利用多项式实现图像几何校正(Matlab实现)

房东的猫 提交于 2021-01-14 06:12:06

1.原理简述:      

      根据两幅图像中的一些已知对应点(控制点对),建立函数关系式,通过坐标变换,实现失真图像的几何校正。

                                      

      

        设两幅图像坐标系统之间畸变关系能用解析式来描述:

                             

         根据上述的函数关系,可以依次计算畸变图像每个像素的矫正坐标值,保持各像素值不变,这样生成一幅矫正图像。

2.实现过程:     

        (1)因此首先要得到多项式,matlab提供了拟合多项式的函数 Isqcurvefit,

                               格式:lsqcurvefit(f,a,x,y)

                 f:符号函数句柄

                a:最开始预估的值(预拟合的未知参数的估计值)。如上面的问题如果我们预估A为1,B为2,则a=[1 2]

                x:我们已经获知的x的值

                y:我们已经获知的x对应的y的值

               函数的返回值为对应多项式系数组成的一维数组。

示例(二次多项式):建立由校正图像到畸变图像的函数

function [F] = fun(a,b)
x = b(:,1);
y = b(:,2);
F = a(1)+a(2)*x+a(3)*y+a(4)*x.^2+a(5)*x.*y+a(6)*y.^2; 
end


x0 = fixedPoints(:,1);
y0 = fixedPoints(:,2);
x1 = movingPoints(:,1);
y1 = movingPoints(:,2);
data = [x1,y1];
a = [1 1 1 1 1 1];
a1 = lsqcurvefit('fun',a,data,x0);
a2 = lsqcurvefit('fun',a,data,y0);

         (2)根据得到的二项式,由校正图像每个像素坐标(x,y)出发,算出在已知畸变图像上的对应坐标(x',y'),使像元一一对应,赋予校正图像对应畸变图像的像元

的像素值,最终得到校正图像。

示例:

J2 = uint8(zeros(size(J)));
for rgb = 1:3
    for i = 1:m
        for j = 1:n
            if round(fun(a1,[i,j]))>=1 && round(fun(a1,[i,j]))<=c && round(fun(a2,[i,j]))>=1 && round(fun(a2,[i,j]))<=d
                 J2(i,j,rgb) = J1(round(fun(a1,[i,j])),round(fun(a2,[i,j])),rgb);
            end
        end
    end
end

          这样生成的图像像素分布不规则,会出现像素挤压、疏密不均的现象,因此最后还需对不规则图像进行灰度内插生成规则的栅格图像。

 

源码:

I = imread('sp.tif');
J = imread('tm.tif');
[m,n] = size(J);
[o,p] = size(I);
%cpselect(J,I);
%xlswrite('data1.xls',fixedPoints);
%xlswrite('data2.xls',movingPoints);


%%重采样
J1 = J(1:m/o:end,1:n/p:end,1:3);
[c,d,q]= size(J1);

fixedPoints = xlsread('data1.xls');
movingPoints = xlsread('data2.xls');
x0 = fixedPoints(:,1);
y0 = fixedPoints(:,2);
x1 = movingPoints(:,1);
y1 = movingPoints(:,2);
data = [x1,y1];
a = [1 1 1 1 1 1];
a1 = lsqcurvefit('fun',a,data,x0);
a2 = lsqcurvefit('fun',a,data,y0);
%多项式几何校正
J2 = uint8(zeros(size(J)));
for rgb = 1:3
    for i = 1:m
        for j = 1:n
            if round(fun(a1,[i,j]))>=1 && round(fun(a1,[i,j]))<=c && round(fun(a2,[i,j]))>=1 && round(fun(a2,[i,j]))<=d
                 J2(i,j,rgb) = J1(round(fun(a1,[i,j])),round(fun(a2,[i,j])),rgb);
            end
    %           J2(round(fun(a1,[i,j])),round(fun(a2,[i,j]))) = J(i,j);
    %           end
        end
    end
end
[x,y] = size(J2);

%根据数据游标取截取区域的左上方点
J3 = imcrop(I,[98 180 60*o/x 60*p/y]);
J4 = imcrop(J2,[41 80 60 60]);
[k,y,z] = size(J3);
[h,t,e] = size(J4);

