归一化交叉相关Normalization cross correlation (NCC)

归一化交叉相关Normalization cross correlation (NCC)

相关系数，图像匹配

NCC正如其名字，是用来描述两个目标的相关程度的，也就是说可以用来刻画目标间的相似性。一般NCC也会被用来进行图像匹配，即在一个图像中搜索与一小块已知区域的NCC最高的区域作为对应匹配，然后对准整幅图像。

假设两幅图像,那么其NCC可如下计算：

其中表示点乘运算。

比如下面两幅图像，我们想对齐

part1.jpg

part2.jpg

首先在一幅图像中选取两个图像都有的区域作为templete

templete.jpg

然后在另一幅图像中选取包含templete的区域

region.jpg

最终对齐的结果如下

result.jpg

1. function NCC 
   

   ---

2. close all 
   

   ---

3. part2 =imread('part1.png'); 
   

   ---

4. part1 = imread('part2.png'); 
   

   ---

5. ---

6. imshow(part2);title('part2') 
   

   ---

7. figure, imshow(part1);title('part1'); 
   

   ---

8. % 选取template和搜索区域region. Note:template的大小必须小于region 
   

   ---

9. figure, 
   

   ---

10. [sub_part2,rect_part2]=imcrop(part2);% template 
    

    ---

11. [sub_part1,rect_part1]=imcrop(part1);% region 
    

    ---

12. ---

13. figure, imshow(sub_part2) 
    

    ---

14. figure, imshow(sub_part1); 
    

    ---

15. ---

16. [x,y,z] = normcorr2(double(sub_part2(:,:,1)),double(sub_part1(:,:,1))); 
    

    ---

17. figure,surf(x,y,z),shading flat 
    

    ---

18. %% 寻找偏置 
    

    ---

19. [~,imax]=max(z(:));% 
    

    ---

20. [yoffset,xoffset]=ind2sub(size(z),imax(1)); 
    

    ---

21. %% 图像对齐 
    

    ---

22. % 配对点在第一幅图像中到边界的距离 
    

    ---

23. ---

24. rect_part1=floor(rect_part1); 
    

    ---

25. left1=rect_part1(1)+xoffset; 
    

    ---

26. right1=size(part1,2)-left1; 
    

    ---

27. up1=rect_part1(2)+yoffset; 
    

    ---

28. down1 = size(part1,1)-left1; 
    

    ---

29. % 配对点在第二幅图像中到边界的距离 
    

    ---

30. rect_part2=floor(rect_part2); 
    

    ---

31. left2=rect_part2(1); 
    

    ---

32. right2=size(part2,2)-left2; 
    

    ---

33. up2=rect_part2(2); 
    

    ---

34. down2 = size(part2,1)-up2; 
    

    ---

35. ---

36. img=zeros(max(up1,up2)+max(down1,down2)+1,max(left1,left2)+max(right1,right2)+1,size(part1,3)); 
    

    ---

37. sx=max(left1,left2)+1; 
    

    ---

38. sy=max(up1,up2)+1; 
    

    ---

39. img(sy-up1+1:sy-up1+size(part1,1),sx-left1+1:sx-left1+size(part1,2),:)=part1; 
    

    ---

40. img(sy-up2+1:sy-up2+size(part2,1),sx-left2+1:sx-left2+size(part2,2),:)=part2; 
    

    ---

41. imshow(uint8(img)); 
    

    ---

42. end 
    

    ---

43. ---

44. ---

45. ---

46. function [x,y,z]=normcorr2(I1,I2) 
    

    ---

47. % I1,I2是单通道图像，即矩阵 
    

    ---

48. % I1 is template 
    

    ---

49. % I2 is the region where match pairs are searched 
    

    ---

50. [m1,n1]=size(I1); 
    

    ---

51. [m2,n2]=size(I2); 
    

    ---

52. z=conv2(I2,rot90(I1,2),'valid'); 
    

    ---

53. im2=cumsum(I2.^2,1); 
    

    ---

54. im2=cumsum(im2,2); 
    

    ---

55. sum1=sum(sum(I1.^2,1),2); 
    

    ---

56. % nz=zeros(m2-m1+1,n2-n1+1); 
    

    ---

57. wrapIm2=zeros(1+m2,1+n2); 
    

    ---

58. wrapIm2(2:end,2:end)=im2; 
    

    ---

59. nz=(wrapIm2(m1+1:m2+1,n1+1:n2+1)+wrapIm2(1:m2-m1+1,1:n2-n1+1)-wrapIm2(1:m2-m1+1,n1+1:n2+1)-wrapIm2(m1+1:m2+1,1:n2-n1+1))*sum1; 
    

    ---

60. nz=sqrt(nz); 
    

    ---

61. z=z./nz; 
    

    ---

62. [x,y]=meshgrid(1:n2-n1+1,1:m2-m1+1); 
    

    ---

63. end 
    

    ---

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有些文献在计算卷积的时候，总说要把矩阵逆排序之后再对应相乘，包括conv2这个函数也是这么计算的。但实际上我们有一个templete和region，直接就是对应位置乘积之后作为卷积结果，也只有这样才能保证在匹配的位置处NCC系数最大，所以在代码里，我先对templete进行了逆序操作，在使用conv2卷积。

另外matlab2016添加了image registration 工具箱，里面可以直接计算NCC系数了，具体参见

http://cn.mathworks.com/help/images/examples/registering-an-image-using-normalized-cross-correlation.html.