TRACKING OF CIRCULAR PATTERNS IN VIDEO SEQUENCES BASED ON FISHER’S INFORMATION ANALYSIS L. Capodiferro, A. Laurenti, G. Monaco, M. Nibaldi, G. Jacovitti Fondazione Ugo Bordoni , Via B. Castiglione 59, 00142 Rome, Italy Ph: +39 6 54802132; Fax: +39 6 54804401; email: licia@fub.it INFOCOM Dpt.,University of Rome “La Sapienza”, via Eudossiana 18, 00184 Rome, Italy Ph: +39 6 44585838; Fax: +39 6 4873300; email: gjacov@infocom.ing.uniroma1.it 1. INTRODUCTION Detection and tracking of circular patterns in images and video sequences is a specific but important task occurring in most image content analysis problems. Among others, let us cite for instance robotic vision in industry, biometrics. etc. One of the most recent applications is ball tracking for sport video analysis , and in particular for soccer video analysis, where ball tracking provides trajectory plots, statistics, virtual replays, etc. [1]. More in general, ball detection and tracking is useful for automatic content- based video indexing for image retrieval in large video repositories or TV channel selection. In the recent years a number of methods for circle detection and location has been proposed. The Circle Hough Transform (CHT) applied to edges has been widely employed along with several modified versions. Other methods rely on contour analysis as well. However, contour based methods are generally highly sensitive to noise due to the high-pass nature of the edge extractors. Correlation based techniques, such as template matching are generally more robust against noise. However, template matching is strongly dependent on the specific pattern to be searched, so that modified correlation methods based on invariants (for instance orientation and size independent methods) have been developed. In this contribution, an alternative technique is presented for patterns exhibiting circular symmetry. Instead of considering specific circular patterns with specific attributes (radius, color, sharpness, etc.) the approach presented here employs a rather simple invariant feature of circular patterns, related to the Fisher information carried by generic patterns with respect to basic geometrical parameters. In essence, it is based on the fact that perfect circular patterns provide per se high Fisher information with respect to scale and null information with respect to orientation. In practical situations where objects do not exhibit perfect circular shape, still Fisher information is a useful index for measuring how much a pattern is circular, and it can be employed for detection and location purposes. To implement such a method it is necessary to calculate the local Fisher information for every possible location of searched pattern. At glance, it is not a simple task. In this contribution, the calculation of the local Fisher information employs a processing scheme consisting of a multi-resolution filter bank. Such a scheme is derived by a suitable image decomposition scheme based on the circular harmonic Gauss-Laguerre family. 2. CONCEPTUAL FRAMEWORK: FISHER INFORMATION IMAGING Let x=[x 1 x 2 ] T denote the coordinates of the real plane R 2 ; Let the observed image f(x) contain a noisy, translated, rotated and scaled copy of a circular template pattern g(x) which has to be extracted. The pattern localization analysis must be performed at each generic point b=[b 1 b 2 ] T of the observed image, so that it is convenient to adopt a polar coordinate system r and γ centered at the position b. Since the observed image may contain multiple circular objects, it is locally explored through a gaussian and isotropic window w(r). The windowed image model becomes then: ( ) () ( ,; , r ir b wrg r a ) γ ν γ ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ (1) where a denotes the scale factor and ( ) , r ν γ denotes the observation noise which is modeled as a sample drawn from a white, zero-mean Gaussian Random field with power density spectrum equal to ( ) 0 4 N . Under the above stated conditions, the Fisher’s information associated to a given pattern with respect to position, rotation and scale has been calculated in [2]. ISBN: 952-15-1364-0