Future Directions

Some directions for future study are recommended below:

(1) In the future, practical applications of PTZ cameras will be further studied. For instance, most image-based traffic surveillance methods adopt a virtual window to detect vehicles [71]. If the view of a PTZ camera is changed, then the position and size of the window must be adjusted manually. Using the dynamic calibration procedure developed in this thesis, the detection window can be arranged automatically. On the other hand, the effects of lens distortion and having a non-fixed principal point need to be handled in order to increase the accuracy of PTZ camera calibration.

(2) Several directions on vehicle detection and tracking deserve further study in the future. On one hand, heavy occlusion of vehicles influences the accuracy of image measurement.

Methods need to be developed to distinguish individual vehicles. Color information of individual tracked cars can be very useful for solving this problem [80]. On another hand, in order to increase the accuracy of foreground segmentation, we will focus on the study of new methods to select adaptive thresholds for handling the change of environment

106

illumination on the road. To achieve a dependable performance, a Neuro-Fuzzy classifier can be desirable for an ITMS.

(3) For future shadow-detection studies, more emphasis will be directed to increase the robustness of the shadow detection under various illumination conditions. First, the Gaussian ratio model built under a specific illumination condition might fail under a considerably different illumination. In traffic monitoring applications, it will be beneficial to build a database of ratio models for different illumination conditions. Additionally, shadow pixels that lie nearmoving vehicles or overlap other vehicles might be misclassified as moving-vehicle pixels. The pixels of the same shadow region may have similar color information to the traffic imagery. The color distribution can be used to find uniform sub-regions and hence the uniform sub-regions can be used to verify the actual shadow region [81].

107

Appendix A

Derivation of Focal Length Equation

In this appendix, the focal length equation will be derived by using only two parallel lines in the image. As shown in Fig. 2-1(a), lines L1 and L2 are two parallel lines, L1 and L2

intersect X-axis and Y-axis at P₁, P₂, P₃ and P₄; the corresponding coordinates of these points in image plane are expressed as follows:

u

2

can be rewritten as

v =

1

108

Applying trigonometric function properties, one can easily find the relationship between

r, s and t. Computing r

² +

f

²

s

²and r²t², one can obtain

Rearranging (A.12), we obtain

φ

109

Substituting (A21) into (A13), we obtain

θ

Using the vanishing point constraints and trigonometric function properties, one can proceed to derive equations that will determine the equation containing ^sec2θ and, finally,

110

Rearranging (A.26), we arrive at:

2 +bm+c=0

am . (A.27)

where m is f² and other variables are listed Table 2-1. This governing equation is presented in Section 2.2 as the focal length equation.

Next, let us discuss how camera parameters affect the sign of coefficient a. For simplicity, the sign of at²is discussed instead of the sign of a

)

(A.28) reveals that the magnitude of the tile angle and pan angle affect the sign of coefficient

a ; the details are listed below:

• a>0, if

φ

>

θ

,

111

• a=0, if

φ

=

θ

or

Y

₃ =0,

• a<0, if

φ

<

θ

.

It is clear that the difference between the absolute value of tilt angle and pan angle determines the sign of coefficient a . When a=0, the focal length equation becomes linear and the focal length can be easily estimated. This completes the derivation of the focal length equation.

When the vanishing point is far from the image center or disappears (for instance, when the tilt angle equals 90 deg) in the image frame, (A.27) cannot be used to find the focal length. Instead the focal length can be easily obtained by the perspective projection equation:

w h w

f

= ^p , (A29)

where w_p is the width between parallel lanes in the image frame.

112

Appendix B

Conversion between Pixel

Coordinates and World Coordinates

In this appendix, we derive the transformation between pixel coordinates and world coordinates. We will explain how focal length and tilt angle are used to obtain the world coordinates of a feature in the ground plane.

A pixel coordinate (u,v) is expressed as a function of world coordinate (X,Y,Z)

113 v v v v f Y h

= −

0 0

sin2φ . (B.6)

Substituting (B.6) into (B.1), it is easy to obtain

v v

v u f h v

v v u f X h

= −

− +

=

0 0

0 1) sin

sinφ ( φ . (B.7)

From (B.6) and (B.7), one can transform the pixel coordinates into their world coordinates.

