R-D analysis of adaptive edge representations

Ventura, R.; Granai, L.

doi:10.1109/mmsp.2002.1203265

Cited by 11 publications

(12 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this figure, the comparison is performed with respect to the number of terms in the expansion, in order to emphasize the approximation properties (the behavior of the coding rate is discussed below). Clearly, overcompleteness and anisotropic refinement allow to outperform the other dictionaries, in terms of approximation rate, which corresponds to the results presented in [8], [9]. As expected, the orthogonal bases offer the lowest approximation rates due to the fact that these kinds of bases cannot deal with the smoothness of edges.…”

Section: A Benefits Of Anisotropysupporting

confidence: 79%

“…Several authors have explored the rate-distortion characteristics of anisotropic systems for representing edge-dominated images [8], [9]. These preliminary studies show that for images that are smooth away from a smooth edge (typically, a rectifiable curve), a -behavior of the form (1) can be reached.…”

Section: B Anisotropic Refinementmentioning

confidence: 99%

“…A possible action of on the generating atom is, thus, given by (7) where is a representation of the Euclidean group (8) is a rotation matrix, and acts as an anisotropic dilation operator (9) It is easy to prove that such a dictionary is overcomplete using the fact that, under the restrictive condition , one gets 2-D continuous wavelets as defined in [10]. It is also worth stressing that, avoiding rotations, the parameter space is a group studied by Bernier and Taylor [31].…”

Section: B Anisotropic Refinement Using Matching Pursuit 1) Generatimentioning

confidence: 99%

See 2 more Smart Citations

Low-rate and flexible image coding with redundant representations

Ventura

Vandergheynst

Frossard

2006

IEEE Trans. on Image Process.

Self Cite

View full text Add to dashboard Cite

Abstract-New breakthroughs in image coding possibly lie in signal decomposition through nonseparable basis functions that can efficiently capture edge characteristics, present in natural images. The work proposed in this paper provides an adaptive way of representing images as a sum of two-dimensional features. It presents a low bit-rate image coding method based on a matching pursuit (MP) expansion, over a dictionary built on anisotropic refinement and rotation of contour-like atoms. This method is shown to provide, at low bit rates, results comparable to the state of the art in image compression, represented here by JPEG2000 and SPIHT, with generally a better visual quality in the MP scheme. The coding artifacts are less annoying than the ringing introduced by wavelets at very low bit rate, due to the smoothing performed by the basis functions used in the MP algorithm. In addition to good compression performances at low bit rates, the new coder has the advantage of producing highly flexible streams. They can easily be decoded at any spatial resolution, different from the original image, and the bitstream can be truncated at any point to match diverse bandwidth requirements. The spatial adaptivity is shown to be more flexible and less complex than transcoding operations generally applied to state of the art codec bitstreams. Due to both its ability for capturing the most important parts of multidimensional signals, and a flexible stream structure, the image coder proposed in this paper represents an interesting solution for low to medium rate image coding in visual communication applications.

show abstract

Section: A Benefits Of Anisotropysupporting

confidence: 79%

Section: B Anisotropic Refinementmentioning

confidence: 99%

Section: B Anisotropic Refinement Using Matching Pursuit 1) Generatimentioning

confidence: 99%

See 1 more Smart Citation

Low-rate and flexible image coding with redundant representations

Ventura

Vandergheynst

Frossard

2006

IEEE Trans. on Image Process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this figure, the comparison is performed with respect to the number of terms in the expansion, in order to emphasize the approximation properties (the behavior of the coding rate is discussed below). Clearly, overcompleteness and anisotropic refinement allow to outperform the other dictionaries, in terms of approximation rate, which corresponds to the results presented in [4,5]. As expected, the orthogonal bases offer the lowest approximation rates due to the fact that these kinds of bases cannot deal with the smoothness of edges.…”

Section: Benefits Of Anisotropysupporting

confidence: 79%

“…Several authors have explored the rate-distortion characteristics of anisotropic systems for representing edge-dominated images [4,5]. These preliminary studies show that for images that are smooth away from a smooth edge (typically a C 2 rectifiable curve), a rate-distortion (R-D) behavior of the form…”

Section: Benefits Of Redundant Transformsmentioning

confidence: 99%

Image Coding Using Redundant Dictionaries

Frossard¹

2006

Signal Processing and Communications

View full text Add to dashboard Cite

This chapter discusses the problem of coding images using very redundant libraries of waveforms, also referred to as dictionaries. We start with a discussion of the shortcomings of classical approaches based on orthonormal bases. More specifically, we show why these redundant dictionaries provide an interesting alternative for image representation. We then introduce a special dictionary of 2-D primitives called anisotropic refinement atoms that are well suited for representing edge-dominated images. Using a simple greedy algorithm, we design an image coder that performs very well at low bit rate. We finally discuss its performance and particular features such as geometric adaptativity and rate scalability. IntroductionImage compression has been key in enabling what already seems to be two of the major success stories of the digital era: rich media experience over the internet and digital photography. What are the technologies laying behind such industry flagships and, more importantly, what are the future of these technologies are some of the central questions of this chapter.We begin with a quick review of the state of the art. Then, identifying some weaknesses of the actual systems together with new requirements from 1

show abstract

Ridgelet transform applied to motion compensated images

Granai¹,

Moschetti²

2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).

Self Cite

View full text Add to dashboard Cite

Wavelet transform is a powerful instrument in catching zero-dimensional singularities. Ridgelets are a powerful instrument in catching and representing monodimensional singularities in bidimensional space.In this paper we propose a hybrid video coder scheme using ridgelet transform for the first approximation of line-edge singularities in displaced frame difference images. We demonstrate the potential of ridgelets and results show substantial improvements when compared to wavelet only.based coder.

show abstract

R-D analysis of adaptive edge representations

Cited by 11 publications

References 7 publications

Low-rate and flexible image coding with redundant representations

Low-rate and flexible image coding with redundant representations

Image Coding Using Redundant Dictionaries

Ridgelet transform applied to motion compensated images

Contact Info

Product

Resources

About