Matlab底层算法实现图像的平移

公式

设初始坐标为$\left(x_0,y_0\right)$的点经过平移$\left(\Delta x,\Delta y\right)$后坐标变为$\left(x_1,y_1\right)$，其关系如下
                                                 $\{\begin{array}{c}{x}_1=x_0+\Delta x\\ y_1=y_0+\Delta y\end{array}$
平移变换的矩阵表示为
                                            $\left[\begin{array}{c}{x}_1\\ y_1\\ 1\end{array}\right]=\left[\begin{array}{ccc}1& 0& \Delta x\\ 0& 1& \Delta y\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_0\\ y_0\\ 1\end{array}\right]=\left[\begin{array}{c}{x}_0+\Delta x\\ y_0+\Delta y\\ 1\end{array}\right]$

源代码

clc
image = imread('D:\2.png');
image_matrix=image(:,:,1);
image_matrix=double(image_matrix);
[height,width,channels]=size(image);
G=zeros(height,width);

%%水平，竖直方向上的平移值
height_move = 20;
width_move= 40;

for i=1:height
    for j=1:width
       %平移后的新坐标
       i1=i+height_move;
       j1=j+width_move;
       if(i1>=0 && i1<=height && j1>=0 && j1<=width)
          G(i1,j1)=image_matrix(i,j);
       else
          G(i,j)=255;
       end
    end
end
image_out = uint8(G);
%显示
subplot(1,2,1);
imshow(image);
subplot(1,2,2);
imshow(image_out);

效果图