"Wavelet Environment Matting"
Pieter Peers, and Philip Dutré

Proceedings of the 14th Eurographics Symposium on Rendering, pages 157-166, June 2003
In this paper we present a novel approach for capturing the environment matte of scene. We impose no restrictions on material properties of the objects in the captured scene and take advantage of the scene characteristics (e.g. material properties and self-shadowing) to minimize recording time and to bound error. Wavelet patterns are emitted, using a CRT monitor, onto the scene in order of importance to efficiently construct the environment matte. This order of importance is obtained by means of a feedback loop that takes advantage of the knowledge learned from previously recorded photographs. Once the recording process is finished, new backdrops can be efficiently placed behind the scene.

Supplementary Material
Additional Notes
  • Addendum:A unfortunate typo sneaked into the paper: DC and Nyquist gain should be sqrt(2) and not 1
  • Non-formal proof of the Error-tree property: if parent node is not important, then the child-nodes are probably not important too. If in formula (5), the weighting function, s is set to 1 or higher, then the amplitude of a wavelet is the same or less for each successive wavelet level. The L2-norm of a pixel, or the recorded photograph, results in a decreasing function in terms of wavelet levels. Consider a specular pixel. In this case a single pixel from the backdrop will determine the value of the pixel and the observed pixel value for successive wavelet levels equals the evaluation of the wavelet at a fixed position. This evaluation returns decreasing values (in terms of wavelet level) since the amplitude is always equal of less. Note that this function may not decrease between two levels, depending on the specific wavelet used, but in general will eventually decrease. An analogue reasoning also holds for other kinds of light interactions.

Related Publications
  • Philip Dutré, and Pieter Peers, "Wavelet Environment Matting", Hierarchical Methods in Computer Graphics, Dagstuhl Seminar 03271, Dagstuhl, Germany, June 29-July 4 2003,
author = {Peers, Pieter and Dutr\'{e}, Philip},
title = {Wavelet Environment Matting},
month = {June},
year = {2003},
pages = {157--166},
booktitle = {Proceedings of the 14th Eurographics Symposium on Rendering},