MATLAB数字图像处理解决方案

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"matlab数字图像处理 - 包含Digital Image Processing第二版问题解决方案的学生手册" 在数字图像处理领域，MATLAB是一个广泛使用的强大工具，它提供了专业的图像处理工具箱，使得用户可以进行图像分析、变换、增强、恢复、压缩等多种操作。这本书"Digital Image Processing Second Edition"由Rafael C. Gonzalez和Richard E. Woods撰写，是该领域的经典教材，而提供的"Problem Solutions – Student Set"则是配套的习题解答，帮助学习者深入理解和应用书中的理论知识。书中的问题解决方案覆盖了所有标有星号的问题，这些解答可以在作者的官方网站（www.imageprocessingbook.com）上获取。例如，问题2.1涉及到视网膜图像的直径计算，利用相似三角形原理来解决。书中提到，通过这种方式，可以计算出对应于点的视网膜图像直径，并且讨论了视网膜的感光区域——黄斑区，将其视为一个近似方形的传感器阵列，大约含有337,000个元素，相当于580x580的数组大小。假设元素间等间距，每行有580个元素和579个空隙，1.5毫米长的线段上有这些元素和空隙，从而可以进一步计算每个元素和间隔的尺寸。 MATLAB图像处理工具箱包括各种函数和算法，如滤波器（如高斯滤波器、中值滤波器）、边缘检测（如Canny算法、Sobel算子）、颜色空间转换（如RGB到灰度、HSV转换）、直方图均衡化、图像分割等。这些工具使用户能够实现复杂的图像处理任务，不仅适用于学术研究，也常用于工业界的各种应用，如医学成像、遥感、机器视觉等。掌握MATLAB数字图像处理不仅需要熟悉MATLAB编程基础，还需要理解图像处理的基本概念和技术，包括像素操作、傅里叶变换、图像变换、噪声与降噪、图像复原、编码与压缩等。通过解决书中的练习题，读者可以逐步提升自己的技能，进阶成为专业的图像处理人士。同时，利用MATLAB的可视化功能，可以直观地观察和分析处理结果，加深对图像处理原理的理解。因此，这本书及其配套的解决方案对学生和专业人士来说都是宝贵的资源，可以帮助他们巩固理论知识并提高实践能力。

12 Chapter 3 Solutions (Students)

used for both negative and positive differences, in which case we have a band [¡T; T ]

in which all pixels of d(x; y) must fall in order for f(x; y) to be declared acceptable.

The second major approach is simply to sum all the pixels in jd(x; y)j and compare the

sum against a threshold S. Note that the absolute value needs to be used to avoid errors

cancelling out. This is a much cruder test, so we will concentrate on the ®rst approach.

There are three fundamental factors that need tight control for difference-based inspec-

tion to work: (1) proper registration, (2) controlled illumination, and (3) noise levels

that are low enough so that difference values are not affected appreciably by variations

due to noise. The ®rst condition basically addresses the requirement that comparisons

be made between corresponding pixels. Two images can be identical, but if they are

displaced with respect to each other, comparing the differences between them makes

no sense. Often, special markings are manufactured into the product for mechanical or

image-based alignment

Controlled illumination (note that |illumination} is not limited to visible light) obviously

is important because changes in illumination can affect dramatically the values in a

difference image. One approach often used in conjunction with illumination control is

intensity scaling based on actual conditions. For example, the products could have one

or more small patches of a tightly controlled color, and the intensity (and perhaps even

color) of each pixels in the entire image would be modi®ed based on the actual versus

expected intensity and/or color of the patches in the image being processed.

Finally, the noise content of a difference image needs to be low enough so that it does

not materially affect comparisons between the golden and input images. Good signal

strength goes a long way toward reducing the effects of noise. Another (sometimes

complementary) approach is to implement image processing techniques (e.g., image

averaging) to reduce noise.

Obviously there are a number if variations of the basic theme just described. For exam-

ple, additional intelligence in the form of tests that are more sophisticated than pixel-by-

pixel threshold comparisons can be implemented. A technique often used in this regard

is to subdivide the golden image into different regions and perform different (usually

more than one) tests in each of the regions, based on expected region content.

Problem 3.17

(a) Consider a 3 £3 mask ®rst. Since all the coef®cients are 1 (we are ignoring the 1/9

Problem 3.19 13

scale factor), the net effect of the lowpass ®lter operation is to add all the gray levels of

pixels under the mask. Initially, it takes 8 additions to produce the response of the mask.

However, when the mask moves one pixel location to the right, it picks up only one new

column. The new response can be computed as

new

= R

old

¡C

+ C

where C

is the sum of pixels under the ®rst column of the mask before it was moved,

and C

is the similar sum in the column it picked up after it moved. This is the basic

box-®lter or moving-average equation. For a 3 £3 mask it takes 2 additions to get C

was already computed). To this we add one subtraction and one addition to get

new

. Thus, a total of 4 arithmetic operations are needed to update the response after

one move. This is a recursive procedure for moving from left to right along one row of

the image. When we get to the end of a row, we move down one pixel (the nature of the

computation is the same) and continue the scan in the opposite direction.

For a mask of size n £ n, (n ¡ 1) additions are needed to obtain C

, plus the single

subtraction and addition needed to obtain R

new

, which gives a total of (n + 1) arith-

metic operations after each move. A brute-force implementation would require n

¡ 1

additions after each move.

Problem 3.19

(a) There are n

points in an n £ n median ®lter mask. Since n is odd, the median

value, ³, is such that there are (n

¡ 1)=2 points with values less than or equal to ³

and the same number with values greater than or equal to ³. However, since the area

A (number of points) in the cluster is less than one half n

, and A and n are integers,

it follows that A is always less than or equal to (n

¡1)=2. Thus, even in the extreme

case when all cluster points are encompassed by the ®lter mask, there are not enough

points in the cluster for any of them to be equal to the value of the median (remember,

we are assuming that all cluster points are lighter or darker than the background points).

Therefore, if the center point in the mask is a cluster point, it will be set to the median

value, which is a background shade, and thus it will be |eliminated} from the cluster.

This conclusion obviously applies to the less extreme case when the number of cluster

points encompassed by the mask is less than the maximum size of the cluster.

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