https://hal.inria.fr/inria-00541855/document

Wavelets on graphs via spectral graph theory

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian $\L$. Given a wavelet generating kernel $g$ and a scale parameter $t$, we define the scaled wavelet operator $T_g^t = g(t\L)$. The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on $g$, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing $\L$. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.

Wavelets on Graphs via Spectral Graph Theory

Two linear time (and hence asymptotically optimal) algorithms for computing the Euclidean distance transform of a two-dimensional binary image are presented. The algorithms are based on the construction and regular sampling of the Voronoi diagram whose sites consist of the unit (feature) pixels in the image. The first algorithm, which is of primarily theoretical interest, constructs the complete Voronoi diagram. The second, more practical, algorithm constructs the Voronoi diagram where it intersects the horizontal lines passing through the image pixel centers. Extensions to higher dimensional images and to other distance functions are also discussed. >

Linear time Euclidean distance transform algorithms

http://www.eng.uwaterloo.ca/%7Edclausi/Papers/Published%202000/Clausi%20-%20Gabor%20parameters%20-%20Pattern%20Recognition%202000.pdf

Designing Gabor filters for optimal texture separability

Skeletonization promises to become a powerful tool for compact shape description, path planning and other applications. However, current techniques can seldom efficiently process real, complicated 3D data sets, such as MRI and CT data of human organs. In this paper, we present an efficient voxel coding-based algorithm for the skeletonization of 3D voxelized objects. The skeletons are interpreted as connected center lines, consisting of sequences of medial points of consecutive clusters. These center lines are initially extracted as paths of voxels, followed by medial point replacement, refinement, smoothing and connection operations. The voxel-coding techniques have been proposed for each of these operations in a uniform and systematic fashion. In addition to preserving basic connectivity and centeredness, the algorithm is characterized by straightforward computation, no sensitivity to object boundary complexity, explicit extraction of ready-to-parameterize and branch-controlled skeletons, and efficient object hole detection. These issues are rarely discussed in traditional methods. A range of 3D medical MRI and CT data sets were used for testing the algorithm, demonstrating its utility.

B. N. Chatterji

Papers

Rotation and scale invariant texture features using discrete wavelet packet transform

Distance functions in digital geometry

Rotation invariant texture classification using even symmetric Gabor filters

Generalized distances in digital geometry

Adaptive contrast enhancement and de-enhancement