改善MATLAB中的Modhausdorffdist性能

Question

有什么方法可以改善此功能的性能？它包含一个嵌套循环。我该如何进行MATLAB矢量化？

有什么办法可以从以下代码中删除for循环？

function [ mhd ] = ModHausdorffDist( A, B )

Asize = size(A);
Bsize = size(B);
% Check if the points have the same dimensions
if Asize(2) ~= Bsize(2)
    error('The dimensions of points in the two sets are not equal');
end
% Calculating the forward HD
fhd = 0;                    % Initialize forward distance to 0
for a = 1:Asize(1)          % Travel the set A to find avg of d(A,B)
    mindist = Inf;          % Initialize minimum distance to Inf
    for b = 1:Bsize(1)      % Travel set B to find the min(d(a,B))
        tempdist = norm(A(a,:)-B(b,:));
        if tempdist < mindist
            mindist = tempdist;
        end
    end
    fhd = fhd + mindist;    % Sum the forward distances
end
fhd = fhd/Asize(1);         % Divide by the total no to get average
% Calculating the reverse HD
rhd = 0;                    % Initialize reverse distance to 0
for b = 1:Bsize(1)          % Travel the set B to find avg of d(B,A)
    mindist = Inf;          % Initialize minimum distance to Inf
    for a = 1:Asize(1)      % Travel set A to find the min(d(b,A))
        tempdist = norm(A(a,:)-B(b,:));
        if tempdist < mindist
            mindist = tempdist;
        end
    end
    rhd = rhd + mindist;    % Sum the reverse distances
end
rhd = rhd/Bsize(1);         % Divide by the total no. to get average
mhd = max(fhd,rhd);         % Find the minimum of fhd/rhd as 
                            % the mod hausdorff dist

end

Answer 1

我会尝试这样的东西

D = bsxfun( @minus, permute( A, [3 1 2] ), permute( B, [1 3 2] ) );
D = sqrt(sum( D.^2, 3 )); % all pair-wise distances. 
% I think there is a pdist2 function that can do this computation
% of the distances. 
f = min( D, [], 1);
fhd = mean(f);
r = min( D, [], 2);
rhd = mean(r);
mhd = max( fhd, rhd );

计算距离矩阵D可以通过查看d_ij的表达：

d_ij^2 = || a_i ||^2 || b_j ||^2-2

这意味着A和B之间的唯一相互作用是通过MATLAB知道可以非常有效地计算的点产品。