数字图像处理实验报告(三四五)

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 all

I = imread('cameraman.tif');

Scale = 1.35; % 将图像放大1.35倍

J1 = imresize(I, Scale, 'nearest'); %using the nearest neighbor interpolation

J2 = imresize(I, Scale, 'bilinear'); %using the bilinear interpolation

imshow(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 imresize

Command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 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 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-neighbor 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' - interpolation 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 kernel's 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, VALUE1, 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.

'Colormap' - (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 perform 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-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 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.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 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 image 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 all

I = 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 output image Theta = -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 Image-- using the bilinear interpolation ');

% 查看imrotate使用帮助

help imrotate

Command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 the 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 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,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 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 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．图像水平镜象

clear all, close all

I = 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flipud ，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);

end

end

figure(1);

subplot(121);imshow(I);title('origine picture');

subplot(122);imshow(Q);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P 0(x 0,

y 0) 转置后的对应点为P (x , y )，转置变换可表述为：

???==0

0x y y x 或 ????????????????????=??????????1100001010100y x y x ，对应的逆变换为：????

????????????????=??????????1100001010100y x y x 或 ???==x y y

x 0

0 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=size(I,1); cols=size(I,2); for i=1:rows for j=1:cols Q(j,i)=I(i,j); end end size(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

1．PIII以上微机；

2．MATLAB6.5；

四、实验心得与体会

实验四图像形态学处理

一．实验目的及要求

1．利用MATLAB研究二值形态学图像处理常用算法；

2．掌握MATLAB形态学图像处理基本操作函数的使用方法；

3．了了解形态学的基本应用。

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．膨胀与腐蚀(Dilation and Erosion)

(1)对简单二值图像进行膨胀与腐蚀

clear all, close all

BW = zeros(9,10);

BW(4:6,4:7) = 1;

BW;

SE = strel('square',3)

BW1 = imdilate(BW,SE)

BW2 = imerode (BW,SE)

figure(1),

subplot(1,2,1), imshow(BW,'notruesize'), title(' Original Image ');

subplot(1,2,2), imshow(BW1,'notruesize'), title(' Dilated Image ');

figure(2),

subplot(1,2,1), imshow(BW,'notruesize'), title(' Original Image ');

subplot(1,2,2), imshow(BW2,'notruesize'), title(' Eroded Image ');

执行程序，所得结果如下：

对实验结果分析如下：

程序中采用结构元素对图像进行腐蚀或者膨胀。腐蚀操作，相当于结构元素的中心点沿被操作图像边缘内部走一圈，所有中心点的轨迹所包围的区域。膨胀操作，相当于结构元素的中心点沿被操作图像边缘外部走一圈，所有中心点的轨迹所包围的区域。实验结果如上图所示，腐蚀以及膨胀的结果也非常明显。

(2)对文本图像进行膨胀与腐蚀

clear all, close all

I = imread('text.tif');

SE = [0,1,0;1,1,1;0,1,0]

BW1 = imdilate(I, SE);

BW2 = imerode (I, SE);

figure(1),

subplot(1,2,1), imshow(I,'notruesize'), title(' Original Image ');

subplot(1,2,2), imshow(BW1,'notruesize'), title(' Dilated Image ');

figure(2),

subplot(1,2,1), imshow(I,'notruesize'), title(' Original Image ');

subplot(1,2,2), imshow(BW2,'notruesize') , title(' Eroded Image ');

执行程序，结果如下：

对实验结果分析如下：

本实验中腐蚀及膨胀原理同上个实验，实验中用其对文本进行腐蚀，可以看出腐蚀与膨胀在文本处理中的作用。其中合理选择结构元素是其关键。由上图的处理效果可以看出，处理的效果并不是很理想，这是由于结构元素选择的并不是很合适。

2. 开、闭运算（Open and Close）

clear all, close all

I = imread('nodules1.tif');

bw = ~im2bw(I,graythresh(I));

se = strel('disk',5);

bw2 = imopen(bw,se);

subplot(1,2,1), imshow(bw), title('Thresholded Image') subplot(1,2,2), imshow(bw2), title('After opening')

bw3 = imclose(bw,se);

figure;

subplot(1,2,1), imshow(bw, 'truesize'), title('Thresholded Image') subplot(1,2,2), imshow(bw3, 'truesize'), title('After Closing')

