Yongduek Seo

Where Are the Ball and Players? Soccer Game Analysis with Color Based Tracking and Image Mosaick

Knowing the locations of the players and the ball on a ground field is important for soccer game analysis. Given an image sequence, we address three main problems: 1) ground field extraction, 2) player and ball tracking and team identification and 3) absolute player positioning. The region of ground field is extracted on the basis of color information, within which all the other processing is restricted. Players are tracked by template matching and Kalman filtering. Occlusion reasoning is done by color histogram back-projection. To find the location of a player, afield model is constructed and a transformation between the input image and the field model is computed using feature points. Otherwise, an image-based mosaicking technique is applied. Using this image-to-model transformation, the absolute positions and the trajectories of players on the field model are determined. We tested our method on real image sequences and the experimental results are given.

Physics-based 3D position analysis of a soccer ball from monocular image sequences

In this paper, we propose a method for locating 3D position of a soccer ball from monocular image sequence of soccer games. Toward this goal, we adopted ground-model-to-image transformation together with physics-based approach, that a ball follows the parabolic trajectory in the air. By using the transformation the heights of a ball can be easily calculated using simple triangular geometric relations given the start and the end position of the ball on the ground. Here the heights of a ball are determined in terms of a players height. Even if the end position of a ball is not given on the ground due to kicking or heading of a falling ball before it touches the ground, the most probable trajectory can be determined by searching based on the physical fact that the ball follows a parabolic trajectory in the air. We have tested and experimented with a real image sequence the results of which seem promising.

Globally optimal line clustering and vanishing point estimation in Manhattan world

The projections of world parallel lines in an image intersect at a single point called the vanishing point (VP). VPs are a key ingredient for various vision tasks including rotation estimation and 3D reconstruction. Urban environments generally exhibit some dominant orthogonal VPs. Given a set of lines extracted from a calibrated image, this paper aims to (1) determine the line clustering, i.e. find which line belongs to which VP, and (2) estimate the associated orthogonal VPs. None of the existing methods is fully satisfactory because of the inherent difficulties of the problem, such as the local minima and the chicken-and-egg aspect. In this paper, we present a new algorithm that solves the problem in a mathematically guaranteed globally optimal manner and can inherently enforce the VP orthogonality. Specifically, we formulate the task as a consensus set maximization problem over the rotation search space, and further solve it efficiently by a branch-and-bound procedure based on the Interval Analysis theory. Our algorithm has been validated successfully on sets of challenging real images as well as synthetic data sets.

Calibration-free augmented reality in perspective

This paper deals with video-based augmented reality and proposes an algorithm for augmenting a real video sequence with views of graphics objects without metric calibration of the video camera by representing the motion of the video camera in projective space. A virtual camera, by which views of graphics objects are generated, is attached to a real camera by specifying image locations of the world coordinate system of the virtual world. The virtual camera is decomposed into calibration and motion components in order to make full use of graphics tools. The projective motion of the real camera recovered from image matches has the function of transferring the virtual camera and makes the virtual camera move according to the motion of the real camera. The virtual camera also follows the change of the internal parameters of the real camera. This paper shows the theoretical and experimental results of our application of nonmetric vision to augmented reality.

About the self-calibration of a rotating and zooming camera: Theory and practice

This paper deals with the uniqueness of the self-calibration of a rotating and zooming camera theoretically. We assume that the principal point and the aspect ratio are fixed but the focal length changes as the camera moves. In this case, at least one inter-image homography is required in order to compute the internal calibration parameters as well as the rotation. We analyze the effects of the deviation of the principal point on the estimation of the focal length and the rotation. The more the camera changes its zoom, the larger the effects are, and the larger the rotation angle is, the smaller the effects are. Thus, we may take the image center as the principal point in practical applications. Experiments using real images are given.

UPnP: An Optimal O(n) Solution to the Absolute Pose Problem with Universal Applicability

A large number of absolute pose algorithms have been presented in the literature. Common performance criteria are computational complexity, geometric optimality, global optimality, structural degeneracies, and the number of solutions. The ability to handle minimal sets of correspondences, resulting solution multiplicity, and generalized cameras are further desirable properties. This paper presents the first PnP solution that unifies all the above desirable properties within a single algorithm. We compare our result to state-of-the-art minimal, non-minimal, central, and non-central PnP algorithms, and demonstrate universal applicability, competitive noise resilience, and superior computational efficiency. Our algorithm is called Unified PnP (UPnP).

A branch-and-bound algorithm for globally optimal calibration of a camera-and-rotation-sensor system

We propose a branch-and-bound algorithm to obtain the globally optimal relative rotation between a camera and the rotation sensor attached to it. Compared to previous methods, our approach directly minimizes the image space error related to the measurements which is very natural for camera-based systems. Our algorithm is based on the observation that we may evaluate the residual when the rotation matrix is known. We propose a feasibility test algorithm for the branch-and-bound to efficiently reduce the search volume of the rotation domain. Experimental results are provided using synthetic and real data sets.

A fast method to minimize L ∞ error norm for geometric vision problems

Minimizing L∞ error norm for some geometric vision problems provides global optimization using the well- developed algorithm called SOCP (second order cone programming). Because the error norm belongs to quasi- convex functions, bisection method is utilized to attain the global optimum. It tests the feasibility of the intersection of all the second order cones due to measurements, repeatedly adjusting the global error level. The computation time increases according to the size of measurement data since the number of second order cones for the feasibility test inflates correspondingly. We observe in this paper that not all the data need be included for the feasibility test because we minimize the maximum of the errors; we may use only a subset of the measurements to obtain the optimal estimate, and therefore we obtain a decreased computation time. In addition, by using L∞ image error instead of L2 Euclidean distance, we show that the problem is still a quasi-convex problem and can be solved by bisection method but with linear programming (LP). Our algorithm and experimental results are provided.

Auto-calibration by linear iteration using the DAC equation

Abstract This paper presents an iterative algorithm for auto-calibration. The proposed algorithm switches between linearly estimating the dual of the absolute conic and the intrinsic parameters, while also incorporating the rank-3 constraint on the intrinsic parameters. The proposed algorithm locates in-between of a non-linear optimization and initial linear computation, and provides robust and sufficiently accurate initial values for a bundle adjustment. The performance of the algorithm is shown for both simulated and real data, especially in the important case of natural (zero skew and unit aspect ratio) cameras.

Real-Time Camera Calibration for Virtual Studio

In this paper, we present an overall algorithm for real-time camera parameter extraction, which is one of the key elements in implementing virtual studio, and we also present a new method for calculating the lens distortion parameter in real time. In a virtual studio, the motion of a virtual camera generating a graphic studio must follow the motion of the real camera in order to generate a realistic video product. This requires the calculation of camera parameters in real-time by analyzing the positions of feature points in the input video. Towards this goal, we first design a special calibration pattern utilizing the concept of cross-ratio, which makes it easy to extract and identify feature points, so that we can calculate the camera parameters from the visible portion of the pattern in real-time. It is important to consider the lens distortion when zoom lenses are used because it causes nonnegligible errors in the computation of the camera parameters. However, the Tsai algorithm, adopted for camera calibration, calculates the lens distortion through nonlinear optimization in triple parameter space, which is inappropriate for our real-time system. Thus, we propose a new linear method by calculating the lens distortion parameter independently, which can be computed fast enough for our real-time application. We implement the whole algorithm using a Pentium PC and Matrox Genesis boards with five processing nodes in order to obtain the processing rate of 30 frames per second, which is the minimum requirement for TV broadcasting. Experimental results show this system can be used practically for realizing a virtual studio.