%%%三维平面拟合
%%%生成随机数据
%内点
mu=[0 0 0]; %均值
S=[2 0 4;0 4 0;4 0 8]; %协方差
data1=mvnrnd(mu,S,300); %产生200个高斯分布数据
%外点
mu=[2 2 2];
S=[8 1 4;1 8 2;4 2 8]; %协方差
data2=mvnrnd(mu,S,100); %产生100个噪声数据
%合并数据
data=[data1',data2'];
iter = 1000;
%%% 绘制数据点
figure;plot3(data(1,:),data(2,:),data(3,:),'o');hold on; % 显示数据点
number = size(data,2); % 总点数
bestParameter1=0; bestParameter2=0; bestParameter3=0; % 最佳匹配的参数
sigma = 1;
pretotal=0; %符合拟合模型的数据的个数
for i=1:iter
%%% 随机选择三个点
idx = randperm(number,3);
sample = data(:,idx);
%%%拟合直线方程 z=ax+by+c
plane = zeros(1,3);
x = sample(:, 1);
y = sample(:, 2);
z = sample(:, 3);
a = ((z(1)-z(2))*(y(1)-y(3)) - (z(1)-z(3))*(y(1)-y(2)))/((x(1)-x(2))*(y(1)-y(3)) - (x(1)-x(3))*(y(1)-y(2)));
b = ((z(1) - z(3)) - a * (x(1) - x(3)))/(y(1)-y(3));
c = z(1) - a * x(1) - b * y(1);
plane = [a b -1 c]
mask=abs(plane*[data; ones(1,size(data,2))]); %求每个数据到拟合平面的距离
total=sum(mask
if total>pretotal %找到符合拟合平面数据最多的拟合平面
pretotal=total;
bestplane=plane; %找到最好的拟合平面
end
end
%显示符合最佳拟合的数据
mask=abs(bestplane*[data; ones(1,size(data,2))]) hold on;
k = 1;
for i=1:length(mask)
if mask(i)
inliers(1,k) = data(1,i);
inliers(2,k) = data(2,i);
plot3(data(1,i),data(2,i),data(3,i),'r+');
k = k+1;
end
end
%%% 绘制最佳匹配平面
bestParameter1 = bestplane(1);
bestParameter2 = bestplane(2);
bestParameter3 = bestplane(4);
xAxis = min(inliers(1,:)):max(inliers(1,:));
yAxis = min(inliers(2,:)):max(inliers(2,:));
[x,y] = meshgrid(xAxis, yAxis);
z = bestParameter1 * x + bestParameter2 * y + bestParameter3;
surf(x, y, z);
title(['bestPlane: z = ',num2str(bestParameter1),'x + ',num2str(bestParameter2),'y + ',num2str(bestParameter3)]);