Paper Info
Title
Fast L1 smoothing splines with an application to Kinect depth data
Abstract
Splines are a popular and attractive way of smoothing noisy data. Computing splines involves minimizing a functional which is a linear combination of a fitting term and a regularization term. The former is classically computed using a (sometimes weighted) L2 norm while the latter ensures smoothness. In this work we propose to replace the L2 norm in the fitting term with an L1 norm, leading to automatic robustness to outliers. To solve the resulting minimization problem we propose an extremely simple and efficient numerical scheme based on split-Bregman iteration and a DCT-based filter. The algorithm is applied to the problem of smoothing and impainting range data, where high-quality results are obtained in short processing times.
Year
DOI
Venue
2013
10.1109/ICIP.2013.6738104
Image Processing
Keywords
Field
DocType
discrete cosine transforms,filtering theory,functional analysis,image reconstruction,iterative methods,minimisation,smoothing methods,splines (mathematics),DCT-based filter,Kinect depth data,L1 norm,fast L1 smoothing splines,fitting term,functional minimization,range data impainting,range data smoothing,regularization term,split-Bregman iteration,Splines,grid data,robust fitting,split-Bregman
Spline (mathematics),Linear combination,Mathematical optimization,Box spline,Computer science,Smoothing spline,Robustness (computer science),Regularization (mathematics),Smoothing,Norm (mathematics)
Conference
ISSN
Citations 
PageRank 
1522-4880
1
0.35
References 
Authors
8
2
Name
Order
Citations
PageRank
Mariano Tepper16812.80
Guillermo Sapiro2148131051.92