Sparse overcomplete Gabor wavelet representation based on local competitions

Abstract

Gabor representations present a number of interesting properties despite the fact that the basis functions are nonorthogonal and provide an overcomplete representation or a nonexact reconstruction. Overcompleteness involves an expansion of the number of coefficients in the transform domain and induces a redundancy that can be further reduced through computational costly iterative algorithms like Matching Pursuit. Here, a biologically plausible algorithm based on competitions between neighboring coefficients is employed for adaptively representing any source image by a selected subset of Gabor functions. This scheme involves a sharper edge localization and a significant reduction of the information redundancy, while, at the same time, the reconstruction quality is preserved. The method is characterized by its biological plausibility and promising results, but it still requires a more in depth theoretical analysis for completing its validation.

Image Segmentation Using a Sparse Coding Model of Cortical Area V1

“…Specifically, in traditional approaches to boundary detection, filters have been applied using linear filtering to generate dense, redundant, representations. Other work has demonstrated that sparse coding can be beneficial for image compression (e.g., Fischer et al, 2006Fischer et al, , 2007Murray and Kreutz-Delgado, 2006;Pece and Petkov, 2000), image restoration (e.g., Elad and Aharon, 2006;Hyvarinen et al, 1998;Mairal et al, 2009), and classification (e.g., Bociu and Pitas, 2004;Mairal et al, 2008;Ramirez et al, 2010;Wright et al, 2009). Here, it has been shown that sparse coding can also be used for boundary detection.…”

An Optimal Solution for Image Edge Detection Problem using Simplified Gabor Wavelet

“…The chain code method is used for the contour extraction. Image reconstruction using local competition Gabor wavelets transformation is described in [26]. This algorithm is based on linear Gabor wavelets followed by a nonlinear iterative algorithm consisting of local competitions between coefficients which aim is reducing the amount of information to be encoded.…”

Self-Invertible 2D Log-Gabor Wavelets

“…The present log-Gabor wavelet scheme has already been shown efficient in many classical image processing applications such as edge extraction in press), image fusion (Redondo et al, in press), image denoising Redondo et al, 2005) and also image compression (Fischer et al, 2006). Here to illustrate the efficiency of the transform we propose to compare its ability to segregate the noise from the signal in an image denoising scenario.…”

“…The present paper fulfills two objectives: first to describe in detail in the Section 2 the proposed selfinvertible log-Gabor wavelet transform which we already employed successfully in a variety of applications such as denoising Redondo et al, 2005), edge extraction (Fischer et al, 2005, in press), image compression (Fischer et al, 2006) and image fusion (Redondo et al, in press), but whose implementation was incomplete or not described in detail in those publications. Second to illustrate (in Section 3) the efficiency of the method in an image denoising scenario.…”