An algorithm for computing intrinsic distance functions and geodesics on sub-manifolds of given by point clouds is introduced in this paper. The basic idea is that, as shown in this paper, intrinsic distance functions and geodesics on general co-dimension sub-manifolds of can be accurately approximated by the extrinsic Euclidean ones computed in a thin offset band surrounding the manifold. This...

The interest in digital image comparison is steadily growing in the computer vision community. The de®nition of a suitable comparison measure for non-binary images is relevant in many image processing applications. Visual tasks like segmentation and classi®cation require the evaluation of equivalence classes. Measures of similarity are also used to evaluate lossy compression algorithms and to d...

Tandem repeats are an important class of DNA repeats and much research has focused on their efficient identification, their use in DNA typing and fingerprinting, and their causative role in trinucleotide repeat diseases such as Huntington Disease, myotonic dystrophy, and Fragile-X mental retardation. We are interested in clustering tandem repeats into groups or families based on sequence simila...

Many natural image sets are samples of a low-dimensional manifold in the space of all possible images. When the image data set is not a linear combination of a small number of basis images, linear dimensionality reduction techniques such as PCA and ICA fail and nonlinear dimensionality reduction techniques are required to automatically determine the intrinsic structure of the image set. Recent ...

This thesis presents research in the field of distance learning. Distance functions are extensively used in various application domains and also serve as an important building block in many types of algorithms. Despite their abundance, until recently only canonical distance functions such as the Euclidean distance have been used, or alternatively various application specific distance functions ...

The classical absolute orientation method is capable of transforming tie points (TPs) from a local coordinate system to a global (geodetic) coordinate system. The method is based only on a unique set of similarity transformation parameters estimated by minimizing the total difference between all ground control points (GCPs) and the fitted points. Nevertheless, it often yields a transformation w...

One of the key steps in 3D object recognition is the matching between an input cloud and a cloud in a database of known objects. This is usually done using a distance function between sets of descriptors. In this paper we propose to study how several distance functions (some already available and other new proposals) behave experimentally using a large freely available household object database...

We present e cient algorithms for two problems of facility location. In both problems we want to determine the location of a single facility with respect to n given sites. In the rst we seek a location that maximizes a weighted distance function between the facility and the sites, and in the second we nd a location that minimizes the sum (or sum of the squares) of the distances of k of the site...

Distances in the well known fuzzy c-means algorithm of Bezdek (1973) are measured by the squared Euclidean distance. Other distances have been used as well in fuzzy clustering. For example, Jajuga (1991) proposed to use the L1-distance and Bobrowski and Bezdek (1991) also used the L∞-distance. For the more general case of Minkowski distance and the case of using a root of the squared Minkowski ...