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| In the last five years, there has been numerous applications of wavelets and multiresolution analysis in many fields of computer graphics as different as geometric modelling, volume visualization or illumination modelling. Classical multiresolution analysis is based on the knowledge of a nested set of functional spaces in which the successive approximations of a given function converge to that function, and can be efficiently computed. This paper first proposes a theoretical framework which enables multiresolution analysis even if the functional spaces are not nested, as long as they still have the property that the successive approximations converge to the given function. Based on this concept we finally introduce a new multiresolution analysis with exact reconstruction for large data sets defined on uniform grids. We construct a one-parameter family of multiresolution analyses which is a blending of Haar and linear multiresolution. |
Results :BLaC-Wavelets stands for Blending of Linear and Constant wavelets. It consists of a one-parameter family of wavelets that performs a blend between Haar- and Linear wavelets. BLaC wavelets enables the user to choose his own compromise between the smoothness and the sharpness of the approximations.With the blending parameter d which can vary between d=0 (constant case) and d=1 (linear case) one obtains the following results: The BLaC-Wavelet for various values of the blending parameter.
Click for a gif movie file Click for an mpeg movie file Partial reconstructions of an image data set.The upper three images are reconstructed using 1% of the wavelet coefficients. An edge detection algorithm was then applied to produce the lower images. They show clearly the effect of the blending parameter: the approximations become smoother as d increases. On the upper images, it can be seen that fuzzy areas appear for d = 1 .(left: d=0, middle d=0.5, right d=1) 
Click for a 768x512 gif image (250Kb)
Partial reconstructions of a volume data set.The BLaC multiresolution analysis was developped for use in the area of scientific visualization where large data sets should be analyzed and visualized. An example of BLaC multiresolution visualization of a volumetric data set is shown on the next pictures. These pictures were obtained using the Stanford Volpack volume renderer, and show the partial reconstructions of a volume data set, using 1% of the wavelet coefficients, for different blending parameters d (see explanations at the top of this page).(from left to right: d = 0., d = 0.43, d = 0.7, d = 1. ) 
Click for 512x512 gif images (90Kb each) |
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