1.m

实现对小孔的高斯滤波

 %以下粗略算一下圆心的坐标
 labmax=max(ma);%横纵坐标的最大值
 labmin=min(ma);%横纵坐标的最小值
 rx=(labmax(1,1)+labmin(1,1))/2;%圆心的横坐标
 ry=(labmax(1,2)+labmin(1,2))/2;%圆心的纵坐标
 r=zeros(1,length(ma(:,1)));
 for m=1:length(ma(:,1))
     r(1,m)=sqrt((ma(m,1)-rx)^2+(ma(m,2)-ry)^2);
 end
 r=sum(r)/length(r);%半径的平均值
 
 
 p1=polyfit(x1,y2,2);
 m1=polyval(p1,x1);
 subplot(222)
 plot(x1,m1,'-')
 title('(X-b).^2=-Y.^2+2*a*Y+R.^2-a.^2')
 p2=polyfit(y1,x2,2);
 m2=polyval(p2,y1);
 subplot(223)
 plot(y1,m2,'-')
 title('(Y-a).^2=-X.^2+2*b*X+R.^2-b.^2')
 xaxis=p1(3);
 yaxis=p2(3);
 x3=x2-xaxis;
 y3=y2-yaxis;
 x4=x3.^2;
 y4=y3.^2;
 p3=polyfit(x4,y4,1)
 m3=polyval(p3,x4);
 subplot(224)
 plot(x4,m3,'-');
 title('横纵坐标之间的线性关系')
 r0=sqrt(p3(2))
 %用偏导数来求
 p4=polyfit(2*x2,y2,2)
 b=-1*p4(2)/2
 
 
  C=N*sum(x1.^2)-sum(x1)*sum(x1);
 D=N*sum(x1.*y1)-sum(x1)*sum(y1);
 E=N*(sum(x1).^3)+N*(sum(x1.*(y1.^2)))-sum(x1.^2+y1.^2)*sum(x1);
 G=N*sum(y1.^2)-sum(y1)*sum(y1);
 H=N*sum((x1.^2).*y1)+N*sum(y1.^3)-sum(x1.^2+y1.^2)*sum(y1);
 a=(H*D-E*G)/(C*G-D*D);
 b=(H*C-E*D)/(D*D-G*C);
 c=-(sum(x1.^2+y1.^2)+a*sum(x1)+b*sum(y1))/N;
 A=-1*a/2
 B=-1*b/2
 R=0.5*sqrt(a*a+b*b-4*c)