One of the attractive features of Self-Organising Maps (SOM) is the so-called “topological preservation property”: observations that are close to each other in the input space (at least locally) remain close to each other in the SOM. In this work, we propose the use of a bootstrap scheme to construct a statistical significance test of the observed proximity among individuals in the SOM. While c...

In this paper, we propose a new scheme to represent threedimensional (3-D) dynamic scenes using a hierarchical decomposition of depth maps. In the hierarchical decomposition, we split a depth map into four types of images: regular mesh, boundary, feature point and number-oflayer (NOL) images. A regular mesh image is obtained by down-sampling a depth map. A boundary image is generated by gatheri...

We present an analysis of bounded-energy low-tension maps between 2-spheres. By deriving sharp estimates for the ratio of length scales on which bubbles of opposite orientation develop, we show that we can establish a ‘quantization estimate’ which constrains the energy of the map to lie near to a discrete energy spectrum. One application is to the asymptotics of the harmonic map flow; we find u...

2D Simulation and Mapping using the Cauchy-Green Complex Barycentric Coordinates Conformal maps are especially useful in geometry processing for computing shape preserving deformations, image warping and manipulating harmonic functions. The Cauchy-Green coordinates are complex-valued barycentric coordinates, which can be used to parameterize a space of conformal maps from a planar domain bounde...

Integration of system process information obtained through an image processing system with an evolving knowledge database to improve the accuracy and predictability of wear particle analysis is the main focus of the paper. The objective is to automate intelligently the analysis process of wear particle using classification via self organizing maps. This is achieved using relationship measuremen...

Integration of system process information obtained through an image processing system with an evolving knowledge database to improve the accuracy and predictability of wear debris analysis is the main focus of the paper. The objective is to automate intelligently the analysis process of wear particle using classification via self-organizing maps. This is achieved using relationship measurements...

Selecting a threshold for the statistical parameter maps in functional MRI (fMRI) is a delicate matter. The use of advanced test statistics and/or the complex dependence structure of the noise may preclude parametric statistical methods for finding appropriate thresholds. Non-parametric statistical methodology has been presented as a feasible alternative. In this paper we discuss resampling-bas...

Many problems arising in dealing with high-dimensional data sets involve connection graphs in which each edge is associated with both an edge weight and a d-dimensional linear transformation. We consider vectorized versions of the PageRank and effective resistance which can be used as basic tools for organizing and analyzing complex data sets. For example, the generalized PageRank and effective...

An irregular pyramid consists of a stack of successively reduced graphs. Each smaller graph is deduced from the preceding one by the contraction or the removal of a set of edges. Using a fixed decimation ratio we need approximatelyO(log(image size)) graphs to encode the whole pyramid. A combinatorial map encodes a planar graph thanks to two permutations encoding the edges and their orientation ...