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计算机视觉是一门多领域交叉的学科，它涉及图像处理、机器学习、模式识别、神经科学等多个方面的知识。浙江大学的这组计算机视觉课件为初学者提供了深入理解和掌握该领域的宝贵资源。下面，我们将针对每个文件名，详细解读其中可能涵盖的知识点。 1. **diglib.pdf**：可能涵盖了数字图书馆或数字图像库相关的技术，如图像存储、检索和管理。在计算机视觉中，图像数据库是研究的基础，用于存储和组织大量图像以便后续分析和处理。 2. **texture.pdf**：纹理分析是计算机视觉中的一个重要课题，主要研究如何从图像中提取纹理特征，用于图像分类、识别或合成。这可能包括纹理模型（如Gabor滤波器、局部二值模式）、纹理分类方法以及纹理在场景理解中的应用。 3. **csppose.pdf**：很可能涉及到计算姿态估计，即确定物体或人体在图像中的位置和方向。常用的方法有关键点检测（如OpenPose）、骨骼追踪和模板匹配等，这些技术广泛应用于人机交互、动作识别等领域。 4. **classifiers.pdf**：分类器在计算机视觉中起着核心作用，用于对图像进行分类或物体识别。可能涵盖了SVM（支持向量机）、决策树、神经网络（如卷积神经网络CNN）等机器学习算法及其在视觉任务中的应用。 5. **imbren.pdf**：可能是关于光照渲染或图像增强的内容，讨论如何改善图像质量，模拟真实光照效果，或者增强图像的某些特性，如对比度、清晰度等。 6. **edgedetection.pdf**：边缘检测是图像处理的基本步骤，用于找出图像中的边界。常见的边缘检测算子有Canny、Sobel、Prewitt等，它们在目标检测、形状分析等任务中有广泛应用。 7. **clustering.pdf**：聚类是无监督学习的一种，用于将相似的图像或特征分组。K-means、DBSCAN等算法在图像分割、物体检测等方面有着重要应用。 8. **stereo.pdf**：立体视觉涉及从两个或多个不同视角获取的图像中重建三维信息。这可能包括匹配算法（如SIFT、SURF）、视差计算和深度映射等技术，常用于自动驾驶、机器人导航等场景。 9. **nonlinearfilts.pdf**：非线性滤波通常用于处理图像噪声或增强特定图像特征，如自适应滤波、中值滤波、高斯金字塔等。它们在图像去噪、细节增强方面表现出色。 10. **colour.pdf**：色彩处理是计算机视觉中的重要环节，涉及到色彩模型（RGB、HSV、YCbCr等）、色彩空间转换、色彩直方图和色彩描述子等。色彩信息在图像分类、目标检测等任务中扮演着重要角色。通过深入学习和实践这些课件中的知识点，初学者可以逐步建立起计算机视觉的理论体系，并具备解决实际问题的能力。从图像预处理到特征提取，再到模型训练和评估，这些课程将帮助你全面了解并掌握计算机视觉的核心技术。

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Computer Vision_A Modern Approach_3rd.rar （27个子文件）

nonlinearfilts.pdf 2.22MB

edgedetection.pdf 3.19MB

csppose.pdf 4.24MB

colour.pdf 2.18MB

chp06_analytical.pdf 709KB

geofeats.pdf 880KB

imbren.pdf 3.59MB

texture.pdf 4.96MB

fitting.pdf 584KB

multipleview.pdf 1.11MB

radiometry.pdf 383KB

probseg.pdf 976KB

aspgrs.pdf 486KB

chp14_affsfm.pdf 1.43MB

sources.pdf 1.36MB

clustering.pdf 2.95MB

diglib.pdf 5.38MB

linearfilters.pdf 6.07MB

relations.pdf 1.69MB

range.pdf 4.2MB

tracking.pdf 1.65MB

probability.pdf 519KB

prosfm.pdf 1.81MB

classifiers.pdf 3.92MB

chp01_cameras.pdf 1.62MB

CONTENTS.pdf 95KB

stereo.pdf 2.32MB

Chapter 8

LINEAR FILTERS

Pictures of zebras and of dalmatians have black and white pixels, and in about the

same number, too. The diﬀerences between the two have to do with the character-

istic appearance of small groups of pixels, rather than individual pixel values. In

this chapter, we introduce methods for obtaining descriptions of the appearance of

a small group of pixels.

Our main strategy will be to use weighted sums of pixel values, using diﬀerent

patterns of weights to ﬁnd diﬀerent image patterns. This process, despite its sim-

plicity, is extremely useful. It allows us to smooth noise in images, and to ﬁnd edges

and other image patterns. We discuss noise in some detail. We also describe some

useful non-linear functions of image neighbourhoods.

8.1 Linear Filters and Convolution

Construct a new array, the same size as the image. Fill each location of this new

array with a weighted sum of the pixel values from the locations surrounding the

corresponding location in the image, using the same set of weights each time.The

result of this procedure is shift-invariant — meaning that the value of the output

depends on the pattern in an image neighbourhood, rather than the position of

the neighbourhood — and linear — meaning that the output for the sum of two

images is the same as the sum of the outputs obtained for the images separately.

The procedure itself is known as linear ﬁltering.

8.1.1 Convolution

We introduce some notation at this point. The pattern of weights used for a linear

ﬁlter is usually referred to as the kernel of the ﬁlter. The process of applying the

ﬁlter is usually referred to as convolution. There is a catch: for reasons that will

appear later (section 8.2.1), it is convenient to write the process in a non-obvious

way.

