Journal article
The minimum barrier distance
Computer vision and image understanding, Vol.117(4), pp.429-437
04/2013
DOI: 10.1016/j.cviu.2012.10.011
Abstract
► We introduce a new distance function on fuzzy subsets. ► Properties of the continuous and digital versions are proved. ► We give an approximation that can be computed efficiently. ► The method is robust to noise, blur and seed point position.
In this paper we introduce a minimum barrier distance, MBD, defined for the (graphs of) real-valued bounded functions fA, whose domain D is a compact subsets of the Euclidean space Rn. The formulation of MBD is presented in the continuous setting, where D is a simply connected region in Rn, as well as in the case where D is a digital scene. The MBD is defined as the minimal value of the barrier strength of a path between the points, which constitutes the length of the smallest interval containing all values of fA along the path.
We present several important properties of MBD, including the theorems: on the equivalence between the MBD ρA and its alternative definition φA; and on the convergence of their digital versions, ρA^ and φA^, to the continuous MBD ρA=φA as we increase a precision of sampling. This last result provides an estimation of the discrepancy between the value of ρA^ and of its approximation φA^. An efficient computational solution for the approximation φA^ of ρA^ is presented. We experimentally investigate the robustness of MBD to noise and blur, as well as its stability with respect to the change of a position of points within the same object (or its background). These experiments are used to compare MBD with other distance functions: fuzzy distance, geodesic distance, and max-arc distance. A favorable outcome for MBD of this comparison suggests that the proposed minimum barrier distance is potentially useful in different imaging tasks, such as image segmentation.
Details
- Title: Subtitle
- The minimum barrier distance
- Creators
- Robin Strand - Centre for Image Analysis, Uppsala University, SwedenKrzysztof Chris Ciesielski - Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USAFilip Malmberg - Centre for Image Analysis, Uppsala University, SwedenPunam K Saha - Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA 52242, USA
- Resource Type
- Journal article
- Publication Details
- Computer vision and image understanding, Vol.117(4), pp.429-437
- Publisher
- Elsevier Inc
- DOI
- 10.1016/j.cviu.2012.10.011
- ISSN
- 1077-3142
- eISSN
- 1090-235X
- Language
- English
- Date published
- 04/2013
- Academic Unit
- Electrical and Computer Engineering; Radiology
- Record Identifier
- 9984051974802771
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