Results 1 - 10
of
16
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
, 2011
"... 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 smoot ..."
Abstract
-
Cited by 21 (8 self)
- Add to MetaCart
(Show Context)
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”.
Combining seminorms in adaptive lifting schemes and applications to image analysis and compression
- Journal of Mathematical Imaging and Vision
, 2006
"... Abstract. In this paper, we present some adaptive wavelet decompositions that can capture the directional nature of images. Our method exploits the properties of seminorms to build lifting structures able to choose between different update filters, the choice being triggered by the local gradient-ty ..."
Abstract
-
Cited by 8 (4 self)
- Add to MetaCart
Abstract. In this paper, we present some adaptive wavelet decompositions that can capture the directional nature of images. Our method exploits the properties of seminorms to build lifting structures able to choose between different update filters, the choice being triggered by the local gradient-type features of the input. In order to deal with the variety and wealth of images, one has to be able to use multiple criteria, giving rise to multiple choice of update filters. We establish the conditions under these decisions can be recovered at synthesis, without the need for transmitting overhead information. Thus, we are able to design invertible and non-redundant schemes that discriminate between different geometrical information to efficiently represent images for lossless compression methods. Keywords: compression adaptive wavelets, perfect reconstruction filter bank, seminorms, lifting scheme, adaptive filter, image 1.
Building adaptive 2D wavelet decompositions by update lifting
- In Proceedings of the IEEE International Conference on Image Processing
, 2002
"... This paper discusses a method for the construction of nonlinear 2D wavelet decompositions using an adaptive update lifting scheme. A very interesting aspect is that the decomposition does not require any bookkeeping, i.e., it is nonredundant, but that it, nevertheless, allows perfect reconstruction. ..."
Abstract
-
Cited by 7 (4 self)
- Add to MetaCart
(Show Context)
This paper discusses a method for the construction of nonlinear 2D wavelet decompositions using an adaptive update lifting scheme. A very interesting aspect is that the decomposition does not require any bookkeeping, i.e., it is nonredundant, but that it, nevertheless, allows perfect reconstruction. The major ingredient of the construction is the so-called decision map which triggers the choice of the update filter. Another interesting point is the possibility of better preserving the edges, even at low resolutions. 1.
Quantization of adaptive 2D wavelet decompositions
- In Proceedings of the IEEE International Conference on Image Processing
"... Classical linear wavelet representations of images have the drawback that they are not well-suited to represent edge information. To overcome this problem, nonlinear multiresolution decompositions are being designed that can take into account the characteristics of the input signal/image. In our pre ..."
Abstract
-
Cited by 2 (2 self)
- Add to MetaCart
(Show Context)
Classical linear wavelet representations of images have the drawback that they are not well-suited to represent edge information. To overcome this problem, nonlinear multiresolution decompositions are being designed that can take into account the characteristics of the input signal/image. In our previous work [1, 2] we have introduced an adaptive lifting framework, that does not require bookkeeping but has the property that it processes edges and homogeneous regions in an image in a different fashion. The current paper discusses the effects of quantization in such an adaptive wavelet decomposition. We provide conditions for recovering the original decisions at the synthesis and for relating the reconstruction error to the quantization error. Such an analysis is essential for the application of these adaptive decompositions in image compression algorithms. 1.
GENERALIZED LIFTING FOR SPARSE IMAGE REPRESENTATION AND CODING
"... This paper investigates the use of generalized lifting to increase the sparseness of wavelet decompositions with application to image representation and coding. As in the bandelet approach, the strategy consists in applying first a separable wavelet decomposition and then in processing the details s ..."
