距离变换

距离变换和线性滤波器，形态学变换处于平等位置，是图像处理的一种方法，通过使用两遍扫描光栅算法可以快速计算到曲线或点集的距离。

应用：

水平集

快速斜切匹配

图像拼接

图像混合的羽化

临近点配准

方法：

首先对图像进行二值化处理，然后给每个像素赋值为离它最近的背景像素点与其距离（Manhattan距离or欧氏距离），得到distance metric(距离矩阵)，那么离边界越远的点越亮。

实现：

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

或者单纯想看这几个距离函数的区别可以用以下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)