Symmetry group extraction from multidimensional real data

Symmetry is an important characteristic of an object or a group of objects. Detecting, locating and analyzing real world symmetries have been a non-trivial computer vision research topic for decades. Robust and efficient symmetry group detection algorithms are desirable since they may benefit many computer vision applications like human activity analysis, shape matching and object recognition. In this dissertation, we study Symmetry-based Recognition from multidimensional real data. The contribution of this dissertation is two-fold (1) a set of novel symmetry group detection algorithms and (2) a set of applications validating the efficacy of the real world symmetry detection algorithms. At the algorithmic level, we propose two novel symmetry group detection algorithms. First, we generalize reflection symmetry detection to a curved glide-reflection symmetry detection problem from real, unsegmented images. Second, we present an effective algorithm for affinely skewed rotation symmetry group detection from real-world images using a frieze-expansion (FE) method that transforms rotation symmetry group detection into a simple one dimensional translation symmetry detection problem. Experimental results for both symmetry detection algorithms on 400+ images demonstrate, quantitatively, superior performance of the proposed algorithms over existing methods. At the application level, we focus on two aspects. First, we propose a novel Bayesian framework for symmetry-driven shape matching and object recognition, where we can incorporate a new symmetry group descriptor into any conventional system. Statistically significant enhancement of shape matching performance over the best state of the art methods on the MPEG-7 data set is observed in our initial experiments. Second, we define and analyze spatiotemporal patterns of human body motion in terms of symmetry distances. This novel use of symmetry for motion analysis leads to quantitative characterizations and unique/detailed motion features that have never been attempted before. The outcome of this dissertation illustrate the challenges as well as the feasibility of computational symmetry.