In particular, given a ﬁlter kernel H, the convolution of the kernel with image

206

Section 8.1. Linear Filters and Convolution 207

F is an image R.Thei, j’th component of R are given by:



u,v

i−u,j−v

u,v

This form is similar to the form given for blurring by taking a local average in

section 8.1.2, though you will need to change the variables in the summation to

demonstrate this.

8.1.2 Example: Smoothing by Averaging

Images typically have the property that the value of a pixel is usually similar to

that of its neighbour. Assume that the image is aﬀected by noise of a form where

we can reasonably expect that this property is preserved; for example, there might

be occasional dead pixels, or small random numbers are added to the pixel values.

It is natural to attempt to reduce the eﬀects of this noise by replacing each pixel

with a weighted average of its neighbours, a process often referred to as smoothing

or blurring.

At ﬁrst guess, we could model the blurring process as replacing the value of a

function at each point with an unweighted (or uniform) average taken over a ﬁxed

region. For example, we could average all pixels within a 2k +1× 2k +1blockof

the pixel of interest. For an input image F, this gives an output

(2k +1)

u=i+k



u=i−k

v=j+k



v=j−k

This is convolution with a kernel that is a 2k +1×2k + 1 block of ones, multiplied

by a constant.

This process is a poor model of blurring — its output does not look like that

of a defocussed camera (ﬁgure 8.1. The reason is clear. Assume that we have an

image in which every point but the center point was zero, and the center point was

one. If we blur this image by forming an unweighted average at each point, the

result will look like a small bright box — but this is not what defocussed cameras

do. We want a blurring process that takes a very small bright dot to a circularly

symmetric region of blur, brighter at the center than at the edges and fading slowly

to darkness. As ﬁgure 8.1 suggests, a set of weights of this form produces a much

more convincing defocus model.

8.1.3 Example: Smoothing with a Gaussian

A good formal model for this fuzzy blob is the symmetric Gaussian kernel

(x, y)=

2πσ

exp



−

+ y

)

2σ



illustrated in ﬁgure 8.2. σ is referred to as the standard deviation of the Gaussian

(or its “sigma”!); the units are inter-pixel spaces, usually referred to as pixels. The

208 Linear Filters Chapter 8

Figure 8.1. Although a uniform local average may seem to give a good blurring model,

it generates eﬀects that are not usually seen in defocussing a lens. The images above

compare the eﬀects of a uniform local average with weighted average. The image at the

top shows a view of grass. On the left in the second row, the result of blurring this image

using a uniform local model and on the right, the result of blurring this image using a

set of Gaussian weights. The degree of blurring in each case is about the same, but the

uniform average produces a set of narrow vertical and horizontal bars — an eﬀect often

known as ringing. The bottom row shows the weights used to blur the image, themselves

rendered as an image; bright points represent large values and dark points represent small

values (in this example the smallest values are zero).

Section 8.1. Linear Filters and Convolution 209

-5

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Figure 8.2. The symmetric Gaussian kernel in 2D. This view shows a kernel scaled so

that its sum is equal to one; this scaling is quite often omitted. The kernel shown has

σ = 1. Convolution with this kernel forms a weighted average which stresses the point at

the center of the convolution window, and incorporates little contribution from those at

the boundary. Notice how the Gaussian is qualitatively similar to our description of the

point spread function of image blur; it is circularly symmetric, has strongest response in

the center, and dies away near the boundaries.

constant term makes the integral over the whole plane equal to one and is often

ignored in smoothing applications. The name comes from the fact that this kernel

has the form of the probability density for a 2D Gaussian random variable with a

particular covariance.

This smoothing kernel forms a weighted average, that weights pixels at its center

much more strongly than at its boundaries. One can justify this approach qualita-

tively: smoothing suppresses noise by enforcing the requirement that pixels should

look like their neighbours; but the requirement that a pixel look like its neighbours

should be less strongly imposed for distant neighbours — we can do this by down-

weighting distant neighbours in the average (ﬁgure 8.3 illustrates that Gaussian

smoothing is eﬀective at suppressing noise).

In applications, a discrete smoothing kernel can be obtained by constructing a

2k +1× 2k + 1 array whose i, j’th value is

2πσ

exp



−

((i − k − 1)

+(j − k − 1)

)

2σ



210 Linear Filters Chapter 8

Notice that some care must be exercised with σ;ifσ is too small, then only one

element of the array will have a non-zero value. If σ is large, then k must be large,

too, otherwise we will be ignoring contributions from pixels that should contribute

with substantial weight. A particular property of smoothing with this kernel is that

if one smoothes an image containing all zeros, except for a single one at the center,

the response will be a Gaussian (exercises). This means that the kernel is behaving

like a defocussed lens — taking a bright spot to a fuzzy blob.

Figure 8.3. In salt-and-pepper noise, we choose pixels uniformly at random, and uni-

formly at random make them either black or white. Gaussian smoothing is particularly

eﬀective at suppressing the eﬀects of salt-and-pepper noise. The top row shows an image,

and versions smoothed by a symmetric Gaussian with σ two pixels and four pixels. The

second row shows an image corrupted by this noise model and corresponding smoothed

versions of the image. Notice that, as the smoothing increases, detail is lost, but the eﬀects

of the noise diminish, too — the smoothed versions of the noisy images look very much

like the smoothed version of the noise-free images.

Convolving an image with a Gaussian is, in essence, the same as forming a

weighted local average. A qualitative analysis gives:

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