Centered Pyramids

Quadtree-like pyramids have the advantage of resulting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous $(L _{ \infty } )$ and the discrete $(l _{ \infty } )$ norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications

Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

The near shift-invariance of the dual-tree complex wavelet transform revisited

The dual-tree complex wavelet transform (DTCWT) is an enhancement of the conventional discrete wavelet transform (DWT) due to a higher degree of shift-invariance and a greater directional selectivity, finding its applications in signal and image processing. This paper presents a quantitative proof of the superiority of the DTCWT over the DWT in case of modulated wavelets.Comment: 15 page

Vector Lifting Schemes for Stereo Image Coding

International audienceMany research efforts have been devoted to the improvement of stereo image coding techniques for storage or transmission. In this paper, we are mainly interested in lossyto- lossless coding schemes for stereo images allowing progressive reconstruction. The most commonly used approaches for stereo compression are based on disparity compensation techniques. The basic principle involved in this technique first consists of estimating the disparity map. Then, one image is considered as a reference and the other is predicted in order to generate a residual image. In this work, we propose a novel approach, based on Vector Lifting Schemes (VLS), which offers the advantage of generating two compact multiresolution representations of the left and the right views. We present two versions of this new scheme. A theoretical analysis of the performance of the considered VLS is also conducted. Experimental results indicate a significant improvement using the proposed structures compared with conventional methods