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104
The easy path wavelet transform: A new adaptive wavelet transform for sparse representation of two-dimensional data
- Multiscale Model. Simul
"... Dedicated to Manfred Tasche on the occasion of his 65th birthday We introduce a new locally adaptive wavelet transform, called Easy Path Wavelet Transform (EPWT), that works along pathways through the array of function values and exploits the local correlations of the data in a simple appropriate ma ..."
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Cited by 137 (9 self)
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Dedicated to Manfred Tasche on the occasion of his 65th birthday We introduce a new locally adaptive wavelet transform, called Easy Path Wavelet Transform (EPWT), that works along pathways through the array of function values and exploits the local correlations of the data in a simple appropriate manner. The usual discrete orthogonal and biorthogonal wavelet transform can be formulated in this approach. The EPWT can be incorporated into a multiresolution analysis structure and generates data dependent scaling spaces and wavelet spaces. Numerical results show the enormous efficiency of the EPWT for representation of two-dimensional data. Key words. wavelet transform along pathways, data compression, adaptive wavelet bases, directed wavelets AMS Subject classifications. 65T60, 42C40, 68U10, 94A08 1
Multiresolution signal decomposition schemes. Part 1: Linear and morphological pyramids
- IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2000
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Direction-adaptive discrete wavelet transform for image compression
, 2007
"... We propose a direction-adaptive DWT (DA-DWT) that locally adapts the filtering directions to image content based on directional lifting. With the adaptive transform, energy compaction is improved for sharp image features. A mathematical analysis based on an anisotropic statistical image model is pr ..."
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Cited by 44 (2 self)
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We propose a direction-adaptive DWT (DA-DWT) that locally adapts the filtering directions to image content based on directional lifting. With the adaptive transform, energy compaction is improved for sharp image features. A mathematical analysis based on an anisotropic statistical image model is presented to quantify the theoretical gain achieved by adapting the filtering directions. The analysis indicates that the proposed DA-DWT is more effective than other lifting-based approaches. Experimental results report a gain of up to 2.5 dB in PSNR over the conventional DWT for typical test images. Subjectively, the reconstruction from the DA-DWT better represents the structure in the image and is visually more pleasing.
Adaptive directional lifting-based wavelet transform for image coding
- IEEE TRANS. IMAGE PROCESS
, 2007
"... We present a novel 2-D wavelet transform scheme of adaptive directional lifting (ADL) in image coding. Instead of alternately applying horizontal and vertical lifting, as in present practice, ADL performs lifting-based prediction in local windows in the direction of high pixel correlation. Hence, it ..."
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Cited by 44 (12 self)
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We present a novel 2-D wavelet transform scheme of adaptive directional lifting (ADL) in image coding. Instead of alternately applying horizontal and vertical lifting, as in present practice, ADL performs lifting-based prediction in local windows in the direction of high pixel correlation. Hence, it adapts far better to the image orientation features in local windows. The ADL transform is achieved by existing 1-D wavelets and is seamlessly integrated into the global wavelet transform. The predicting and updating signals of ADL can be derived even at the fractional pixel precision level to achieve high directional resolution, while still maintaining perfect reconstruction. To enhance the ADL performance, a rate-distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features. Experimental results show that the proposed ADL-based image coding technique outperforms JPEG 2000 in both PSNR and visual quality, with the improvement up to 2.0 dB on images with rich orientation features.
Adaptive polyphase subband decomposition structures for image compression
- IEEE Transactions on Image Processing
, 2000
"... Abstract—Subband decomposition techniques have been extensively used for data coding and analysis. In most filter banks, the goal is to obtain subsampled signals corresponding to different spectral regions of the original data. However, this approach leads to various artifacts in images having spati ..."
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Cited by 42 (11 self)
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Abstract—Subband decomposition techniques have been extensively used for data coding and analysis. In most filter banks, the goal is to obtain subsampled signals corresponding to different spectral regions of the original data. However, this approach leads to various artifacts in images having spatially varying characteristics, such as images containing text, subtitles, or sharp edges. In this paper, adaptive filter banks with perfect reconstruction property are presented for such images. The filters of the decomposition structure which can be either linear or nonlinear vary according to the nature of the signal. This leads to improved image compression ratios. Simulation examples are presented. Index Terms—Adaptive polyphase structures, adaptive subband decomposition, image coding, lifting structures. I.
Video Coding with Motion-Compensated Lifted Wavelet Transforms
, 2004
"... This article explores the e#ciency of motion-compensated three-dimensional transform coding, a compression scheme that employs a motion-compensated transform for a group of pictures. We investigate this coding scheme experimentally and theoretically. The practical coding scheme employs in temporal d ..."