114

Appendix C

RGB Color Ratio Model of Shadow Pixels

In an outdoor daytime environment, there are two light sources, namely, a light point source and a diffused extended light source. In the following derivation, the road is assumed as to be Lambertian, with a constant reflectance in a traffic scene. The radiance

L

_lit of the light reflected at a given point on a surface in the scene is formulated as [82]

) respectively; λ is the wavelength;iis the angle of incidence between the illumination direction and the surface normal at a considered point; e is the reflection angle between the surface normal and the viewing direction; and g is the phase angle illumination direction and the viewing direction. When sunlight occlusion creates shadows, the radiance

L

_shadow of the reflected light becomes

)

where )

L′

a(

λ

is the ambient reflection term in presence of the occluding object. To simplify the analysis, the design assumes that the ambient light coming from the sky is not influenced by the presence of the occluding objects, that is,

L

a′(

λ

)=

L

a(

λ

).

The model is derived based on an RGB mode. The color components of the reflected intensity reaching the RGB sensors at a point (x,y) in the 2D image plane can be expressed

115 wavelengths λ. We assume that the scene radiance and the image irradiance are the same because the situation is considered a Lambertian scene under uniform illumination [83]. For a point in direct light, the sensor measurements are

[ ]

When a point is in the shadow, the sensor measurements are

∫

Λ similar in a traffic scene, for each object point of the road surface, the RGB measurement ratio between the lit and the shadow condition is approximately constant:

) .

116

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122

Vita

姓名: 戴任詔 性別: 男

生日: 中華民國 51 年 4 月 22 日 籍貫: 台灣省台中縣

論文題目: 中文: 交通參數估測系統之攝影機參數校正與影像追蹤

英文: Camera Calibration and Image Tracking for Traffic Parameter Estimation

學歷:

1. 民國 74 年 6 月 國立清華大學動力機械工程學系畢業 2. 民國 81 年 6 月 國立交通大學控制工程研究所畢業

3. 民國 88 年 9 月 國立交通大學電機及控制工程研究所博士班

經歷:

1. 76 年 6 月～76 年 11 月 羽田機械 助理工程師 2. 76 年 12 月～79 年 3 月 三陽工業 二級助理研究員

3. 81 年 9 月～迄今 明新科技大學 機械工程系講師

123

Publication List

Journal paper

[1] K. T. Song and J. C. Tai, “Dynamic Calibration of Pan-Tilt-Zoom Cameras,” IEEE

Trans. Systems, Man, and Cybernetics, Part B. vol. 36, no. 5, in press. [4 點].

[2] J. C. Tai, S. T. Tseng, C. P. Lin, and K. T. Song, “Real-Time Image Tracking for Automatic Traffic Monitoring and Enforcement Applications,” Image and Vision Computing, vol. 22, no. 6, pp. 485–501, 2004 [1.2 點].

[3] J. C. Tai and K. T. Song, “On the Parametric Approach to the MEMS Mask Design,” (in Chinese) Journal of Technology, vol. 17, no. 1, pp. 73–82, 2002. [0 點].

[4] K. T. Song and J. C. Tai, “Real-Time Background Estimation of Traffic Imagery Using Group-Based Histogram,” revised, Journal of Information Science and Engineering.

[5] K. T. Song and J. C. Tai, “Image-Based Traffic Monitoring with Shadow Suppression,”

revised, Proceedings of the IEEE.

[6] K. T. Song and J. C. Tai, “Automatic Contour Initialization and Multi-Vehicle Tracking for Vision-Based Traffic Monitoring,” submitted to International Journal of Imaging

Systems and Technology.

Conference paper

[1] K. T. Song and J. C. Tai, “Image-Based Turn Ratio Measurement at Road Intersection,”

in Proc. of The IEEE International Conference on Image Processing, Genova, Italy, 2005, pp. I-1077–1080.

[2] J. C. Tai and K. T. Song, “Background Segmentation and its Application to Traffic Monitoring Using Modified Histogram,” in Proc. of 2004 IEEE International

Conference on Networking, Sensing & Control, Taipei, Taiwan, 2004, pp. 13–18.

[3] J. C. Tai and K. T. Song, “Automatic contour initialization for image tracking of multi-lane vehicles and motorcycles,” in Proc. of the IEEE 6th International Conference

on Intelligent Transportation Systems, Shanghai, 2003, pp.808–813.

[4] C. P. Lin, J. C. Tai and K. T. Song, “Traffic monitoring based on real-time image tracking,” Proc. of. 2003 IEEE International Conference on Robotics and Automation, Taipei, 2003, pp.2091–2096.

[5] J. C. Tai and K. T. Song, “Design of a Novel Electrostatic Linear Stepping Micromotor, ” in Proc. of the 6th International Conference on Mechatronics Technology, Kitakyushu, Japan, 2002, pp.411–416.

在文檔中 交通參數估測系統之攝影機參數校正與影像追蹤 (頁 119-137)