Abstract
-
Cited by 1 (0 self)
- Add to MetaCart
(Show Context)
This paper investigates the use of generalized lifting to increase the sparseness of wavelet decompositions with application to image representation and coding. As in the bandelet approach, the strategy consists in applying first a separable wavelet decomposition and then in processing the details subbands to further decorrelate the signal representation. For this second step, we use a generalized lifting [13] which allows nonlinear processing of the details subbands. In this paper, the generalized lifting design is based on the pdf of the details coefficients after the separable wavelet decomposition and its goal is to minimize the coefficients energy. Both separable and non separable approaches are investigated. The generalized lifting is shown to reduce significantly the energy and the entropy of the representation. Furthermore, a simple quantification and entropy coding strategy is used to compare the rate-distortion characteristics of wavelet, bandelet and the proposed approach based on generalized lifting. Promising results are demonstrated. Index Terms — Generalized lifting, wavelets, bandelets, image coding, sparse representation, nonlinear lifting
Adaptive Lifting Schemes Combining Seminorms for Lossless Image Compression
, 2005
"... We present a new class of adaptive wavelet decompositions that can capture the directional nature of picture information. Our method exploits the properties of seminorms to build lifting structures able to choose between different update filters, the choice being triggered by a local gradient of the ..."
Abstract
-
Cited by 1 (0 self)
- Add to MetaCart
(Show Context)
We present a new class of adaptive wavelet decompositions that can capture the directional nature of picture information. Our method exploits the properties of seminorms to build lifting structures able to choose between different update filters, the choice being triggered by a local gradient of the input. In order to discriminate between different geometrical information, the system makes use of multiple criteria, giving rise to multiple choice of update filters. We establish the conditions under which these decisions can be recovered at synthesis, without the need for transmitting overhead information.
Content-Adaptive Multiresolution Analyses
- In Advanced Concepts for Intelligent Vision Systems
, 2004
"... In this paper we present a technique for building adaptive wavelets by means of an extension of the lifting scheme and analyze the stability of the resulting decompositions. Our scheme comprises an adaptive update lifting and a fixed prediction lifting step. The adaptivity consists hereof that the ..."
Abstract
-
Cited by 1 (1 self)
- Add to MetaCart
In this paper we present a technique for building adaptive wavelets by means of an extension of the lifting scheme and analyze the stability of the resulting decompositions. Our scheme comprises an adaptive update lifting and a fixed prediction lifting step. The adaptivity consists hereof that the system can choose between two different update filters, and that this choice is triggered by the local gradient of the original signal. If the gradient is large (in some seminorm sense) it chooses one filter, if it is small the other. We derive necessary and sufficient conditions for the invertibility of such an adaptive system for various scenarios. Furthermore, we present some examples to illustrate our theoretical results. We also discuss the effects of quantization in such an adaptive wavelet decomposition and provide conditions for recovering the original decisions at the synthesis and for relating the reconstruction error to the quantization error. Such an analysis is essential for the application of these adaptive decompositions in image compression.
Author manuscript, published in "SAMPTA'09, Marseille: France (2009)" Nonlinear Locally Adaptive Wavelet Filter
, 2010
"... In this paper we introduce a new construction of nonlinear locally adaptive wavelet filter banks by connecting the lifting scheme with the idea of image smoothing by nonlinear diffusion methods. 1. ..."
Abstract
- Add to MetaCart
(Show Context)
In this paper we introduce a new construction of nonlinear locally adaptive wavelet filter banks by connecting the lifting scheme with the idea of image smoothing by nonlinear diffusion methods. 1.
Quantization of Adaptive Wavelets for Image Compression
, 2004
"... In this paper we investigate the potential of a special class of adaptive wavelet schemes to yield an effective representation for compression purposes. In particular, we analyze the effect of a scalar uniform quantization in an adaptive multiresolution analysis based on a lifting implementation. We ..."
Abstract
- Add to MetaCart
(Show Context)
In this paper we investigate the potential of a special class of adaptive wavelet schemes to yield an effective representation for compression purposes. In particular, we analyze the effect of a scalar uniform quantization in an adaptive multiresolution analysis based on a lifting implementation. We provide conditions for recovering the original decisions at synthesis and we provide expressions that relate the reconstruction error to the quantization error. Such an analysis is essential for the application of our adaptive decompositions in lossy image compression algorithms. 1.
