距離變換

轉自：http://blog.csdn.net/abcjennifer/article/details/7617883 

距離變換和線性濾波器，形態學變換處於平等位置，是圖像處理的一種方法，通過使用兩遍掃描光柵算法可以快速計算到曲線或點集的距離。

應用：

水平集

快速斜切匹配

圖像拼接

圖像混合的羽化

臨近點配準

方法：

首先對圖像進行二值化處理，然後給每個像素賦值爲離它最近的背景像素點與其距離（Manhattan距離or歐氏距離），得到distance metric(距離矩陣)，那麼離邊界越遠的點越亮。

                      

Imgori=imread('test.jpg');
I=rgb2gray(Imgori);
subplot(2,3,1);imshow(I);title('origin');

Threshold=100;
F=I>Threshold;%front
%B=I<=Threshold;%background
subplot(2,3,4);imshow(F,[]);title('binary');

T=bwdist(F,'chessboard');
subplot(2,3,2);imshow(T,[]);title('chessboard distance transform')
%the chessboard distance between (x1,y1) and (x2,y2) is max(│x1 – x2│,│y1 – y2│).

T=bwdist(F,'cityblock');
subplot(2,3,3);imshow(T,[]);title('chessboard distance transform')
%the cityblock distance between (x1,y1) and (x2,y2) is │x1 – x2│ + │y1 – y2│.

T=bwdist(F,'euclidean');
subplot(2,3,5);imshow(T,[]);title('euclidean distance transform')
%use Euclidean distance

T=bwdist(F,'quasi-euclidean');
subplot(2,3,6);imshow(T,[]);title('quasi-euclidean distance transform')
%use quasi-Euclidean distance

或者單純想看這幾個距離函數的區別可以用以下code：

bw = zeros(200,200); bw(50,50) = 1; bw(50,150) = 1;
bw(150,100) = 1;
D1 = bwdist(bw,'euclidean');
D2 = bwdist(bw,'cityblock');
D3 = bwdist(bw,'chessboard');
D4 = bwdist(bw,'quasi-euclidean');
figure
subplot(2,2,1), subimage(mat2gray(D1)), title('Euclidean')
hold on, imcontour(D1)
subplot(2,2,2), subimage(mat2gray(D2)), title('City block')
hold on, imcontour(D2)
subplot(2,2,3), subimage(mat2gray(D3)), title('Chessboard')
hold on, imcontour(D3)
subplot(2,2,4), subimage(mat2gray(D4)), title('Quasi-Euclidean')
hold on, imcontour(D4)