_wrapping_window(coord_corner);
        [wl_right,wr_right] = fdct_wrapping_window(coord_right);
        switch is_real
         case 0
          wrapped_data = fftshift(fft2(ifftshift(C{j}{l})))/sqrt(prod(size(C{j}{l})));
          wrapped_data = rot90(wrapped_data,(quadrant-1));
         case 1
          x = C{j}{l} + sqrt(-1)*C{j}{l+nbangles(j)/2};
          wrapped_data = fftshift(fft2(ifftshift(x)))/sqrt(prod(size(x)))/sqrt(2);
          wrapped_data = rot90(wrapped_data,(quadrant-1));
        end;
        wrapped_data = wrapped_data .* (wl_left .* wr_right);
 
        % Unwrapping data
        for row = Y_corner
            cols = left_line(row) + mod((0:(width_wedge-1))-(left_line(row)-first_col),width_wedge);
            admissible_cols = round(1/2*(cols+1+abs(cols-1)));
            new_row = 1 + mod(row - first_row, length_corner_wedge);
            Xj(row,admissible_cols) = Xj(row,admissible_cols) + wrapped_data(new_row,:);
                                % We use the following property: in an assignment
                                % A(B) = C where B and C are vectors, if
                                % some value x repeats in B, then the
                                % last occurrence of x is the one
                                % corresponding to the eventual assignment.
        end;

        % Regular wedges
        length_wedge = floor(4*M_vert) - floor(M_vert);
        Y = 1:length_wedge;
        first_row = floor(4*M_vert)+2-ceil((length_wedge+1)/2)+...
            mod(length_wedge+1,2)*(quadrant-2 == mod(quadrant-2,2));
        for subl = 2:(nbangles_perquad-1);
            l = l+1;
            width_wedge = wedge_endpoints(subl+1) - wedge_endpoints(subl-1) + 1;
            slope_wedge = ((floor(4*M_horiz)+1) - wedge_endpoints(subl))/floor(4*M_vert);
            left_line = round(wedge_endpoints(subl-1) + slope_wedge*(Y - 1));
            [wrapped_XX, wrapped_YY] = deal(zeros(length_wedge,width_wedge));
            first_col = floor(4*M_horiz)+2-ceil((width_wedge+1)/2)+...
                mod(width_wedge+1,2)*(quadrant-3 == mod(quadrant-3,2));
            for row = Y
                cols = left_line(row) + mod((0:(width_wedge-1))-(left_line(row)-first_col),width_wedge);
                new_row = 1 + mod(row - first_row, length_wedge);
                wrapped_XX(new_row,:) = XX(row,cols);
                wrapped_YY(new_row,:) = YY(row,cols);
            end;
            slope_wedge_left = ((floor(4*M_horiz)+1) - wedge_midpoints(subl-1))/floor(4*M_vert);
            mid_line_left = wedge_midpoints(subl-1) + slope_wedge_left*(wrapped_YY - 1);
            coord_left = 1/2 + floor(4*M_vert)/(wedge_endpoints(subl) - wedge_endpoints(subl-1)) * ...
                (wrapped_XX - mid_line_left)./(floor(4*M_vert)+1 - wrapped_YY);
            slope_wedge_right = ((floor(4*M_horiz)+1) - wedge_midpoints(subl))/floor(4*M_vert);
            mid_line_right = wedge_midpoints(subl) + slope_wedge_right*(wrapped_YY - 1);
            coord_right = 1/2 + floor(4*M_vert)/(wedge_endpoints(subl+1) - wedge_endpoints(subl)) * ...
                (wrapped_XX - mid_line_right)./(floor(4*M_vert)+1 - wrapped_YY);
            wl_left = fdct_wrapping_window(coord_left);
            [wl_right,wr_right] = fdct_wrapping_window(coord_right);
            switch is_real
             case 0
              wrapped_data = fftshift(fft2(ifftshift(C{j}{l})))/sqrt(prod(size(C{j}{l})));
              wrapped_data = rot90(wrapped_data,(quadrant-1));
             case 1
              x = C{j}{l} + sqrt(-1)*C{j}{l+nbangles(j)/2};
              wrapped_data = fftshift(fft2(ifftshift(x)))/sqrt(prod(size(x)))/sqrt(2);
              wrapped_data = rot90(wrapped_data,(quadrant-1));
            end;
            wrapped_data = wrapped_data .* (wl_left .* wr_right);
            