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Cited by 39 (13 self)
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This article explores the e#ciency of motion-compensated three-dimensional transform coding, a compression scheme that employs a motion-compensated transform for a group of pictures. We investigate this coding scheme experimentally and theoretically. The practical coding scheme employs in temporal direction a wavelet decomposition with motion-compensated lifting steps. Further, we compare the experimental results to that of a predictive video codec with single-hypothesis motion compensation and comparable computational complexity. The experiments show that the 5/3 wavelet kernel outperforms both the Haar kernel and, in many cases, the reference scheme utilizing single-hypothesis motion-compensated predictive coding. The theoretical investigation models this motion-compensated subband coding scheme for a group of K pictures with a signal model for K motion-compensated pictures that are decorrelated by a linear transform. We utilize the Karhunen-Loeve Transform to obtain theoretical performance bounds at high bit-rates and compare to both optimum intra-frame coding of individual motion-compensated pictures and single-hypothesis motion-compensated predictive coding. The investigation shows that motion-compensated three-dimensional transform coding can outperform predictive coding with single-hypothesis motion compensation by up to 0.5 bits/sample. Preprint submitted to Elsevier Science 30 April 2004 Key words: Video Coding, Motion Compensation, Adaptive Wavelets, Lifting, Three-Dimensional Subband Coding of Video 1
Adaptive wavelet transforms via lifting
, 1999
"... This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into prediction and update stages. We adapt the prediction stage to the signal structure and ..."
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Cited by 31 (3 self)
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This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into prediction and update stages. We adapt the prediction stage to the signal structure and design the update stage to preserve the desirable properties of the wavelet transform. We incorporate this adaptivity into the redundant and non-redundant transforms; the resulting transforms are scale and spatially adaptive. We study applications to signal estimation; our new transforms show improved denoising performance over existing (non-adaptive) orthogonal transforms.
Total variation improved wavelet thresholding in image compression
- In Proc. Seventh International Conference on Image Processing
, 2000
"... In this paper, we propose using Partial Differential Equation (PDE) techniques in wavelet based image processing to reduce edge artifacts generated by wavelet thresholding. We employ minimization techniques, in particular the minimization of total variation (TV), to modify the retained standard wave ..."
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Cited by 31 (0 self)
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In this paper, we propose using Partial Differential Equation (PDE) techniques in wavelet based image processing to reduce edge artifacts generated by wavelet thresholding. We employ minimization techniques, in particular the minimization of total variation (TV), to modify the retained standard wavelet coefficients so that the reconstructed images have less oscillations near edges. Numerical experiments show that this approach improves the reconstructed image quality in wavelet compression and in denoising. 1.
Compact Representation of Images by Edge Adapted Multiscale Transforms
, 2001
"... We introduce new multiscale representations for images which incorporate a speci c geometric treatment of edges. The associated transforms are inherently nonlinear and non tensor product in contrast to classical wavelet basis decompositions over which they exhibit visual improvement in terms of comp ..."
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Cited by 30 (0 self)
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We introduce new multiscale representations for images which incorporate a speci c geometric treatment of edges. The associated transforms are inherently nonlinear and non tensor product in contrast to classical wavelet basis decompositions over which they exhibit visual improvement in terms of compression. This approach can be viewed as a bridge between edge detection and the nonlinear multiresolution representations of Ami Harten.
C-BDAM -- compressed batched dynamic adaptive meshes for terrain rendering
- COMPUTER GRAPHICS FORUM
, 2006
"... We describe a compressed multiresolution representation for supporting interactive rendering of very large planar and spherical terrain surfaces. The technique, called Compressed Batched Dynamic Adaptive Meshes (C-BDAM), is an extension of the BDAM and P-BDAM chunked level-of-detail hierarchy. In th ..."
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Cited by 27 (5 self)
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We describe a compressed multiresolution representation for supporting interactive rendering of very large planar and spherical terrain surfaces. The technique, called Compressed Batched Dynamic Adaptive Meshes (C-BDAM), is an extension of the BDAM and P-BDAM chunked level-of-detail hierarchy. In the C-BDAM approach, all patches share the same regular triangulation connectivity and incrementally encode their vertex attributes using a quantized representation of the difference with respect to values predicted from the coarser level. The structure provides a number of benefits: simplicity of data structures, overall geometric continuity for planar and spherical domains, support for variable resolution input data, management of multiple vertex attributes, efficient compression and fast construction times, ability to support maximum-error metrics, real-time decompression and shaded rendering with configurable variable level-of-detail extraction, and runtime detail synthesis. The efficiency of the approach and the achieved compression rates are demonstrated on a number of test cases, including the interactive visualization of a 29 gigasample reconstruction of the whole planet Earth created from high resolution SRTM data.
