Haar-LikeWavelets over Tetrahedra

In this paper we define a Haar-like wavelets basis that form a basis for L2(T,S,μ), μ being the Lebesgue measure and S the σ -algebra of all tetrahedra generated from a subdivision method of the T tetrahedron. As 3D objects are, in general, modeled by tetrahedral grids, this basis allows the multiresolution representation of scalar functions defined on polyhedral volumes, like colour, brightness, density and other properties of an 3D object.

Trabecular Bone Image Segmentation Using Wavelet and Marker-Controlled Watershed Transformation

This paper presents a new strategy for the segmentation of trabecular bone image. This kind of image is acquired with microcomputed tomography (micro-CT) to assess bone microarchitecture based chiefly on bone mineral density (BMD) measurements to improve fracture risk prediction. Disease osteoporosis can be predicted from features of CT image where a bone region may consist of several disjoint pieces. It relies on a multiresolution representation of the image by the wavelet transform to compute the multiscale morphological gradient. The coefficients of detail found at the different scales are used to determine the markers and homogeneous regions that are extracted with the watershed algorithm. The method reduces the tendency of the watershed algorithm to oversegment and results in closed homogeneous regions. The performance of the proposed segmentation scheme is presented via experimental results obtained with a broad series of images.