Multi-Resolution Data Analysis using Wavelet Transform and Data Reduction of 3D Object Surfaces

Research objectives:
The research objective is aimed at developing methods for extracting multi-resolution information on surfaces of 3D objects using the wavelet transform. The wavelet transform allows multi-resolution feature selection and extraction. Three-dimensional object surfaces typically contain multi-resolution levels of topological information such as object edges and even noise. The innovation of this research concerns the use of 3D multi-resolution analysis for an improved data analysis method. This method is to be built to impact a data reduction process that reduces information without losing important features. The data analysis process acts as a data interpretation task, guiding a reduction process in choosing the data to be reduced first according to the levels of relevance or significance to a user. This method can be used for enhancing 3D object surfaces and, in particular, for filtering noisy data.

Methodology and Results:
A multi-resolution analysis method using a wavelet transform has been developed based on Quincunx wavelets, and provides very fine information extraction. This method has been tested on many types of images and is suitable for multi-resolution information extraction and noise removal. A degree of relevance is associated with each resolution in order to select the resolutions that are the most relevant to a user accomplishing a specific task when visualizing the data. This part of a data reduction process, which is driven by the degrees of relevance requires that data with low levels of relevance are reduced first. This method allows multi-resolution models to be built such that the order of display can be set according to the degrees of relevance.

This work was conducted at both the IRIS lab and Le2i (France) by Marc Toubin under the supervision of C. Dumont, Fred Truchetet (Thesis Chair), and M. A. Abidi. This work was supported by DOE's University Research Program in Robotics under grant DOE-DE-FG02-86NE3796, and The European Community.

• Papers

D. L. Page, M. Toubin, C. Dumont, and M. A. Abidi, Multi-resolution Wavelet Analysis for Simplification and Visualization of Multi-Textured Meshes, Submitted to the 12th Annual Symposium Electronic Imaging 2000: Science and Technology, SPIE Photonics West, San Jose, California USA, 23-28 January 2000

M. Toubin, C. Dumont, E. P. Verrechia, O. Lalligant, A. Diou, F. Truchetet, and M. A. Abidi, A Multi-scale Analysis of shell growth increments using wavelet transform, To be published in Computers and Geosciences, Journal of the International Association for Mathematical Geology. M. Toubin, C. Dumont, F.Truchetet, M. Abidi, Multi-resolution simplification of 3D multi-modal objects using a 2D quincunx wavelet analysis, To be published to SPIE Photonics East, Boston 19-22 Sept. 99.

M. Toubin, F. Truchetet, E. P. Verrecchia, C. Dumont, M. A. Abidi, A 3D Multi-resolution Description of Range Images through 2D Quincunx Wavelet Analysis, accepted to SPIE AeroSense (Aerospace/Defense Sensing, Simulation and Controls),   5-9 Orlando USA, April 99

M. Toubin, O. Lalligant, A. Diou, F. Truchetet, E. P. Verrechia, C. Dumont, M. A. Abidi, A Multi-scale Analysis for the Characterization of 3D objects,  SPIE Conference on Intelligent Robots and Computer Vision XVII: Algorithms, Techniques, and Active vision, Boston (USA), 1-6 Nov. 1998,3522, pp 414-423, 1998