One of the problems in the analysis of a 3D signal is the estimation of important 3D features present in the signal. Estimation of locally planar features in 3D image volumes or video sequences, for instance, may be of crucial importance in a number of applications such as geometry estimation, video coding and denoising, and tracking of objects in video sequences. Such features are commonly found in video sequences in the form of moving edges of objects and convey most of the useful information.

We have developed a novel representation tool which uses basis functions, termed as planelets, resembling planar structures and having compact support in space-time and spatiotemporal frequency. The representation is translation invariant, offers good directional selectivity, and can be computed efficiently.

We have shown that the new representation, while being fast, produces video denoising results which compare favourably to one of the best known methods. The translation-invariant (TI) planelet denoising proves to be effective in removing both blocky and fake texture kind of artifacts, and is particularly good in reconstructing some of the details that are smoothed out with the translation-invariant wavelet (TIW) method. The computational complexity of our algorithm is O(n) as compared to O(N + l³N) for TIW denoising, where n and N respectively denote the size of analysis window and the size of video sequence (resolution of each frame times the number of frames) and l is length of the wavelet filter. While being faster by orders of magnitude, our algorithm still compares favourably to the 3D TIW for all our experiments.

Relevant Publications

• NM Rajpoot, RG Wilson, Z Yao,
  Planelets: A New Analysis Tool for Planar Feature Extraction,
  in Proceedings 5th International Workshop on Image Analysis for Multimedia Interactive Services (WIAMIS'04), Lisbon (Portugal), April 2004
  

• RG Wilson, NM Rajpoot,
  Image Volume Denoising Using A Fourier-Wavelet Basis,
  in Proceedings 6th Baiona Workshop on Signal Processing in Communications (Baiona SPC'2003), Baiona (Spain), September 2003