MATLAB图像变换

Question

以下代码描述了图像 I 的仿射变换，

T = [sx, 0, 0;...
      0, sy, 0;...
      0, 0, 1];
tform = maketform('affine', T);
[J,cdata,rdata] = imtransform(I,tform);

得到变换后的图像J后，我想在图像J上找到I(5,5)的合适像素值。

我该怎么办？

我的代码是

function test()
    sx = 0.5; sy = 1;
    theta = pi/4;
    Ts = [sx, 0, 0;...
    0, sy, 0;...
    0, 0, 1];
    Tr = [cos(theta) -sin(theta) 0;...
          sin(theta) cos(theta), 0; ...
          0, 0, 1];
    T = Ts*Tr;

    I = imread('image_0002.jpg');
    tform = maketform('affine', T);
    [J,xdata,ydata] = imtransform(I,tform);
    h = ydata(2) - ydata(1);
    w = xdata(2) - xdata(1);

    %%
    gridOx = meshgrid(1:50:size(I,2), 1:50:size(I,1));
    gridOy = meshgrid(1:50:size(I,1), 1:50:size(I,2))';
    go = [gridOy(:), gridOx(:), ones(length(gridOx(:)),1)];

    for i=1:size(go,1)
        I = makept(I, go(i,1), go(i,2));
    end
    imshow(I);

    %%
    gt = T*go';

    TL = T*[1,1,1]';
    BL = T*[size(I,1), 1, 1]';
    TR = T*[1, size(I,2), 1]';
    BR = T*[size(I,1), size(I,2), 1]';
    minr = min([TL(1), TR(1), BL(1), BR(1)]);
    minc = min([TL(2), TR(2), BL(2), BR(2)]);

    %%
    gt = int32(round(gt));
    r = gt(1,:) - minr+1;
    c = gt(2,:) - minc+1;

    figure,hold on;
    for i=1:length(r)
        J = makept(J, r(i), c(i));
        plot(gt(1, i), gt(2, i));
    end
    figure, imshow(J);

    close all;
end

function I = makept(I, r, c)
    mr = max(r-2,1);
    mc = max(c-2,1);
    maxr = min(r+2,size(I,1));
    maxc = min(c+2,size(I,2));

    I(mr:maxr, mc:maxc,:) = 0;
    I(mr:maxr, mc:maxc,1) = 255;
end

Answer 1

您可以像转换图像一样转换像素坐标。

appropriatePixel = J(T*[5;5;1]);

编辑

您发布的代码已经很接近了。永远记住，对于图像，图像的原点在左上角，并且图像尺寸的顺序是列-行，这与矩阵不同。您在某些地方考虑到了这一点，但并非在所有地方都考虑到了这一点。

下面的代码应该可以解决问题。 gt = T*go 改为使用 T 的转置，minc 和 minr 互换。

function airplane()
       close all
       sx = 0.5; sy = 1;
       theta = pi/4;
       Ts = [sx, 0, 0;...
       0, sy, 0;...
       0, 0, 1];
       Tr = [cos(theta) -sin(theta) 0;...
           sin(theta) cos(theta), 0; ...
           0, 0, 1];
       T = Ts*Tr;

       I = imread('airplane2.png');
       tform = maketform('affine', T);
       [J,xdata,ydata] = imtransform(I,tform);

        %% 
       gridOx = meshgrid(1:50:size(I,2), 1:50:size(I,1));
       gridOy = meshgrid(1:50:size(I,1), 1:50:size(I,2))';
       go = [gridOx(:), gridOy(:), ones(length(gridOx(:)),1)];

       figure; imshow(I); hold on;
       scatter(go(:,1), go(:,2), 25, 'rs', 'filled');

       %%
       gt = T'*go'; 

       TL = T*[1,1,1]';
       BL = T*[size(I,1), 1, 1]';
       TR = T*[1, size(I,2), 1]';
       BR = T*[size(I,1), size(I,2), 1]';
       minc = min([TL(1), TR(1), BL(1), BR(1)]);
       minr = min([TL(2), TR(2), BL(2), BR(2)]);


       %%
       gt = int32(round(gt));
       r = gt(1,:) - minr+1;
       c = gt(2,:) - minc+1;

       figure; imshow(J);hold on;
       scatter(c, r, 25, 'rs', 'filled');

end

结果：

Answer 2

我找到了另一种方法.. 使用 'tformfwd'.. 我们需要应用缩放，并在 http://blogs.mathworks.com/steve/2006/02/14/spatial-transformations-maketform-tformfwd-and-tforminv/ 中进行了解释

         function [new_im, grn, gcn] = transformImage(I, gr, gc, TM)
              [new_im xdata ydata] = imtransform(I, TM);
              w = xdata(2)-xdata(1) +1;
              h = ydata(2)-ydata(1)+1;
              scalex = size(new_im,2)/w;
              scaley = size(new_im,1)/h;

              % cartesian coordinates
              go = [gc(:), gr(:)];

              %% cartesian coordinates
              NPt = tformfwd(TM, go);

              % convert to image coordinates
              NPtImage(:,1) = NPt(:,1) - xdata(1) + 1;
              NPtImage(:,2) = NPt(:,2) - ydata(1) + 1;
              NPtImage(:,1) = NPtImage(:,1)*scalex;
              NPtImage(:,2) = NPtImage(:,2)*scaley;
              NPtImage = round(NPtImage);

              grn = NPtImage(:,2);
              gcn = NPtImage(:,1);
              grn = reshape(grn, size(gr,1), size(gr,2));
              gcn = reshape(gcn, size(gc,1), size(gc,2));

              showimgs = false;
              if showimgs
                  I = uint8(I);
                  new_im = uint8(new_im);

                  figure, imshow(I), hold on;
                  for i=1:size(go,1)
                      plot(go(i,1), go(i,2), 'r*');
                  end

                  figure, imshow(new_im, 'XData', xdata, 'YData', ydata);
                  hold on
                  axis on
                  for i=1:size(go,1)
                      plot(NPt(i,1), NPt(i,2), 'r*')
                  end

                  tmpim = new_im;
                  for i=1:size(NPtImage,1)
                      tmpim = makept(tmpim, NPtImage(i,2), NPtImage(i,1), 'b');
                  end
                  figure, imshow(tmpim);
              end

              end


              function I = makept(I, r, c, color)
              mr = max(r-2,1);
              mc = max(c-2,1);
              maxr = min(r+2,size(I,1));
              maxc = min(c+2,size(I,2));

              I(mr:maxr, mc:maxc,:) = 0;

              if strcmp(color, 'r')
                  I(mr:maxr, mc:maxc,1) = 255;
              else
                  I(mr:maxr, mc:maxc,3) = 255;
              end
              end