Dynamic Programming for Detecting, Tracking, and Matching Deformable Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of the ACM (JACM)
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
A Grouping Principle and Four Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Metrics Can Be Approximated by Geo-Cuts, Or Global Optimization of Length/Area and Flux
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Near-optimal detection of geometric objects by fast multiscale methods
IEEE Transactions on Information Theory
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
JBEAM: multiscale curve coding via beamlets
IEEE Transactions on Image Processing
Hi-index | 0.00 |
We consider Holder smoothness classes of surfaces for which we construct piecewise polynomial approximation networks, which are graphs with polynomial pieces as nodes and edges between polynomial pieces that are in 'good continuation' of each other. Little known to the community, a similar construction was used by Kolmogorov and Tikhomirov in their proof of their celebrated entropy results for Holder classes. We show how to use such networks in the context of detecting geometric objects buried in noise to approximate the scan statistic, yielding an optimization problem akin to the Traveling Salesman. In the same context, we describe an alternative approach based on computing the longest path in the network after appropriate thresholding. For the special case of curves, we also formalize the notion of 'good continuation' between beamlets in any dimension, obtaining more economical piecewise linear approximation networks for curves. We include some numerical experiments illustrating the use of the beamlet network in characterizing the filamentarity content of 3D data sets, and show that even a rudimentary notion of good continuity may bring substantial improvement.