数字图像处理-第五章

图像退化/复原处理的模型
5.1 A Model of the Image Degradation/Restoration Process.
Given g(x,y), some knowledge about the degradation function H , and some knowledge about the additive noise term N(x,y), the ˆ ( x, y),of the objective of restoration is to obtain an estimate, f original image. 给定g(x,y)、一些关于退化函数H的知识和一些关于加性噪声 ˆ ( x, y) N(x,y) 的知识、复原的目标就是得到原图像的一个估计 f We want the estimate to be as close as possible to the original input image. 我们要使这个估计尽可能地接近原始的输入图像。
因为在MATLAB中，数组索引是从1开始记数，而不是从0开 始记数，所以在傅里叶变换及其反变换中，MATLAB中的F(1,1) and f (1,1 ) 对应理论教科书中的数学公式中的F(0,0), and f (0,0 )
4.1 The 2-D Discrete Fourier Transform P(108) Computing the 2-D DFT yields transform points in the
4.4 Obtaining Frequency Domain Filters from Spatial Filters 4.4 由空间域滤波器获得频率域滤波器
Preview P(142)
The objective of restoration is to improve a given image in some predefined sense.
Preview P(142)
For example, contrast stretching is considered an enhancement technique because it is based primarily on the pleasing aspects it might present to the viewer, whereas removal of image blur by applying a deblurring function is considered a restoration technique. 例如对比度拉伸是一种增强技术，因为它主要目的是为图 像观察者提供一个更好的视觉效果，而复原技术则考虑用去模 糊函数来消除图像的模糊。 In this chapter we explore how to use MATLAB and IPT capabilities to model degradation phenomena and to formulate restoration solutions. 本章主要研究如何使用MATLAB和IPT把退化现象模型化 及将复原的求解进行公式化。
Fig.4.3(c)
Implementation for Figure 4.4 (P116)
[X,Y]=meshgrid(-3:0.18:3); Z=exp(-(X.^2+Y.^2)); %2 mesh(X,Y,Z); %3 grid off; %4 axis off %5 fz=fftshift(Z); %6 mesh(fz); %7 grid off; axis off %8 x=-3.5:0.1:3.5; %9 fx=exp(-(x.^2)); %10 plot(x,fx); %11 grid off; %12 axis([-3.5 3.5 0 1.1]); %13
复原通过使用退化现象的先验知识，试图重建或恢复一幅退 化的图像。
Preview P(142)
Thus , restoration techniques are oriented toward modeling the degradation and qpplying the inverse process in order to recover the original image. 恢复技术趋向于将退化模型化，并用退化的逆过程来恢复得 到原始图像。 This approach usually involves formulating a criterion of goodness that yields an optimal estimate of the desired result. 这种方法通常包含把优度准则公式化，它将产生期望的结果 的一个最优估计。 By contrast, enhancement techniques basically are heuristic procedures designed to manipulate an image in order to take advantage of the psychophysical aspects of the human visual system. 相比而言，增强技术基本上是启发式的过程，对图像的操 作是利用了人类视频系统的心理物理方面的特性。
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Example 4.1 Effects of Filtering with and without padding
复原的目的是在预定义的意义上改善给定的图像。
Although there are areas of overlab between image enhancement and image restoration, the former is largely a subjective process,while image restoration is for the most part an objective process. 尽管图像增强和图像复原之间有重叠的部分，但前者主要是 主观的处理，而图像复原大部分是客观的处理。 Restoration attempts to reconstruct or recover an image that has been degraded using a priori knowledge of the degradation phenomenon.
(a) A simple image
Fig.4.3(a)
Fig.4.3(b)
(b) Fourier spectrum (c) Centered spectrum (d) Spectrum enhanced by a log transformation
f = imread('image.tif'); ff = fft2(f);absff = abs(ff); imshow(absff,[]); fs = fftshift(absff);imshow(fs,[]);
离散傅里叶逆变换由下式给出：
M 1 N 1 x 0 y 0 ux vy ) M N
1 f (x , y ) MN
F (u ,v )e
j 2 (
Because array indices in MATLAB start at 1, rather than 0, F(1,1) and f (1,1 ) in MATLAB correspond to the mathematical quantities F(0,0), and f (0,0 ) in the transform and its inverse.
ˆ ( x, y) In general, the more we know about H and h, the closer f will be to f(x,y). ˆ ( x, y) 就越接近f(x,y) f 通过，我们对H 和知道得越多，
实例说明
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4.1 The 2-D Discrete Fourier Transform P(108) The inverse , discrete Fourier transform is given by:
Fig.4.2(a)
(a) A simple image
Fig.4.3(a)
Fig.4.3(b)
(b) Fourier spectrum (c) Centered spectrum (d) Spectrum enhanced by a log transformation
Fig.4.3(c)
Fig.4.3(d)
rectangular interval shown in Fig.4.2(a). as the Red rectangluar shows. 计算变换得到如图所示的矩形区间中变换坐标点，如红色矩 形所示。 The dashed rectangles are periodic repetitions.The shaded region shows that the values of F(u,v) encompass four back-toback quarter periods that meet at the point. 虚线矩形是周期重复，阴影区 是四个相邻部分（每个部分是四 分之周期）组成，这四个部分相 交于一个公共点
5.1 A Model of the Image Degradation/Restoration Process.
As Fig.5.1 shows, the degradation process is modeled in this chapter as a degradation function that ,together with an additive noise term, operates on an input image f(x,y) to produce a degraded image g(x,y): 如图5.1所示，本章中用退化函数把退化过程模型化，它和 加性噪声项一起，作用于输入图像f(x,y), 产生一幅退化的图像 g(x,y)