Publication

The Euclidean k-Distance Transformartion in Arbitrary Dimensions - a Separable Implementation

Olivier Cuisenaire
2005
Conference Papers

Abstract

The signed k-distance transformation (k-DT) computes the k nearest prototypes from each location on a discrete regular grid within a given D dimensional volume. We propose a new k-DT algorithm that divides the problem into D 1-dimensional problems and compare its accuracy and computational complexity to the existing raster-scanning and propagation approaches.

Official source

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Olivier Cuisenaire
2005
Conference Papers

Abstract

Official source

Related concepts (23)

Four-dimensional space

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z).

Three-dimensional space

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds. Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space.

Dimensional analysis

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed. The term dimensional analysis is also used to refer to conversion of units from one dimensional unit to another, which can be used to evaluate scientific formulae.

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