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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]

This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the properties of linear phase shifts in the spherical harmonic domain, which suggest a mechanism for constructing finite-impulse-response (FIR) filters. We show that those filters have desirable properties, such as being associative, mapping spherical functions to spherical functions, allowing directional filtering, and being defined by relatively simple equations. We provide examples of the filters for both spherical and manifold data. [ABSTRACT FROM PUBLISHER]

Ranking data is a type of data obtained in some elections, in customer surveys, as well as from web search results. Such data may be considered as a type of signal defined on the group of permutations of n objects, denoted S_n. There exists a Fourier transform for S_n obtained from group representation theory, which is well known in the mathematics literature. However, previous work has not approached the transform from a signal processing perspective: in particular, there is no discussion of what constitutes “magnitude” and “phase,” nor any analysis of what phase information might tell us beyond a well-known connection to group translation. This paper explores the properties of the phase spectrum of ranking data; in particular, a novel contribution is the formulation of the bispectrum for ranking data, which may be used for studying phase linearity. Analysis of two well-known ranking data sets shows that they are surprisingly well fit by linear phase approximations. [ABSTRACT FROM AUTHOR]

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]

Describes a spatially adaptive demosaicing algorithm that is based on the Jacobian matrix of the color map and neighborhood voting. Definition of demosaicing; Computational requirements of the algorithm; Improvement of the algorithm on published algorithms in terms of complexity or image quality.

Presents information on a study which is concerned with the properties of orientational estimators, the n x p orthogonal matrices. Measure of variance for a parallel estimator; Fisher-von Mises matrix distribution; Concepts of a parallel estimator and divergence; Lower bound for the divergence of a parallel estimator.

Proposes a multiresolution form of the singular value decomposition (SVD). Notation and conventions; How the multiresolution SVD may be constructed; Complexity analysis; Interpretation of decomposition; Calculations for the Markov-1 model.

Describes a procedure for estimating the parameters associated with a linear-phase signal from noisy measurements. Discussion of the parameter estimation methods for minimizing normalized criterion; How to obtain insight into the optimal estimation formulae; Algorithm's implementation; Conclusions.

Digital camera sensors usually contain defective pixels that either arise during the manufacturing process, or develop over time. These defects though small in number, are very noticeable to an experienced eye when looking at images captured from the camera. As a result it becomes extremely important for the sensor manufacturing companies to develop methods which would reduce these manufacturing errors. There have been a number of algorithms proposed for online detection of sensor defects in the literature, but there is no standard method of fairly comparing algorithms given that each algorithm uses thresholds in a different way. This paper presents a novel idea which makes use of the Receiver Operating Characteristics (ROC) curve for comparison among the various bad pixel correction algorithms. We demonstrate how the characteristics of the ROC curve can be used for determining the effectiveness of the algorithms and hence help us to decide which of the algorithms perform better than the others. Experimental results comparing two such bad pixel detection algorithms are provided1. [ABSTRACT FROM AUTHOR]