执行程序，结果如下：

对以上实验结果分析如下：

开运算和闭运算与腐蚀和膨胀操作有所不同，其具体差异表现在，开运算是先腐蚀后膨胀，闭运算是先膨胀后腐蚀。通俗的说，开运算与腐蚀操作不同的是，它包含了所有在被操作对象内部的结构元素，而腐蚀操作仅是包含中心点；闭运算也是类似与膨胀操作不同，它包含了所有与被操作对象有交集的结构元素，而膨胀操作仅是包含中心点。处理结果如上，可以看出物体与原图有所不同，开运算消除了一些小像素，而闭运算使图像边缘变得光滑了许多，消除了散枝。

3. 击中/击不中变换（hit-and-miss operation）

clear all, close all

bw = [0 0 0 0 0 0

0 0 1 1 0 0

0 1 1 1 1 0

0 1 1 1 1 0

0 0 1 1 0 0

0 0 1 0 0 0]

interval = [0 -1 -1

1 1 -1

0 1 0]

bw2 = bwhitmiss(bw,interval)

subplot(1,3,1), imshow(bw,'notruesize'), title(' Original Image ');

subplot(1,3,2), imshow(interval, 'truesize'), title(' Interval Image ');

subplot(1,3,3), imshow(bw2,'notruesize') , title('after hit/miss transformation');

执行程序，所得结果如下：

对以上实验结果分析如下：

击中击不中操作，是用结构元素与原图像进行比较，可以把结构元素想象成一个模板，模板有一个中心点。用该中心点在原图像上扫描，能使模板完全重合的中心点保留下来，如上图实验结果所示，处理后的图像比原图像小了好多，这是因为只有符合结构元素的像素被保留了下来，即被击中的像素保留了下来。

4．细化与骨架抽取

clear all, close all

BW = ~ imread('logo.tif');

BW1 = bwmorph(BW,'thin',Inf);

BW2 = bwmorph(BW,'skel',Inf);

subplot(1,3,1), imshow(BW), title(' Original Image ');

subplot(1,3,2), imshow(BW1), title(' Thinned Image ');

subplot(1,3,3), imshow(BW2), title(' Image skeleton');

%查看bwmorph函数使用说明

help bwmorph

Command窗口显示如下：

BWMORPH Morphological operations on binary image.

BW2 = BWMORPH(BW1,OPERATION) applies a specific

morphological operation to the binary image BW1.

BW2 = BWMORPH(BW1,OPERATION,N) applies the operation N times. N can be Inf, in which case the operation is repeated

until the image no longer changes.

OPERATION is a string that can have one of these values:

'bothat' Subtract the input image from its closing

'bridge' Bridge previously unconnected pixels

'clean' Remove isolated pixels (1's surrounded by 0's)

'close' Perform binary closure (dilation followed by

erosion)

'diag' Diagonal fill to eliminate 8-connectivity of

background

'dilate' Perform dilation using the structuring element

ones(3)

'erode' Perform erosion using the structuring element

ones(3)

'fill' Fill isolated interior pixels (0's surrounded by

1's)

'hbreak' Remove H-connected pixels

'majority' Set a pixel to 1 if five or more pixels in its

3-by-3 neighborhood are 1's

'open' Perform binary opening (erosion followed by

dilation)

'remove' Set a pixel to 0 if its 4-connected neighbors

are all 1's, thus leaving only boundary

pixels

'shrink' With N = Inf, shrink objects to points; shrink

objects with holes to connected rings

'skel' With N = Inf, remove pixels on the boundaries

of objects without allowing objects to break

apart

'spur' Remove end points of lines without removing

small objects completely.

'thicken' With N = Inf, thicken objects by adding pixels

to the exterior of objects without connected

previously unconnected objects

'thin' With N = Inf, remove pixels so that an object