Visualization of multidimensional shape and texture features in laser range data using complex-valued Gabor wavelets

Abstract

This paper describes a new method for visualization and analysis of multivariate laser range data using complex-valued non-orthogonal Gabor wavelets, principal component analysis and a topological mapping network. The initial data set that provides both shape and texture information is encoded in terms of both amplitude and phase of a complex valued 2D image function. A set of carefully designed oriented Gabor filters performs a decomposition of the data and allows for retrieving local shape and texture features. The feature vector obtained from this method is multidimensional and in order to evaluate similar data features, further subspace methods to transform the data onto visualizable attributes, such as R,G,B, have to be determined. For this purpose, a feature-based visualization pipeline is proposed consisting of principal component analysis, normalization and a topological mapping network. This process finally renders a R,G,B subspace representation of the multidimensional feature vector. Our method is primarily applied to the visual analysis of features in human faces-but is not restricted to that.

Self-Invertible 2D Log-Gabor Wavelets

“…And, even without exact reconstruction they have been shown useful for image restoration applications (Cristóbal and Navarro, 1994;Kovesi, 1999;Mingolla et al, 1999;Christiansen, 2002). In parallel, different methods for reconstruction improvement have been proposed to recover the highest frequencies (Nestares et al, 1998), to avoid excessive low-pass overlapping (Field, 1987), to improve the reconstruction (Daugman, 1988;Lee, 1996) or to cover more uniformly the Fourier domain (Gross and Koch, 1995).…”

“…Last fifteen years oriented band-pass multiresolution transforms have arisen with increased importance thanks to the development of steerable pyramids (Simoncelli et al, 1992), Gabor multiresolutions (Gross and Koch, 1995;Nestares et al, 1998;Ro et al, 2001), complex-valued wavelets (Gross and Koch, 1995;Kingsbury, 2001;Portilla and Simoncelli, 2000), curvelets (Starck et al, 2002) and contourlets (Do and Vetterli, 2005), to name a few.…”

A Framework for Physically-Based Information Visualization

“…We have to be aware that our model corresponds to a multidimensional graph visualization problem [12] and is prone to all problems associated with subspace procedures [1]. Consequently, in order to prevent the system from convergence to a local minimum, tightly related objects should be positioned as close as possible to each other upon initialization.…”

“…Information Visualization [6] or [1]. Here, mathematical projection algorithms were introduced to map data into subspaces, while preserving their most important features.…”

“…Recalling some foundations of data base research we formalize the information retrieval process as follows: Let A={A 1 , .., A k } be a set of attributes (key words) and let's consider n objects O={O 1 , .., O n }, where each object O i is assigned to a score vector s i of dimension k. The component s il represents the relative importance of document O i with respect to key word A l and is assumed to be bounded by [0,1].…”