Matlab傅立叶描述符有什么问题？

Question

我正在使用 Gonzalez frdescp 函数来获取边界的傅立叶描述符。我使用这段代码，得到了两组完全不同的数字，它们描述了两个相同但比例不同的形状。

怎么了？

im = imread('c:\classes\a1.png');
im = im2bw(im);
b = bwboundaries(im);
f = frdescp(b{1}); // fourier descriptors for the boundary of the first object ( my   pic only contains one object anyway )
// Normalization
f = f(2:20); // getting the first 20 & deleting the dc component
f = abs(f) ;
f = f/f(1);

为什么相同但比例不同的两个圆圈会得到不同的描述符？

Answer 1

问题是 frdescp 代码(我使用了 this code ，应该与您提到的相同)也是为了使傅立叶描述符居中而编写的。

如果您想以正确的方式描述您的形状，则必须保留一些关于表示直流分量的描述符是对称的。

下图总结了这个概念:

为了解决您的问题(以及其他类似您的问题)，我编写了以下两个函数:

function descriptors = fourierdescriptor( boundary )
    %I assume that the boundary is a N x 2 matrix
    %Also, N must be an even number

    np = size(boundary, 1);

    s = boundary(:, 1) + i*boundary(:, 2);

    descriptors = fft(s);

    descriptors = [descriptors((1+(np/2)):end); descriptors(1:np/2)];
end

function significativedescriptors = getsignificativedescriptors( alldescriptors, num )
    %num is the number of significative descriptors (in your example, is was 20)
    %In the following, I assume that num and size(alldescriptors,1) are even numbers

    dim = size(alldescriptors, 1);

    if num >= dim
        significativedescriptors = alldescriptors;
    else
        a = (dim/2 - num/2) + 1;
        b = dim/2 + num/2;

        significativedescriptors = alldescriptors(a : b);
    end
end

知道了，你可以按如下方式使用上面的函数:

im = imread('test.jpg');
im = im2bw(im);
b = bwboundaries(im);
b = b{1};

%force the number of boundary points to be even
if mod(size(b,1), 2) ~= 0
    b = [b; b(end, :)];
end

%define the number of significative descriptors I want to extract (it must be even)
numdescr = 20;

%Now, you can extract all fourier descriptors...
f = fourierdescriptor(b);
%...and get only the most significative:
f_sign = getsignificativedescriptors(f, numdescr);