1、实验三 图像的几何变换实验三 图像的几何变换一实验目的及要求掌握图像几何变换的基本原理，熟练掌握数字图像的缩放、旋转、平移、镜像和转置的基本原理及其MATLAB编程实现方法。二、实验内容（一）研究以下程序，分析程序功能；输入执行各命令行，认真观察命令执行的结果。熟悉程序中所使用函数的调用方法，改变有关参数，观察试验结果。1. 图像缩放clear all, close allI = imread(cameraman.tif);Scale = 1.35; % 将图像放大1.35倍J1 = imresize(I, Scale, nearest); % using the nearest neighb
2、or interpolationJ2 = imresize(I, Scale, bilinear); % using the bilinear interpolationimshow(I), title(Original Image);figure, imshow(J1), title(Resized Image- using the nearest neighbor interpolation );figure, imshow(J2), title(Resized Image- using the bilinear interpolation );% 查看imresize使用帮助help i
3、mresizeCommand窗口显示如下：IMRESIZE Resize image. B = IMRESIZE(A, SCALE) returns an image that is SCALE times the size of A, which is a grayscale, RGB, or binary image. B = IMRESIZE(A, NUMROWS NUMCOLS) resizes the image so that it has the specified number of rows and columns. Either NUMROWS or NUMCOLS may
4、 be NaN, in which case IMRESIZE computes the number of rows or columns automatically in order to preserve the image aspect ratio. Y, NEWMAP = IMRESIZE(X, MAP, SCALE) resizes an indexed image. Y, NEWMAP = IMRESIZE(X, MAP, NUMROWS NUMCOLS) resizes an indexed image. To control the interpolation method
5、used by IMRESIZE, add a METHOD argument to any of the syntaxes above, like this: IMRESIZE(A, SCALE, METHOD) IMRESIZE(A, NUMROWS NUMCOLS, METHOD), IMRESIZE(X, MAP, M, METHOD) IMRESIZE(X, MAP, NUMROWS NUMCOLS, METHOD) METHOD can be a string naming a general interpolation method: nearest - nearest-neig
6、hbor interpolation bilinear - bilinear interpolation bicubic - cubic interpolation; the default method METHOD can also be a string naming an interpolation kernel: box - interpolation with a box-shaped kernel triangle - interpolation with a triangular kernel (equivalent to bilinear) cubic - interpola
7、tion with a cubic kernel (equivalent to bicubic) lanczos2 - interpolation with a Lanczos-2 kernel lanczos3 - interpolation with a Lanczos-3 kernel Finally, METHOD can be a two-element cell array of the form f,w, where f is the function handle for a custom interpolation kernel, and w is the custom ke
8、rnels width. f(x) must be zero outside the interval -w/2 = x w/2. Your function handle f may be called with a scalar or a vector input. You can achieve additional control over IMRESIZE by using parameter/value pairs following any of the syntaxes above. For example: B = IMRESIZE(A, SCALE, PARAM1, VAL
9、UE1, PARAM2, VALUE2, .) Parameters include: Antialiasing - true or false; specifies whether to perform antialiasing when shrinking an image. The default value depends on the interpolation method you choose. For the nearest method, the default is false; for all other methods, the default is true. Col
10、ormap - (only relevant for indexed images) original or optimized; if original, then the output newmap is the same as the input map. If it is optimized, then a new optimized colormap is created. The default value is optimized. Dither - (only for indexed images) true or false; specifies whether to per
11、form color dithering. The default value is true. Method - As described above OutputSize - A two-element vector, MROWS NCOLS, specifying the output size. One element may be NaN, in which case the other value is computed automatically to preserve the aspect ratio of the image. Scale - A scalar or two-
12、element vector specifying the resize scale factors. If it is a scalar, the same scale factor is applied to each dimension. If it is a vector, it contains the scale factors for the row and column dimensions, respectively. Examples - Shrink by factor of two using the defaults of bicubic interpolation
13、and antialiasing. I = imread(rice.png); J = imresize(I, 0.5); figure, imshow(I), figure, imshow(J) Shrink by factor of two using nearest-neighbor interpolation. (This is the fastest method, but it has the lowest quality.) J2 = imresize(I, 0.5, nearest); Resize an indexed image. X, map = imread(trees
14、.tif); Y, newmap = imresize(X, map, 0.5); imshow(Y, newmap) Resize an RGB image to have 64 rows. The number of columns is computed automatically. RGB = imread(peppers.png); RGB2 = imresize(RGB, 64 NaN); Note - The function IMRESIZE in previous versions of the Image Processing Toolbox used a somewhat
15、 different algorithm by default. If you need the same results produced by the previous implementation, call the function IMRESIZE_OLD. Class Support - The input image A can be numeric or logical and it must be nonsparse. The output image is of the same class as the input image. The input indexed ima
