距離變換和線性濾波器，形態學變換處於平等位置，是影象處理的一種方法，通過使用兩遍掃描光柵演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

影象拼接

影象混合的羽化

臨近點配準

方法：

首先對影象進行二值化處理，然後給每個畫素賦值為離它最近的背景畫素點與其距離（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。

實現：

1. Imgori=imread('test.jpg');
2. I=rgb2gray(Imgori);
3. subplot(2,3,1);imshow(I);title('origin'
   );
4. Threshold=100;
5. F=I>Threshold;%front
6. %B=I<=Threshold;%background
7. subplot(2,3,4);imshow(F,[]);title('binary');
8. T=bwdist(F,'chessboard');
9. subplot(2,3,2);imshow(T,[]);title('chessboard distance transform')
10. %the chessboard distance between (x1,y1) and (x2,y2) is max(│x1 – x2│,│y1 – y2│).
11. T=bwdist(F,'cityblock'
    );
12. subplot(2,3,3);imshow(T,[]);title('chessboard distance transform')
13. %the cityblock distance between (x1,y1) and (x2,y2) is │x1 – x2│ + │y1 – y2│.
14. T=bwdist(F,'euclidean');
15. subplot(2,3,5);imshow(T,[]);title('euclidean distance transform')
16. %use Euclidean distance
17. T=bwdist(F,'quasi-euclidean');
18. subplot(2,3,6);imshow(T,[]);title('quasi-euclidean distance transform'
    )
19. %use quasi-Euclidean distance

或者單純想看這幾個距離函式的區別可以用以下code：

1. bw = zeros(200,200); bw(50,50) = 1; bw(50,150) = 1;
2. bw(150,100) = 1;
3. D1 = bwdist(bw,'euclidean');
4. D2 = bwdist(bw,'cityblock');
5. D3 = bwdist(bw,'chessboard');
6. D4 = bwdist(bw,'quasi-euclidean');
7. figure
8. subplot(2,2,1), subimage(mat2gray(D1)), title('Euclidean')
9. hold on, imcontour(D1)
10. subplot(2,2,2), subimage(mat2gray(D2)), title('City block')
11. hold on, imcontour(D2)
12. subplot(2,2,3), subimage(mat2gray(D3)), title('Chessboard')
13. hold on, imcontour(D3)
14. subplot(2,2,4), subimage(mat2gray(D4)), title('Quasi-Euclidean')
15. hold on, imcontour(D4)