MATLAB:定位手掌最大内切圆

最近要做的一件事就是：对于一份给定的手掌图，要定位可寻的最大内切圆。做了近12个小时，才终于解决了这个问题，下面记录一下过程。

1、图片在MATLAB里是个矩阵，如何在矩阵作圆：

function [] = DrawCircle( Image, Centre, Radius )
figure, imshow(Image), hold on;
t = 0:0.01:2*pi;
x = round(Radius*cos(t) + Centre(1));
y = round(Radius*sin(t) + Centre(2));
%fill(x, y, 'w');
plot(x, y, '-r','LineWidth', 1);
plot(Centre(1), Centre(2), '*r');
end

2、如何实现内切圆心的定位：

% GA algorithm
optionsOrigin = gaoptimset('Generations', 50,...
                           'PopInitRange',[0;min(Width,Length)],...
                           'PopulationSize',ceil(min(Width,Length)/10));
[x, fval] = ga(@fitnessfcn, 3, optionsOrigin);
Centre = [x(1), x(2)];
Radius = fval;
str = sprintf('\nCentre = %f, Radius = %f', Centre, Radius);
disp(str);

3、如何实现内切圆圆半径的确定；

function [ Result ] = CalRadius( Centre, Radius)
global BinaryImage
r = floor(linspace(Radius, 0, ceil(log(Radius+1)+1)));
N = length(r);
t = 0:0.01:2*pi;
n = length(t);
for i = 1:1:N
    disp(r(i));
    x = floor(Centre(1) + r(i)*sin(t));
    y = floor(Centre(2) + r(i)*cos(t));
    BlackPointFound = false;
    for j = 1:1:n
        if BinaryImage(y(j), x(j))==0
            BlackPointFound = true;
            break;
        else
            continue;
        end
    end
    if false == BlackPointFound
        Result = r(i);
        return;
    end
end
Result=0;
end

5、结果思考

速度慢：智能算法没进一步精确

圆半径精度不足：采的迭代算法不够细致，但过于细致会使速度下降