%%重采样
%双线性内插法
u = h/k;
v = t/y;
itp = uint8(zeros(k,y,3));
for rgb = 1:3
    for i = ceil(1/u):k-1
        iu = floor(i*u);
        for j = ceil(1/v):y-1 
            jv = floor(j*v);
            itp(i,j,rgb) = (1-(i*u-iu))*(1-(j*v-jv))*J4(iu,jv,rgb)...
                       +(1-(i*u-iu))*(j*v-jv)*J4(iu,jv+1,rgb)...
                       +(i*u-iu)*(1-(j*v-jv))*J4(iu+1,jv,rgb)...
                       +(i*u-iu)*(j*v-jv)*J4(iu+1,jv+1,rgb);
        end
    end
end
%去黑边
for rgb = 1:3
    for i = 1:3 
        for j = 1:175
          itp(i,j,rgb) = J4(ceil(i*u),ceil(j*v),rgb);
          itp(145,j,rgb) = J4(43,ceil(j*v),rgb);
        end
    end
    for j = 1:2
        for i = 1:145
           itp(i,j,rgb) = J4(ceil(i*u),ceil(j*v),rgb);
           itp(i,175,rgb) = J4(ceil(i*u),61,rgb);
        end
    end
end
imwrite(J3,'Core1.bmp','bmp');
imwrite(itp,'Core2.bmp','bmp');

subplot(231),imshow(J),title('待配准图像');
subplot(232),imshow(I),title('基准图像');
subplot(233),imshow(J2),title('多项式几何校正后');        
subplot(234),imshow(J3),title('基准影像裁剪后');
subplot(235),imshow(itp),title('校正影像裁剪重采样后');



% %基准图重采样
% kh = zuixiaogongbeishu(k,h);
% yt = zuixiaogongbeishu(y,t);
% u = h/kh;v = t/yt;
% J5 = J3(1:k/kh:end,1:y/yt:end,1:3);
% %配准图 双线性内插法重采样
% itp = uint8(zeros(kh,yt,3));
% for rgb = 1:3
%     for i = floor(1/u):kh-1
%         iu = floor(i*u);
%         for j = floor(1/v):yt-1 
%             jv = floor(j*v);
%             itp(i,j,rgb) = (1-(i*u-iu))*(1-(j*v-jv))*J4(iu,jv,rgb)...
%                        +(1-(i*u-iu))*(j*v-jv)*J4(iu,jv+1,rgb)...
%                        +(i*u-iu)*(1-(j*v-jv))*J4(iu+1,jv,rgb)...
%                        +(i*u-iu)*(j*v-jv)*J4(iu+1,jv+1,rgb);
%         end
%     end
% end
% %去黑边
% for rgb = 1:3
%     for i = 1:144 
%         for j = 1:10675
%           itp(i,j,rgb) = J4(ceil(i*u),ceil(j*v),rgb);
%         end
%     end
%     for j = 1:175
%         for i = 1:6235
%            itp(i,j,rgb) = J4(ceil(i*u),ceil(j*v),rgb);
%         end
%     end
% end
% 
% itp1 = uint8(zeros(6193,10615,3));
% itp1(1:6193,1:10615,1:3) = itp(1:6193,1:10615,1:3);
% imwrite(J5,'Crop1.bmp','bmp');
% J5 = imread('Crop1.bmp');
% imwrite(itp1,'Crop2.bmp','bmp');
% J6 = imread('Crop2.bmp');

% subplot(231),imshow(J),title('待配准图像');
% subplot(232),imshow(I),title('基准图像');
% subplot(233),imshow(J2),title('多项式几何校正后');        
% subplot(234),imshow(J5),title('基准影像裁剪重采样后');
% subplot(235),imshow(J6),title('校正影像裁剪重采样后');

% a = imread('基准.bmp');
% b = imread('重采样后图像.bmp');
% c = imcrop(a,[1,100,100,100]);
% d = imcrop(b,[1,100,100,100]);
% imwrite(c,'Core3.bmp','bmp');
% imwrite(d,'Core4.bmp','bmp');

 

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