A novel fast and reduced redundancy structure for multiscale directional filter banks

2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Analysis and Modeling of Statistical Properties of FMDFB Subband Coefficients

Fast Multiscale Directional Filter Bank (FMDFB) is an image representation scheme used in several image processing applications. The statistical nature of the FMDFB subbands is analyzed, and a mathematical model of FMDFB coefficients is proposed. Experimental results are justified by goodness-of-fit tests

ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets

Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient of sparsely approximating and also of analyzing in the sense of, for instance, detecting their direction. Shearlets are a directional representation system extending the wavelet framework, which overcomes those deficiencies. Similar to wavelets, shearlets allow a faithful implementation and fast associated transforms. In this paper, we will introduce a comprehensive carefully documented software package coined ShearLab 3D (www.ShearLab.org) and discuss its algorithmic details. This package provides MATLAB code for a novel faithful algorithmic realization of the 2D and 3D shearlet transform (and their inverses) associated with compactly supported universal shearlet systems incorporating the option of using CUDA. We will present extensive numerical experiments in 2D and 3D concerning denoising, inpainting, and feature extraction, comparing the performance of ShearLab 3D with similar transform-based algorithms such as curvelets, contourlets, or surfacelets. In the spirit of reproducible reseaerch, all scripts are accessible on www.ShearLab.org.Comment: There is another shearlet software package (http://www.mathematik.uni-kl.de/imagepro/members/haeuser/ffst/) by S. H\"auser and G. Steidl. We will include this in a revisio

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

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 nonredundant contourlet transform (NRCT): a multiresolution and multidirection image representation with perfect reconstruction property

Multiresolution and multidirection image representation has recently been an attractive research area, in which multiresolution corresponds to varying scale of structure in images, while multidirection deals with the oriented nature of image structure. Numerous new systems, such as the contourlet transform, have been developed. The contourlet transform has the benefit of efficiently capturing the oriented geometrical structures of images; however, it has the drawback of a 4/3 redundancy in its oversampling ratio. In order to eliminate the redundancy, this thesis proposes a progressive version of the contourlet transform which can be calculated with critical sampling. The new proposed image representation is called the nonredundant contourlet transform (NRCT), which is constructed with an efficient framework of filter banks. In addition to critical sampling, the proposed NRCT possesses many valuable properties including perfect reconstruction, sparse expression, multiresolution, and multidirection. Numerical experiments demonstrate that the novel NRCT has better peak signal-to-noise performance than the traditional contourlet transform. Moreover, for low ratios of retained coefficients, the NRCT outperforms the wavelet transform which is a standard method for the critically sampled representation of images. -- After examining the computational complexity of the nonredundant contourlet transform, this thesis applies the NRCT to fingerprint image compression, since fingerprint images are examples of images with oriented structures. Based on an appropriately designed filter bank structure, the NRCT is easily compatible with the wavelet transform. Hence a new transform is created called the semi-NRCT, which takes the advantages of the directional selectivity of the NRCT and the lower complexity of the wavelet transform. Finally, this thesis proposes a new fingerprint image compression scheme based on the semi-NRCT. The semi-NRCT-based fingerprint image compression is compared with other transform-based compressions, for example the wavelet-based and the contourlet-based algorithms, and is shown to perform favorably