The DOI matches its Crossref record; 50 of the 50 references it cites were found in a registry or an index.
Edge-avoiding wavelets and their applications
Abstract
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.
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Cites
Scale-space and edge detection using anisotropic diffusion
Perona, P., & Malik, J. (1990) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.56205 · Cited by 12,119
Orthonormal bases of compactly supported wavelets
Daubechies, I. (1988) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160410705 · Cited by 8,190
Bilateral Filtering for Gray and Color Images
Tomasi, C., & Manduchi, R. (2002) · Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271) · doi:10.1109/iccv.1998.710815 · Cited by 8,177
The Laplacian pyramid as a compact image code
Burt, P., & Adelson, E. (1983) · IEEE Transactions on Communications · doi:10.1109/tcom.1983.1095851 · Cited by 6,077
A two-dimensional interpolation function for irregularly-spaced data
Shepard, D. (1968) · Proceedings of the 1968 23rd ACM national conference on - · doi:10.1145/800186.810616 · Cited by 5,079
Biorthogonal bases of compactly supported wavelets
Cohen, A., Daubechies, I., & Feauveau, J. ‐. (1992) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160450502 · Cited by 2,667
Gortler, S. J., Grzeszczuk, R., Szeliski, R., & Cohen, M. F. (1996) · Proceedings of the 23rd annual conference on Computer graphics and interactive techniques · doi:10.1145/237170.237200 · Cited by 2,458
The Lifting Scheme: A Construction of Second Generation Wavelets
Sweldens, W. (1998) · SIAM Journal on Mathematical Analysis · doi:10.1137/s0036141095289051 · Cited by 2,207
Fattal, R. (2008) · ACM Transactions on Graphics · doi:10.1145/1360612.1360671 · Cited by 2,114
Self-citationPérez, P., Gangnet, M., & Blake, A. (2003) · ACM SIGGRAPH 2003 Papers · doi:10.1145/1201775.882269 · Cited by 2,020
Cited by
He, K., Sun, J., & Tang, X. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2012.213 · Cited by 5,546
Image smoothing via L0gradient minimization
Xu, L., Lu, C., Xu, Y., & Jia, J. (2011) · Proceedings of the 2011 SIGGRAPH Asia Conference · doi:10.1145/2024156.2024208 · Cited by 873
Image smoothing via L0gradient minimization
Xu, L., Lu, C., Xu, Y., & Jia, J. (2011) · ACM Transactions on Graphics · doi:10.1145/2070781.2024208 · Cited by 786
Fast Image Processing with Fully-Convolutional Networks
Chen, Q., Xu, J., & Koltun, V. (2017) · 2017 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.273 · Cited by 341
Metadata
- Authors
- Fattal, R.
- Venue
- ACM Transactions on Graphics
- Published
- 2009-07-27
- Volume
- 28
- Issue
- 3
- Pages
- 1-10
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W2096768337
- Cited by
- 294
- References
- 50
- FWCI
- 20.89
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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