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Measurement for deriving kinematic parameters: numerical methods
Published in Youlian Hong, Roger Bartlett, Routledge Handbook of Biomechanics and Human Movement Science, 2008
The direct linear transformation (DLT) method (Abdel-Aziz and Karara, 1971; Marzan and Karara, 1975; Walton, 1981) has been one of the most widely used camera calibration and reconstruction algorithms. The relationship between the object space coordinates and the image plane coordinates are described by a set of 11 DLT parameters in this method. The DLT parameters are mutually dependent since 11 parameters are derived from 10 camera parameters (Hatze, 1988; Kwon, 2005).
Vehicle trajectory data extraction from the horizontal curves of mountainous roads
Published in Transportation Letters, 2022
V.A. Bharat Kumar Anna, Suvin P. Venthuruthiyil, Mallikarjuna Chunchu
For computer vision applications such as video-based traffic analysis, it is essential to calibrate the extrinsic parameters for developing the relationship between any two images or image and real-world coordinates. The camera calibration techniques are numerous and are broadly classified into four categories. They are: full-scale non-linear optimization, computing perspective transformation matrix using linear equations, two-plane method, and geometric technique (Tsai 1987). Among these various techniques, the three-vanishing point technique proposed by Wang and Tsai (1991) uses a planar hexagonal pattern for the calibration. The main assumption of this technique is that the target image or the real-world study region is a plane. The major disadvantage of this approach is, creating the hexagonal pattern with three pairs of parallel lines on the real field is practically difficult (Fung 2003). Another problem with this approach is that, a priori parameter information is required for calibration. Schoepflin and Dailey (2003) proposed a two vanishing point technique that identifies parallel and perpendicular lines in the image. Creating a square or rectangle pattern that has two vanishing points on the real-world field is easier than the hexagonal pattern. Fung (2003) proposed a two vanishing point technique by using the road lane markings for calibration. The major drawback of this approach is the ill-conditioning effect that occurs due to near parallel lines. He (2007) proposed a calibration method using a single vanishing point from the lane markings to overcome the errors caused by ill-conditioning. This method doesn’t assume any extrinsic parameters to be known a priori. Direct linear transformation (DLT) is a technique where internal parameters and orientation of the camera are represented by a group of coefficients and define a linear transformation between the 3D real world and image planes (Tsai 1987; Chen, Armstrong, and Raftopoulos 1994). This approach doesn’t consider the lens distortion and solves the calibration problem using linear equations for homogeneous coordinates (Dubrofsky 2009). Thus, DLT is a relatively simple and accurate technique, and that permits great flexibility in camera setup such as the position and orientation. All the existing techniques perform camera calibration by considering the real-world region as a planar region. However, in the context of the present study, the existing image processing tools have the following limitations: The major pre-requisite for the existing tools is that the study location should be a planar region.The developed tools for co-ordinate conversion from image plane to world plane are limited to straight road sections.