Exact Linear Time Euclidean Distance Transforms of Grid Line Sampled Shapes

2015 ◽  
pp. 645-656 ◽  
Author(s):  
Joakim Lindblad ◽  
Nataša Sladoje
Keyword(s):  
Euclidean Distance ◽  
Linear Time ◽  
Grid Line ◽  
Distance Transforms

scholarly journals N-D Linear Time Exact Signed Euclidean Distance Transform

2003 ◽  
Author(s):  
Nicholas J. Tustison ◽  
Marcelo Siqueira ◽  
James Gee
Keyword(s):  
Computer Vision ◽  
Euclidean Distance ◽  
Linear Time ◽  
Small Time ◽  
Direct Application ◽  
Distance Transform ◽  
Fast Computation ◽  
Distance Transforms ◽  
Euclidean Distance Transform ◽  
Image Pixels

Fast computation of distance transforms find direct application in various computer vision problems. Currently there exists two image filters in the ITK library which can be used to generate distance maps. Unfortunately, these filters produce only approximations to the Euclidean Distance Transform (EDT). We introduce into the ITK library a third EDT filter which was developed by Maurer {} . In contrast to other algorithms, this algorithm produces the exact signed squared EDT using integer arithmetic. The complexity, which is formally verified, is O(n) O(n) with a small time constant where n n is the number of image pixels.

On the Euclidean Minimum Spanning Tree Problem

2005 ◽  
Vol 1 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Sanguthevar Rajasekaran
Keyword(s):  
Spanning Tree ◽  
Euclidean Distance ◽  
Minimum Spanning Tree ◽  
Linear Time ◽  
Randomized Algorithm ◽  
Weighted Graph ◽  
Deterministic Algorithm ◽  
Probabilistic Algorithms ◽  
Tree Algorithms ◽  
Minimum Spanning Tree Problem

Given a weighted graph G(V;E), a minimum spanning tree for G can be obtained in linear time using a randomized algorithm or nearly linear time using a deterministic algorithm. Given n points in the plane, we can construct a graph with these points as nodes and an edge between every pair of nodes. The weight on any edge is the Euclidean distance between the two points. Finding a minimum spanning tree for this graph is known as the Euclidean minimum spanning tree problem (EMSTP). The minimum spanning tree algorithms alluded to before will run in time O(n2) (or nearly O(n2)) on this graph. In this note we point out that it is possible to devise simple algorithms for EMSTP in k- dimensions (for any constant k) whose expected run time is O(n), under the assumption that the points are uniformly distributed in the space of interest.CR Categories: F2.2 Nonnumerical Algorithms and Problems; G.3 Probabilistic Algorithms

TWO ALGORITHMS FOR COMPUTING THE EUCLIDEAN DISTANCE TRANSFORM

2001 ◽  
Vol 01 (04) ◽  
pp. 635-645 ◽  
Author(s):  
MARINA L. GAVRILOVA ◽  
MUHAMMAD H. ALSUWAIYEL
Keyword(s):  
Parallel Algorithm ◽  
Euclidean Distance ◽  
Linear Array ◽  
Linear Time ◽  
Sequential Algorithm ◽  
Distance Transform ◽  
Optimal Algorithms ◽  
Euclidean Metric ◽  
Input Size ◽  
Feature Transform

Given an n × n binary image of white and black pixels, we present two optimal algorithms for computing the distance transform and the nearest feature transform using the Euclidean metric. The first algorithm is a fast sequential algorithm that runs in linear time in the input size. The second is a parallel algorithm that runs in O(n2/p) time on a linear array of p processors, p, 1 ≤ p ≤ n.

DATA PARALLEL COMPUTATION OF EUCLIDEAN DISTANCE TRANSFORMS

1992 ◽  
Vol 02 (04) ◽  
pp. 331-339 ◽  
Author(s):  
TERRY BOSSOMAIER ◽  
NATALINA ISIDORO ◽  
ADRIAN LOEFF
Keyword(s):  
High Speed ◽  
Euclidean Distance ◽  
Maximum Error ◽  
Parallel Computers ◽  
Data Sets ◽  
Data Parallel ◽  
Distance Transforms ◽  
Diverse Data ◽  
Mimd Architectures ◽  
New Strategies

The Euclidean Distance Transform is an important, but computationally expensive, technique of computational geometry, with applications in many areas including image processing, graphics and pattern recognition. Since the data sets used are typically large, one might hope that parallel computers would be suitable for its determination. We show that existing parallel algorithms perform poorly on certain data sets and introduce new strategies. These achieve high speed on diverse data sets, but fail occasionally in pathological cases. We determine the maximum error in such cases and demonstrate that it is satisfactorily low. Although adequate efficiency is achievable on SIMD machines, we demonstrate that problems of this kind are data parallel yet best suited to MIMD architectures.

A COMBINATORIAL APPROACH TO FINGERPRINT BINARIZATION AND MINUTIAE EXTRACTION USING EUCLIDEAN DISTANCE TRANSFORM

2007 ◽  
Vol 21 (07) ◽  
pp. 1141-1158 ◽  
Author(s):  
XUEFENG LIANG ◽  
ARIJIT BISHNU ◽  
TETSUO ASANO
Keyword(s):  
Euclidean Distance ◽  
Linear Time ◽  
Time Algorithm ◽  
Distance Transform ◽  
Fingerprint Matching ◽  
Fingerprint Image ◽  
Binary Images ◽  
Minutiae Extraction ◽  
Euclidean Distance Transform ◽  
Matching Techniques

Most of the fingerprint matching techniques require extraction of minutiae that are ridge endings or bifurcations of ridge lines in a fingerprint image. Crucial to this step is either detecting ridges from the gray-level image or binarizing the image and then extracting the minutiae. In this work, we firstly exploit the property of almost equal width of ridges and valleys for binarization. Computing the width of arbitrary shapes is a nontrivial task. So, we estimate the width using Euclidean distance transform (EDT) and provide a near-linear time algorithm for binarization. Secondly, instead of using thinned binary images for minutiae extraction, we detect minutiae straightaway from the binarized fingerprint images using EDT. We also use EDT values to get rid of spurs and bridges in the fingerprint image. Unlike many other previous methods, our work depends minimally on arbitrary selection of parameters.

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