            % Unwrapping data
            for row = Y
                cols = left_line(row) + mod((0:(width_wedge-1))-(left_line(row)-first_col),width_wedge);
                new_row = 1 + mod(row - first_row, length_wedge);
                Xj(row,cols) = Xj(row,cols) + wrapped_data(new_row,:);
            end;

        end;    % for subl
        
        % Right corner wedge
        l = l+1;
        width_wedge = 4*floor(4*M_horiz) + 3 - wedge_endpoints(end) - wedge_endpoints(end-1);
        slope_wedge = ((floor(4*M_horiz)+1) - wedge_endpoints(end))/floor(4*M_vert);
        left_line = round(wedge_endpoints(end-1) + slope_wedge*(Y_corner - 1));
        [wrapped_XX, wrapped_YY] = deal(zeros(length_corner_wedge,width_wedge));
        first_row = floor(4*M_vert)+2-ceil((length_corner_wedge+1)/2)+...
            mod(length_corner_wedge+1,2)*(quadrant-2 == mod(quadrant-2,2));
        first_col = floor(4*M_horiz)+2-ceil((width_wedge+1)/2)+...
            mod(width_wedge+1,2)*(quadrant-3 == mod(quadrant-3,2));

  

 

  
1
  
2
  
3
  
4
  
5
  
6
  
7
  
8
  
9
  
10
  
11
  
12
  
13
  
14
  
15
  
16
  
17
  
18
  
19
  
20
  
21
  
22
  
23
  
24
  
25
  
26
  
27
  
28
  
29
  
30
  
31
  
32
  
33
  
34
  
35
  
36
  
37
  
38
  
39
  
40
  
41
  
42
  
43
  
44
  
45
  
46
  
47
  
48
  
49
  
50
  
51
  
52
  
53
  
54
  
55
  
56
  
57
  
58
  
59
  
60
  
61
  
62
  
63
  
64
  
65
  
66
  
67
  
68
  
69
  
70
  
71
  
72
  
73
  
74
  
75
  
76
  
77
  
78
  
79
  
80
  
81
  
82
  
83
  
84
  
85
  
86
  
87
  
88
  
89
  
90
  
91
  
92
  
93
  
94
  
95
  
96
  
97
  
98
  
99
  
100
  
101
  
102
  
103
  
104
  
105
  
106
  
107
  
108
  
109
  
110
  
111
  
112
  
113
  
114
  
115
  
116
  
117
  
118
  
119
  
120
  
121
  
122
  
123
  
124
  
125
  
126
  
127
  
128
  
129
  
130
  
131
  
132
  
133
  
134
  
135
  
136
  
137
  
138
  
139
  
140
  
141
  
142
  
143
  
144
  
145
  
146
  
147
  
148
  
149
  
150
  
151
  
152
  
153
  
154
  
155
  
156
  
157
  
158
  
159
  
160
  
161
  
162
  
163
  
164
  
165
  
166
  
167
  
168
  
169
  
170
  
171
  
172
  
173
  
174
  
175
  
176
  
177
  
178
  
179
  
180
  
181
  
182
  
183
  
184
  
185
  
186
  
187
  
188
  
189
  
190
  
191
  
192
  
193
  
194
  
195
  
196
  
197
  
198
  
199
  
200
  
201
  
202
  
203
  
204
  
205
  
206
  
207
  
208
  
209
  
210
  
211
  
212
  
213
  
214
  
215
  
216
  
217
  
218
  
219
  
220
  
221
  
222
  
223
  
224
  
225
  
226
  
227
  
228
  
229
  
230
  
231
  
232
  
233
  
234
  
235
  
236
  
237
  
238
  
239
  
240
  
241
  
242
  
243
 

三、运行结果

四、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
[1] 蔡利梅.MATLAB图像处理——理论、算法与实例分析[M].清华大学出版社，2020.
[2]杨丹,赵海滨,龙哲.MATLAB图像处理实例详解[M].清华大学出版社，2013.
[3]周品.MATLAB图像处理与图形用户界面设计[M].清华大学出版社，2013.
[4]刘成龙.精通MATLAB图像处理[M].清华大学出版社，2015.

文章来源: qq912100926.blog.csdn.net，作者：海神之光，版权归原作者所有，如需转载，请联系作者。

原文链接：qq912100926.blog.csdn.net/article/details/115683311