Steerable Filters Generated with the Hypercomplex Dual-Tree Wavelet Transform

Wedekind, Jan; Amavasai, B.P.; Dutton, Ken

doi:10.1109/icspc.2007.4728563

Cited by 4 publications

(1 citation statement)

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“…A 2-D extension has been proposed in [120] and the construction of Hilbert transform pairs of wavelet bases can be found in [121]. Note that previous works dealing with multidimensional extensions have been first reported for instance in [122] and then in [123,124] using the notion of hypercomplex wavelets.…”

Section: Complexifying Discrete Wavelets With Hilbert and Rieszmentioning

confidence: 99%

A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity

et al. 2011

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International audienceThe 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 multi-scale 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 de-compositions 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

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