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Extending Distance Computation - Propagating Derivatives
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Centre for Image Analysis.ORCID iD: 0000-0002-4405-6888
2010 (English)In: Proceedings SSBA 2010 / [ed] Cris Luengo and Milan Gavrilovic, Uppsala: Centre for Image Analysis , 2010, 39-42 p.Conference paper (Other academic)
Abstract [en]

In this paper we present a technique to extend distance computation  algorithms that compute global distances from a series of local  updates. This includes algorithms such as the fast marching method  (FMM) and the chamfering algorithm for weighted distances. In  addition to the value of a distance function or distance map, we  derive formulas to compute the gradient and higher order partial  derivatives of the distance function within the same framework. The  approach is based on symbolic differentiation of the update scheme,  which makes it general and straight forward to apply to almost any  distance computation scheme. The main result is a novel set of  ``derivative maps'' that are computed along with the ordinary  distance maps. Apart from the theory itself, these maps and this  technique may be used to compute skeletons and parameterizations  such as Riemannian Normal Coordinates and Gauss Normal Coordinates.

Place, publisher, year, edition, pages
Uppsala: Centre for Image Analysis , 2010. 39-42 p.
, Centre for Image Analysis Report Series, ISSN 1100-6641 ; 34
National Category
Computer Vision and Robotics (Autonomous Systems)
Research subject
Computerized Image Analysis
URN: urn:nbn:se:uu:diva-142812OAI: oai:DiVA.org:uu-142812DiVA: diva2:388277
Symposium on Image Analysis
Available from: 2011-01-17 Created: 2011-01-17 Last updated: 2016-04-22Bibliographically approved

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