光学三维机器视觉手册：光学计量与成像技术解析

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"Handbook of 3D Machine Vision: Optical Metrology and Imaging 完整高清扫描 pdf" 《三维机器视觉手册：光学计量与成像》是一部深入探讨三维成像技术的专业著作，针对非侵入性、非接触式光学方法（光学计量与成像）进行了详尽阐述。随着3D电影的不断推出和3D电视的出现，三维成像技术已逐渐融入日常生活。然而，对于科学家和工程师来说，选择众多的3D视觉方法可能会感到困惑，而这本书正是填补了这一领域的空白，提供了一个全面且综合的参考资料。该手册首先介绍了研究较为成熟的立体视觉方法，并说明如何利用随机散斑图案或空间-时间变化模式显著提高立体视觉的效果。接下来，它讨论了在流体力学中作为主要实验手段的立体粒子图像测速法，以及在计算机科学应用中易于实现且稳健的结构光技术。此外，还涵盖了用于微纳米尺度测量的数字全息显微术，以及利用光栅、干涉法和条纹投影技术精确测量动态可变形自然物体的方法。书中还描述了不依赖三角测量来恢复三维形状的技术，如飞行时间技术及单轴三维形状测量，以及不限于表面捕捉的三维测量技术，如三维超声波、光学相干断层扫描和三维内窥镜。此外，书中还探讨了新颖的三维成像技术在生物识别领域的应用，这在安全和公共安全方面可能具有重要的意义。本书由该领域的领军人物和重要成像技术的发明者撰写，是一本权威且最新的手册，有助于读者理解三维成像技术的核心，并根据需求选择合适的三维成像技术。对于每种技术，书中都提供了数学基础，总结了成功的应用案例，并讨论了其局限性。通过阅读此书，读者将能够深入了解各种3D成像方法的原理，包括它们在不同领域的应用及其潜在的限制，从而在实际工作中做出明智的选择。无论是在科学研究、工程设计还是生物医学领域，这部手册都将提供宝贵的指导和参考。

Stereo Vision

Soon-Yong Park and Seung-Hae Baek

Stereo vision has been of interest to the computer and robot vision commu-

nity. This chapter introduces fundamental theories of stereo vision such as

stereo calibration, rectication, and matching. Practical examples of stereo

calibration and rectication are also presented. In addition, several stereo

matching techniques are briey introduced and their performance is com-

pared by using a couple of reference stereo images.

CONTENTS

1.1 Introduction .................................................................................................... 2

1.2 Stereo Geometry ............................................................................................4

1.3 Stereo Calibration ..........................................................................................9

1.3.1 Pinhole Camera Model .....................................................................9

1.3.2 Direct Calibration ............................................................................ 11

1.4 Stereo Rectication ......................................................................................13

1.4.1 Epipolar Geometry ..........................................................................13

1.4.2 Rectication of Camera Matrices ................................................... 13

1.5 Calibration and Rectication Examples ................................................... 16

1.5.1 Calibration Example ........................................................................ 16

1.5.2 Rectication Example ......................................................................18

1.6 3D Reconstruction .......................................................................................19

1.6.1 Simple Triangulation .......................................................................19

1.6.2 Solution of a Linear Equation .........................................................20

1.7 Stereo Matching ...........................................................................................21

1.7.1 Sum of Squared Difference ............................................................23

1.7.2 Scan-Line Optimization ..................................................................24

1.7.3 Semiglobal Matching.......................................................................25

1.7.4 Belief Propagation ............................................................................27

1.7.5 Performance Comparisons ............................................................. 28

1.8 Conclusions ...................................................................................................30

References ...............................................................................................................31

2 Handbook of 3D Machine Vision: Optical Metrology and Imaging

1.1 Introduction

Stereo vision is motivated from the human vision system, which can perceive

depth properties of a scene. The human vision system obtains two different

images of a scene from the slightly different views of the eyes and interprets

the images for depth perception. Because depth perception is one of the pow-

erful abilities of the human vision system, stereo vision has many application

areas, such as three-dimensional (3D) scene reconstruction, object recogni-

tion, entertainment, robot navigation, etc. To obtain the depth information of

a scene from a pair of images, it needs to solve one of the inherent problems in

stereo vision, called the correspondence problem. Because two different image

planes are dened in stereo vision, the projections of an object into the planes

are represented with respect to different image coordinates. Therefore, the

correspondence problem can be dened as determining the coordinate dif-

ference between the images of the object. Solving the stereo correspondence

problem is called stereo matching. The result of stereo matching is commonly

represented by a disparity map whose intensity represents the coordinate

difference between corresponding image points, called disparity.

In general, a stereo vision system consists of two identical vision cameras,

which capture the left and right images of an object. A conventional congu-

ration of a stereo vision system is shown in Figure1.1. A 3D point W on the

surface of a real object is projected into the image planes of the cameras. Thus,

two two-dimensional (2D) points, p

and p

, on the image planes are the pro-

jections of point W. As mentioned in the previous paragraph, the correspon-

dence problem is to nd points p

and p

between stereo images. Finding

stereo correspondences needs a huge number of computations because the

Left image plane

Right image plane

Object

Left camera Right camera

FIGURE 1.1

Stereo correspondence problem.

