Search

In this paper we put under the same umbrella several well known results and establish several new results related to the shape based tools which treat the objects ellipticity issues. We start with a derivation of an explicit and closed formula for the computation of the ellipticity measures, from an infinite family, introduced recently. The new formula enables a fast computation of such measures, since it does not require any optimizing procedure for the computation, as it was the case before. In addition, the established formula enables an easy theoretical manipulation. As a result, we have discovered new shape features, as they are: (i) The average shape ellipticity measure , which might be interpreted as an average value of the estimated similarities between the shape considered and all the ellipses whose axes length ratio belongs to a certain, predefined, interval; (ii) The maximal shape ellipticity measure , which might be understood as the maximal possible similarity estimate between a given shape and an ellipses. Some of the other results obtained relate strongly to the well-known measures and methods broadly used in shape based object analysis tasks. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we identify some of the limitations of current-day shape-matching techniques. We provide examples of how contour-based shape-matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape-matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates. [Copyright &y& Elsevier]

Abstract: Stochastic search methods, such as the annealed particle filter (APF) and its variants, are used widely in human pose tracking due to their reliability. In this paper, we propose a method that improves stochastic search by using two novel steps: first, by reusing samples across annealing layers, and second, by fitting an adaptive parametric density to the samples for diffusion. We compare our proposed method, called parametric annealing (PA), to APF as well as to the recently published interacting simulating annealing (ISA) on the Human Eva I dataset. The results show that PA tracks more accurately than APF despite using less than 50% of the samples, and also tracks more accurately than an ISA configuration that uses the same number of samples. Furthermore, we describe a framework to select the optimum parameters for APF, ISA, and PA that takes into account their stochastic nature. Using our framework, the computational overhead for tracking may be reduced by up to 40% with no loss of performance. Finally, we compare our method to discriminative methods. [Copyright &y& Elsevier]

Abstract: Let denote the symmetric group on and the stabilizer subgroup of . We derive algorithms for computing Fourier transforms of left and right -invariant signals that require a total of additions and scalar multiplications. Furthermore we show that the convolution of such signals can also be computed in time linear in . [Copyright &y& Elsevier]