16、ge X can be uint8, uint16, or double. See also imresize_old, imrotate, imtransform, tformarray. Reference page in Help browser doc imresize执行程序所得结果如下：改变参数Scale =0.5得到图形结果如下：对以上实验结果，分析如下：通过查看命令窗口查看imresize函数的使用方法。本实验中利用了形式B = imresize(A,m,method)。实验中method采用了，nearest(默认值)最近邻插值 方法和bilinear双线性插值方法，由图片显
17、示结果可以看出，双线性插值方法要好于最近邻插值方法。这是由于最近邻插值方法仅是取离其最近的一个像素的像素值，而双线性插值方法采用了其周围的像素值参与计算，所以更能适应图像的局部特征。m为放大倍数，由上面实验结果可以明显看出，放大1.35倍和0.5倍的效果差异。2. 图像旋转clear all, close allI = imread(cameraman.tif);Theta = 45; % 将图像逆时针旋转45。J1 = imrotate(I, Theta, nearest); % using the nearest neighbor interpolation%and enlarge the
18、 output imageTheta = -45; % 将图像顺时针旋转45。J2 = imrotate(I, Theta, bilinear, crop); % using the bilinear interpolation % and crops the output image imshow(I), title(Original Image);figure, imshow(J1), title(Rotated Image- using the nearest neighbor interpolation );figure, imshow(J2), title( Rotated Imag
19、e- using the bilinear interpolation );% 查看imrotate使用帮助help imrotateCommand窗口显示如下：IMROTATE Rotate image. B = IMROTATE(A,ANGLE) rotates image A by ANGLE degrees in a counterclockwise direction around its center point. To rotate the image clockwise, specify a negative value for ANGLE. IMROTATE makes th
20、e output image B large enough to contain the entire rotated image. IMROTATE uses nearest neighbor interpolation, setting the values of pixels in B that are outside the rotated image to 0 (zero). B = IMROTATE(A,ANGLE,METHOD) rotates image A, using the interpolation method specified by METHOD. METHOD
21、is a string that can have one of the following values. The default value is enclosed in braces (). nearest Nearest neighbor interpolation bilinear Bilinear interpolation bicubic Bicubic interpolation. Note: This interpolation method can produce pixel values outside the original range. B = IMROTATE(A
22、,ANGLE,METHOD,BBOX) rotates image A, where BBOX specifies the size of the output image B. BBOX is a text string that can have either of the following values. The default value is enclosed in braces (). loose Make output image B large enough to contain the entire rotated image. B is generally larger
23、than A. crop Make output image B the same size as the input image A, cropping the rotated image to fit. Class Support - The input image can be numeric or logical. The output image is of the same class as the input image. Example - % This example brings image I into horizontal alignment by % rotating
24、 the image by -1 degree. I = fitsread(solarspectra.fts); I = mat2gray(I); J = imrotate(I,-1,bilinear,crop); figure, imshow(I), figure, imshow(J) See also imcrop, imresize, imtransform, tformarray. Reference page in Help browser doc imrotate执行程序所得结果如下：改变参数，Theta = 135和-135时，所得结果如下：实验结果分析如下：通过查看命令窗口了解
25、imrotate函数的使用。本实验中采用了函数的两种形式，B = imrotate(A,angle,method)和B = imrotate(A,angle,method,bbox)。实验中，method的设置及其原理同上个实验。实验中，bbox设置为了“crop”,其作用是为了使输出图像和输入图像大小相同，可以看出当设置了该参数是，图像明显被裁减了，这是因为图像旋转后面积变大了，而该参数的设置使图像须保持原来的大小i，因而图像被裁减了，未设置该参数时默认大小可以显示整个旋转后的图像。Angle为旋转角度，分别设置为了45和-45、135和-135，由上面两组图可以看出明显的效果和差异 3图像
26、水平镜象clear all, close allI = imread(cameraman.tif);I1 = flipdim(I,2); I2 = flipdim(I,1);figure(1), subplot(1,2,1), imshow(I);subplot(1,2,2), imshow(I1);figure(2), subplot(2,1,1), imshow(I);subplot(2,1,2), imshow(I2);执行程序，所得结果如下：对实验结果分析如下：flipdim 函数的使用方法如下。B = flipdim(A,dim)沿指定的维翻转矩阵。当dim=1时，行翻转，等同于fl
27、ipud ，当dim=2时，列翻转，等同于fliplr 。由上图可以看出翻转的效果。(二)用MATLAB编程实现以下图像几何变换1图像平移 程序代码如下： clc,clear all;I = imread(cameraman.tif);rows=size(I,1);cols=size(I,2);movx=50;movy=50;for i=1:rows for j=1:cols Q(i+movx,j+movy)=I(i,j); endendfigure(1);subplot(121);imshow(I);title(origine picture);subplot(122);imshow(Q);
28、title(modified picture);执行程序结果如下：实验分析如下：实验中，每个像素值以及其对应的坐标x和y都被平移了50，表现在整个图像上，即向右下角平移sqrt(50*50+50*50),显示结果如上图所示。2图像转置图像的转置是将给定图像像素的x坐标和y坐标互换的几何变换，设点P0(x0, y0) 转置后的对应点为P(x, y)，转置变换可表述为： 或 ，对应的逆变换为： 或 转置后图像的宽、高发生改变，即输出图像的高度为原始图像的宽度，输出图像的宽度为原始图像的高度。 程序代码如下： clc,clear all;I = imread(cameraman.tif);rows=
29、size(I,1);cols=size(I,2);for i=1:rows for j=1:cols Q(j,i)=I(i,j); endendsize(I),size(Q)figure(1);subplot(121);imshow(I);title(origine picture);subplot(122);imshow(Q);title(modified picture); 执行程序，所得结果如下： 实验分析如下： 设图像中某个像素为p(j,i)，则其值为被p(i,j)被代替,其中p为整个图像的像素矩阵。对图像中的所有像素.逐列、逐行的进行此计算，即可实现转置。实验结果如上图所示，明显看出，转置后图像的宽、高发生改变，即输出图像的高度为原始图像的宽度，输出图像的宽度为原始图像的高度，整个图像被“转置”了。三、实验设备1PIII以上微机；2MATLAB6.5；四、实验心得与体会
