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Some remarks on multiscale transformations, stability, and biorthogonality
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Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
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Multiresolution analysis for surfaces of arbitrary topological type
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The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
LCIS: a boundary hierarchy for detail-preserving contrast reduction
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Wavelet Methods for Second-Order Elliptic Problems, Preconditioning, and Adaptivity
SIAM Journal on Scientific Computing
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Gradient domain high dynamic range compression
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Fast bilateral filtering for the display of high-dynamic-range images
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ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
ACM SIGGRAPH 2004 Papers
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SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
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IEEE Transactions on Image Processing
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IEEE Transactions on Image Processing
EGSR'08 Proceedings of the Nineteenth Eurographics conference on Rendering
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Edge-avoiding À-Trous wavelet transform for fast global illumination filtering
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ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part III
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Antialiasing recovery for edit propagation
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Computer Graphics Forum
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ACM Transactions on Graphics (TOG)
WYSIWYG computational photography via viewfinder editing
ACM Transactions on Graphics (TOG)
Image coarsening by using space-filling curve for decomposition-based image enhancement
Journal of Visual Communication and Image Representation
Fast multi-scale detail decomposition via accelerated iterative shrinkage
SIGGRAPH Asia 2013 Technical Briefs
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We propose a new family of second-generation wavelets constructed using a robust data-prediction lifting scheme. The support of these new wavelets is constructed based on the edge content of the image and avoids having pixels from both sides of an edge. Multi-resolution analysis, based on these new edge-avoiding wavelets, shows a better decorrelation of the data compared to common linear translation-invariant multi-resolution analyses. The reduced inter-scale correlation allows us to avoid halo artifacts in band-independent multi-scale processing without taking any special precautions. We thus achieve nonlinear data-dependent multi-scale edge-preserving image filtering and processing at computation times which are linear in the number of image pixels. The new wavelets encode, in their shape, the smoothness information of the image at every scale. We use this to derive a new edge-aware interpolation scheme that achieves results, previously computed by solving an inhomogeneous Laplace equation, through an explicit computation. We thus avoid the difficulties in solving large and poorly-conditioned systems of equations. We demonstrate the effectiveness of the new wavelet basis for various computational photography applications such as multi-scale dynamic-range compression, edge-preserving smoothing and detail enhancement, and image colorization.