圖像拼接——多波段融合(multi blend)

概述

圖像拼接一般包括warp(映射), compensation(光照補償)和blend(融合)三部分。
warp部分主要取決於相機參數估計的準確性，光照補償主要用於解決不同圖像曝光不同所帶來的輸出圖像的不同局部的光照差異，而blend則用於融合不同圖像之間的重疊部分，一般使用線性加權的方式來得到最終的輸出圖像。

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多波段融合(multi blend)

多波段融合的基本思想是圖像可以分解爲不同頻率的圖像的疊加（類似於傅里葉變換），在不同的頻率上，應該使用不同的權重來進行融合，在低頻部分應該使用波長較寬的加權信號（例如高斯核函數中sigma比較大），在高頻部分應該使用較窄的加權信號（例如高斯核函數的sigma比較小），其算法如下：

1. 計算輸入圖像的高斯金字塔。如果輸入圖像是A,B ，則計算GA0,GA1,GA2,GA3,… 和GB0,GB1,GB2,GB3,… (如何計算高斯金字塔？)
2. 計算輸入圖像的拉普拉斯金字塔。記爲LA0,LA1,LA2,LA3,… 和LB0,LB1,LB2,LB3,… (如何計算拉普拉斯金字塔？)
3. 將處於同一級的拉普拉斯金字塔進行融合。例如在拼接縫兩側使用簡單的線性融合。記輸出圖像爲C ，則這裏得到LC0,LC1…
4. 將高層的拉普拉斯金字塔依次擴展直至和LC0 相同分辨率。我們記做LC00,LC11,LC22…
5. 將4中得到的圖像依次疊加，則得到最終的輸出圖像C 。

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代碼實現

使用matlab實現多波段算法如下：

function C = multi_blend(A, B);

%resize A,B,C to the same size
A_size = size(A);
B_size = size(B);
C_size = [512,512];
if(A_size ~= C_size)
    A = imresize(A,C_size);
end
if(B_size ~= C_size)
    B = imresize(B,C_size);
end

%gaussian kernel
kernel=fspecial('gaussian',[5 5],1);

%obtain the Gauss Pyramid
G_A0 = A;
G_A1 = conv2(G_A0,kernel,'same');
G_A1 = G_A1(2:2:size(G_A1,1),2:2:size(G_A1,2));
G_A2 = conv2(G_A1,kernel,'same');
G_A2 = G_A2(2:2:size(G_A2,1),2:2:size(G_A2,2));
G_A3 = conv2(G_A2,kernel,'same');
G_A3 = G_A3(2:2:size(G_A3,1),2:2:size(G_A3,2));
G_A4 = conv2(G_A3,kernel,'same');
G_A4 = G_A4(2:2:size(G_A4,1),2:2:size(G_A4,2));
G_A5 = conv2(G_A4,kernel,'same');
G_A5 = G_A5(2:2:size(G_A5,1),2:2:size(G_A5,2));

G_B0 = B;
G_B1 = conv2(G_B0,kernel,'same');
G_B1 = G_B1(2:2:size(G_B1,1),2:2:size(G_B1,2));
G_B2 = conv2(G_B1,kernel,'same');
G_B2 = G_B2(2:2:size(G_B2,1),2:2:size(G_B2,2));
G_B3 = conv2(G_B2,kernel,'same');
G_B3 = G_B3(2:2:size(G_B3,1),2:2:size(G_B3,2));
G_B4 = conv2(G_B3,kernel,'same');
G_B4 = G_B4(2:2:size(G_B4,1),2:2:size(G_B4,2));
G_B5 = conv2(G_B4,kernel,'same');
G_B5 = G_B5(2:2:size(G_B5,1),2:2:size(G_B5,2));

%get Laplacian Pyramid
L_A0 = double(G_A0)-imresize(G_A1,size(G_A0));
L_A1 = double(G_A1)-imresize(G_A2,size(G_A1));
L_A2 = double(G_A2)-imresize(G_A3,size(G_A2));
L_A3 = double(G_A3)-imresize(G_A4,size(G_A3));
L_A4 = double(G_A4)-imresize(G_A5,size(G_A4));
L_A5 = double(G_A5);

L_B0 = double(G_B0)-imresize(G_B1,size(G_B0));
L_B1 = double(G_B1)-imresize(G_B2,size(G_B1));
L_B2 = double(G_B2)-imresize(G_B3,size(G_B2));
L_B3 = double(G_B3)-imresize(G_B4,size(G_B3));
L_B4 = double(G_B4)-imresize(G_B5,size(G_B4));
L_B5 = double(G_B5);

%construct the mask
size0 = size(L_A0);
mask0 = zeros(size0);
mask0(:,1:size0(2)/2)=1;
mask0(:,size0(2)/2-5:1:size0(2)/2+5)=repmat(1:-0.1:0,[size0(1) 1]);
size1 = size(L_A1);
mask1 = zeros(size1);
mask1(:,1:size1(2)/2)=1;
mask1(:,size1(2)/2-5:1:size1(2)/2+5)=repmat(1:-0.1:0,[size1(1) 1]);
size2 = size(L_A2);
mask2 = zeros(size2);
mask2(:,1:size2(2)/2)=1;
mask2(:,size2(2)/2-5:1:size2(2)/2+5)=repmat(1:-0.1:0,[size2(1) 1]);
size3 = size(L_A3);
mask3 = zeros(size3);
mask3(:,1:size3(2)/2)=1;
mask3(:,size3(2)/2-5:1:size3(2)/2+5)=repmat(1:-0.1:0,[size3(1) 1]);
size4 = size(L_A4);
mask4 = zeros(size4);
mask4(:,1:size4(2)/2)=1;
mask4(:,size4(2)/2-5:1:size4(2)/2+5)=repmat(1:-0.1:0,[size4(1) 1]);
size5 = size(L_A5);
mask5 = zeros(size5);
mask5(:,1:size5(2)/2)=1;
mask5(:,size5(2)/2-5:1:size5(2)/2+5)=repmat(1:-0.1:0,[size5(1) 1]);

%obtain the output
L_C0 = L_A0 .* mask0 + L_B0 .* (1-mask0);
L_C1 = L_A1 .* mask1 + L_B1 .* (1-mask1);
L_C2 = L_A2 .* mask2 + L_B2 .* (1-mask2);
L_C3 = L_A3 .* mask3 + L_B3 .* (1-mask3);
L_C4 = L_A4 .* mask4 + L_B4 .* (1-mask4);
L_C5 = L_A5 .* mask5 + L_B5 .* (1-mask5);
C = L_C0+imresize(L_C1,size0)+imresize(L_C2,size0)+imresize(L_C3,size0)+imresize(L_C4,size0)+imresize(L_C5,size0);

figure(1);
imshow(A);
figure(2);
imshow(B);
figure(3);
imshow(uint8(C));

end

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實驗效果：

輸入兩張光照差別很大的圖像：

左半部分使用左圖，右半部分使用右圖，進行多波段融合得到如下：

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每個波段融合使用的掩膜如下（白色代表左圖成分，黑色代表右圖成分）：

其中前四幅圖爲顯示方便做了偏移處理。

參考

1. P. Burt and E. Adelson. A multiresolution spline with application to image mosaics. ACM Transactions on Graphics, 2(4):217–236, 1983.
2. Matthew Brown and David G. Lowe. Automatic Panoramic Image Stitching using Invariant Features.