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Video technology has now reached a level of sophistication that allows easy digitization. Digital video can be easily edited, reproduced, incorporated into databases, and posted on intra- and Internet sites for clinical use and demonstration purposes. Numerous methods exist for the production of digital video (Mandar & Grantier, 2001)
Conventional two–dimensional video is a mature technology in both professional environments and home entertainment. A multitude of analog and digital video formats is available today, tailored to the demands and requirements of different user groups. Efficient coding schemes have been developed for various target bit rates, ranging from less than 100 kilobit per second for video conferencing applications to several megabit per second for broadcast quality TV (Wurmlin, Lamboray, Staadt, & Gross, 2002). Multi-camera acquisition methods can successfully identify the states of the repetitive motion and capture 3D objects by using a static installation of cameras surrounding the motion volume (Matusik, Buehler, Raskar, Gortler, & Mcmillan, 2000).
Human motion capture consists of the recording of human body movements for immediate or delayed analysis and playback. The information captured can be as simple as the body position in space or as complex as the deformations of the face and muscle masses. Optical tracker systems typically use small markers attached on the body of the subject and a set of two or more cameras focused on the subject to capture its motions (Kolahi, Hoviattalab, Rezaeian, Alizadeh, Bostan, & Mokhtarzadeh, 2007).
Calibration of cameras is considered as an important issue in computer vision. Accurate calibration of cameras is especially crucial for applications that involve quantitative measurements such as dimensional measurements, depth from stereoscopy, or motion from images (Weng, Cohen, & Herniou, 1992)
Camera calibration in the context of three dimensional (3D) machine vision in the process of determining the internal camera geometric and optical characteristic and/or the 3D position and orientation of the camera frame relative to a certain world coordinate system (Tsai, 1987). The most commonly used camera calibration method is perhaps the DLT (direct linear transformation) method originally reported by Abdel-Aziz and Karara. The DLT method uses a set of control points whose object space/plane coordinates are already known. The control points are normally fixed to a rigid frame, known as the calibration frame. The problem is essentially to calculate the mapping between the 2D image space coordinates and the 3D object space coordinates (Pourcelot, Audigie, Degueurce, Geiger, & Denoix, 2000).
The Direct Linear Transformation (Abdel-Aziz & Karara, 1971) equations are:
(1) in which (u,v) are the digitized co-ordinates of a point, (X,Y,Z) are the object's space co-ordinates, and (L
1, L
2, L
11) the unknown DLT parameters of each camera. DLT equation could be extended for matrices of camera calibration and 3D reconstruction equation.
Camera calibration is done to find mapping variables between 2D coordinate (u,v) at the image plane, which is the pixel frame, and the 3D coordinate in the real world (X,Y,Z). In general, at least 6 predefined reference points are needed (Kolahi, Hoviattalab, Rezaeian, Alizadeh, Bostan, & Mokhtarzadeh, 2007)
The equation for the accuracy of camera calibration is as follows:
(2)Based on the matrix in equation (1), there are 11 unknown variables, L1 to L11, so 11 equations are needed to solve it. Equation (3) is derived from equation (1) for camera calibration.
(3)The Moore-Penrose inverse (A+), also known as pseudoinverse, is a common solution to solve matrix equation:
,
(4)