Carlos Cuevas

Daniel Berjón, Carlos Cuevas, Narciso García

Augmented reality applications are beginning to change the way sports are broadcast, providing richer experiences and valuable insights to fans. The first step of augmented reality systems is camera calibration, possibly based on detecting the line markings of the playing field. Most existing proposals for line detection rely on edge detection and Hough transform, but radial distortion and extraneous edges cause inaccurate or spurious detections of line markings. We propose a novel strategy to automatically and accurately segment and classify line markings. First, line points are segmented thanks to a stochastic watershed transform that is robust to radial distortions, since it makes no assumptions about line straightness, and is unaffected by the presence of players or the ball. The line points are then linked to primitive structures (straight lines and ellipses) thanks to a very efficient procedure that makes no assumptions about the number of primitives that appear in each image. The strategy has been tested on a new and public database composed by 60 annotated images from matches in five stadiums. The results obtained have proven that the proposed strategy is more robust and accurate than existing approaches, achieving successful line mark detection even in challenging conditions.

Daniel Berjón, Guillermo Gallego, Carlos Cuevas et al.

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.