3Stereo Vision

disparity of every image point should be determined to obtain a 2D disparity

or depth map. For example, if the resolution of each image is N × M, a brute

force approach for nding all correspondences needs (N × M)

computations.

To reduce the computation complexity of the stereo matching problem, the

3D geometry of a stereo vision system should be considered so that stereo

matching is restricted to certain image areas. To know the stereo geometry,

calibration of a stereo vision with respect to a reference coordinate system

is needed. A direct calibration method is presented to obtain a geometric

relationship between the two cameras, which is represented by 3D Euclidean

transformations, rotation, and translation. From the stereo calibration, we

know that stereo correspondences are related by a 2D point-to-line projec-

tion, called epipolar geometry.

The epipolar geometry between the stereo images provides a very strong

constraint to nd stereo correspondences. The epipolar constraint is essen-

tial in stereo matching because an image point in one image has its conju-

gate point on an epipolar line in the other image, while the epipolar line is

derived by the original point. Therefore, the computation complexity and

time of stereo correspondences can be greatly reduced. If the epipolar lines

are parallel to the horizontal image axis, stereo matching can be done in an

effective and fast way since the correspondences between stereo images lie

only along the same horizontal line. For this reason, it is better to convert

nonparallel epipolar lines to parallel ones. In terms of stereo conguration,

this is the same as converting a general stereo conguration to the parallel

stereo conguration, which is called stereo rectication. Rectication of stereo

images transforms all epipolar lines in the stereo images parallel to the hori-

zontal image axis. Therefore, in the rectied stereo images, corresponding

image points are always in the same horizontal lines. This geometric prop-

erty also greatly reduces computation time for stereo matching.

For many years, various stereo matching techniques have been introduced.

Most stereo matching techniques are categorized into two types. In terms of

matching cost and energy aggregation, they are categorized as either local

or global stereo matching techniques. Local stereo matching techniques use

image templates dened in both stereo images to measure their correlation

[14,15]. Common techniques are SAD (sum of absolute difference), SSD (sum

of squared difference), and NCC (normalized cross correlation).

In the template-based method, a cost function is dened based on the simi-

larity between two image templates of their left and right images. Suppose

an image template is dened from the left image and many comparing tem-

plates are dened along an epipolar line in the right image. Then a matching

template from the right image is determined in the sense of minimizing the

matching cost. Local matching techniques are useful when only some parts

in an image are of interest for obtaining the depth map of the area.

By the way, most recent investigations in stereo vision address global

error minimization. In global matching methods, a cost function is dened

in terms of image data and depth continuity [14]. The data term measures

4 Handbook of 3D Machine Vision: Optical Metrology and Imaging

the similarity of matching templates, while the continuity term additionally

measures the global matching cost based on the disparities of adjacent image

pixels. In other words, the disparity of an image point is determined not only

from its image properties but also from disparity continuities around it. The

global approaches produce more accurate results than the local methods.

However, high computation time is needed. Examples of global matching

are belief propagation (BP) [3,10,12], semiglobal matching (SGM) [7,8], graph

cut (GC) [2], and cooperative region (CR) [19], among others.

In terms of the density of a disparity map, stereo matching techniques are

divided into two categories: dense and sparse matching methods. The dense

matching method decides the disparity of every image pixel, thus produc-

ing a disparity map in which resolution is the same as that of stereo images.

Obtaining the disparity of every pixel produces very dense depth informa-

tion. However, the dense matching method needs high computation time.

On the other hand, the sparse matching method computes the disparities of

only some image pixels. Feature-based stereo matching techniques belong to

this method. Image features are relevant subjects in an image such as corners

or edges. Therefore, obtaining disparities of feature points is easier and more

robust than obtaining featureless points.

This chapter presents fundamental theories and practices of stereo vision.

In Section 1.2, the stereo geometry is presented to dene the epipolar geome-

try and constraint. In Section 1.3, calibration of a stereo vision system, which

describes the geometric relationship between two independent camera coor-

dinate systems, is presented. In Section 1.4, rectication of stereo images,

which aligns epipolar lines along the same horizontal lines, is presented.

Section 1.5 shows some practical examples of stereo calibration and rectica-

tion. In Section 1.6, two simple methods to compute 3D coordinates from a

pair of stereo correspondences are presented. In Section 1.7, basic theories of

several stereo matching techniques are briey introduced and their perfor-

mances are compared using standard stereo test images.

1.2 Stereo Geometry

In this section, the epipolar geometry of a stereo vision system is presented

in order to understand the epipolar constraint. In a pair of stereo images, two

corresponding points in the left and right images are always on the epipolar

lines, which are dened in the stereo image planes. Figure1.2 shows the

geometry of a stereo vision system. Here, O

and O

are the centers of the left

and right cameras, respectively. In the two image planes Π

and Π

, 2D image

points p

and p

are the projections of a 3D point W to each image plane.

Since W is projected toward the center of each camera, p

and p

lie on the

projection lines from W to both centers.

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