Distance transformations in arbitrary dimensions

  title={Distance transformations in arbitrary dimensions},
  author={Gunilla Borgefors},
  journal={Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing},
  • G. Borgefors
  • Published 1 September 1984
  • Computer Science
  • Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing
Some Weighted Distance Transforms in Four Dimensions
In this paper, optimal real and integer weights are computed for one type of 4D weighted distance transforms.
Chamfer Distances with Integer Neighborhoods
Results of a systematic search for approximations of the Euclidean distance in the two-dimensional case for neighborhoods of sizes up to 21 × 21 and scaling factors up to 1000 are presented.
Distance transformations in digital images
  • G. Borgefors
  • Computer Science
    Comput. Vis. Graph. Image Process.
  • 1986
Weighted digital distance transforms in four dimensions
On Digital Distance Transforms in Three Dimensions
A new type of valid distance transforms (DTs) have been discovered, where optimality is defined as minimizing the maximum difference from the true Euclidean distance, thus making the DTs as direction independent as possible.
Some Sequential Algorithms for a Generalized Distance Transformation Based on Minkowski Operations
A generalized distance transformation (GDT) of binary images and the related medial axis transformation (MAT) are discussed and different sequential algorithms are proposed for computing such GDTs.
Optimum design of chamfer distance transforms
A new concept of critical local distances is presented which reduces the computational complexity of the chamfer distance transform without increasing the maximum approximation error.
The Distance Transform and its Computation
How the distance transform has to be used in achieving the goals of these applications is discussed; instead, it concentrates on the basics of distances and on algorithms for computing a distance transformation in an appropriate manner.


On Generalized Distance Transformation of Digitized Pictures
A subclass of GDTB, called a local minimum filter family ofGDTB (LMF-GDTB), characterized by a series of local minimum filters with varying neighborhoods, is discussed in detail, and it is proved that any binary picture can be reconstructed exactly from its skeleton with the distance value on it.
Distance functions on digital pictures
Sequential Operations in Digital Picture Processing
The relative merits of performing local operations on ~ digitized picture in parallel or sequentially are discussed and some applications of the connected component and distance functions are presented.
A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance
The problem of obtaining the skeleton of a digitized figure is reduced to an optimal policy problem. A hierarchy of methods of defining the skeleton is proposed; in the more complicated ones, the
Application Of An Iterative Feature Matching Algorithm To Terminal Homing
MACHAL is applied to a low order feature matching in a relatively sparse feature space, characteristic of terminal homing problems, and a probability model for the algorithm is developed and its validity tested by Monte Carlo simulation.
Euclidean distance mapping
On artificial intelligence
Artificial intelligence (AI) is a fundamentally interdisciplinary subject, combining ideas from psychology, computer science, linguistics, mathematics and even philosophy (see, for example, Sloman,
Parametric Correspondence and Chamfer Matching: Two New Techniques for Image Matching
The matching of image and map features is performed rapidly by a new technique, called "chamfer matching", that compares the shapes of two collections of shape fragments, at a cost proportional to linear dimension, rather than area.