关于摄像头自动对焦校准

Chapter 1

CAMERA CALIBRATION

Camera calibration is a necessary step in 3D computer vision in order to extract

metric information from 2D images. It has been studied extensively in computer vi-

sion and photogrammetry, and even recently new techniques have been proposed. In

this chapter, we review the techniques prop osed in the literature include those using

3D apparatus (two or three planes orthogonal to each other, or a plane undergoing

a pure translation, etc.), 2D objects (planar patterns undergoing unknown mo-

tions), 1D objects (wand with dots) and unknown scene points in the environment

vision ([12, 11, 33, 10, 37, 35, 22, 9] to cite a few). According to the dimension of the

calibration objects, we can classify those techniques roughly into three categories.

3D reference object based calibration. Camera calibration is performed by ob-

serving a calibration object whose geometry in 3-D space is known with very

good precision. Calibration can be done very efficiently [8]. The calibra-

tion object usually consists of two or three planes orthogonal to each other.

Sometimes, a plane undergoing a precisely known translation is also used [33],

which equivalently provides 3D reference points. This approach requires an

expensive calibration apparatus and an elab orate setup.

2D plane based calibration. Techniques in this category requires to observe a

1

2 Camera Calibration Chapter 1

calibrated by observing a moving line around a fixed point, such as a string

of balls hanging from the ceiling.

Self-calibration. Techniques in this category do not use any calibration object,

and can be considered as 0D approach because only image point correspon-

up to a similarity [20, 17]. Although no calibration objects are necessary, a

large number of parameters need to be estimated, resulting in a much harder

mathematical problem.

Other techniques exist: vanishing points for orthogonal directions [4, 19], and cali-

bration from pure rotation [16, 30].

Before going further, I’d like to point out that no single calibration technique

is the b est for all. It really depends on the situation a user needs to deal with.

Following are my few recommendations:

• Calibration with apparatus vs. self-calibration. Whenever possible, if we

can pre-calibrate a camera, we should do it with a calibration apparatus.

only a subset of camera intrinsic parameters are to be calibrated. Along the

same line as the previous recommendation, whenever possible, partial self-

calibration is preferred because the number of parameters to be estimated is

smaller. Take an example of 3D reconstruction with a camera with variable

focal length. It is preferable to pre-calibrate the pixel aspect ratio and the

pixel skewness.

• Calibration with 3D vs. 2D apparatus. Highest accuracy can usually be

obtained by using a 3D apparatus, so it should be used when accuracy is

indispensable and when it is affordable to make and use a 3D apparatus. From

the feedback I received from computer vision researchers and practitioners

Section 1.2. Notation and Problem Statement 3

useful especially for calibration of a camera network. To calibrate the relative

geometry between multiple cameras as well as their intrinsic parameters, it

1

the back. This is not a problem for 1D objects. We can for example use a

string of balls hanging from the ceiling.

This chapter is organized as follows. Section 1.2 describes the camera model

and introduces the concept of the absolute conic which is important for camera

calibration. Section 1.3 presents the calibration techniques using a 3D apparatus.

Section 1.4 describes a calibration technique by observing a freely moving planar

pattern (2D object). Its extension for stereo calibration is also addressed. Sec-

tion 1.5 describes a relatively new technique which uses a set of collinear points (1D

object). Section 1.6 briefly introduces the self-calibration approach and provides

4 Camera Calibration Chapter 1

We use

e

x to denote the augmented vector by adding 1 as the last element:

[u, v, 1]

. A camera is modeled by the usual pinhole (see

image plane is positioned between the scene point and the optical center, which is

mathematically equivalent to the physical setup under which the image plane is in

the other side with respect to the optical center. The relationship between the 3D

point M and its image projection m is given by

m = A

R t

M ≡ P

M , (1.2.1)

£

R t

¤

(1.2.3)

where s is an arbitrary scale factor, (R, t), called the extrinsic parameters, is the

rotation and translation which relates the world coordinate system to the camera

Section 1.2. Notation and Problem Statement 5