[快速阅读八] Matlab中bwlookup的实现及其在计算二值图像的欧拉数、面积及其他morph变形中的应用。...

　　以前看过matlab的bwlookup函数，但是总感觉有点神秘，一直没有去仔细分析，最近在分析计算二值图像的欧拉数时，发现自己写的代码和matlab的总是对不少，于是又去翻了下matlab的源代码，看到了matlab里实现欧拉数的代码非常简单，如下所示：

if n==4
    lut = 4*[0 0.25 0.25 0 0.25 0  .5 -0.25 0.25  0.5  0 -0.25 0 ...
             -0.25 -0.25 0] + 2;
else
    lut = 4*[0 0.25 0.25 0 0.25 0 -.5 -0.25 0.25 -0.5  0 -0.25 0 ...
             -0.25 -0.25 0] + 2;
end
% Need to zero-pad the input
b = padarray(a,[1 1],'both');

weights = bwlookup(b,lut);
if coder.isColumnMajor
    e = (sum(weights(:),'double') - 2*numel(b)) / 4;
else
    e = (sum(sum(weights,2,'double'),1,'double') - 2*numel(b)) / 4;
end

　　在内部就是调用了bwlookup函数，那没办法了，就仔细看了M的帮助文档，发现原来这个函数真的非常简单，我们贴下M的帮助文档：

　　A = bwlookup(BW,lut)

　　The bwlookup function performs these steps to determine the value of each pixel in the processed image A:

• Locate the pixel neighborhood in input image BW based on the coordinates of the target pixel in A. The function zero-pads border pixels of image BW when the neighborhood extends past the edge of BW.

• Calculate an index, idx, based on the binary pixel pattern of the neighborhood.

• Set the target pixel in A as the value of the lookup table at the index idx, in other words, the value of lut(idx).

2-by-2 Neighborhood Lookup

For 2-by-2 neighborhoods, there are four pixels in each neighborhood. Each binary pixel has two possible states, therefore the total number of permutations is 24 and the length of the lookup table lut is 16.

To find the value of the target output pixel at (row, column) coordinate (r,c), bwlookup uses the 2-by-2 pixel neighborhood in the input binary image BW whose top left pixel is at coordinate (r,c). The index idx into the lookup table is the weighted sum of the four pixels in the neighborhood, plus 1.