2007
DOI: 10.1016/j.imavis.2006.06.020
|View full text |Cite
|
Sign up to set email alerts
|

Discrete bisector function and Euclidean skeleton in 2D and 3D

Abstract: International audienceWe propose a new definition and an exact algorithm for the discrete bisector function, which is an important tool for analyzing and filtering Euclidean skeletons. We also introduce a new thinning algorithm which produces homotopic discrete Euclidean skeletons. These algorithms, which are valid both in 2D and 3D, are integrated in a skeletonization method which is based on exact transformations, allows the filtering of skeletons, and is computationally efficient

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
97
0

Year Published

2009
2009
2019
2019

Publication Types

Select...
6
3
1

Relationship

5
5

Authors

Journals

citations
Cited by 76 publications
(97 citation statements)
references
References 24 publications
0
97
0
Order By: Relevance
“…In discrete grids (Z 2 , Z 3 , or Z 4 ), such transformations can be defined and efficiently implemented thanks to the notion of simple point (Kong and Rosenfeld (1989); Bertrand (1994); Couprie and Bertrand (2009)): intuitively, a point of an object is called simple if it can be deleted from this object without altering its topology. A typical topology-preserving transformation based on simple points deletion, that we call guided homotopic thinning (Davies and Plummer (1981); Couprie et al (2007)), may be described as follows. The input data consists of a set X of points in the grid (called object), and a subset K ⊂ X (called constraint set).…”
Section: Introductionmentioning
confidence: 99%
“…In discrete grids (Z 2 , Z 3 , or Z 4 ), such transformations can be defined and efficiently implemented thanks to the notion of simple point (Kong and Rosenfeld (1989); Bertrand (1994); Couprie and Bertrand (2009)): intuitively, a point of an object is called simple if it can be deleted from this object without altering its topology. A typical topology-preserving transformation based on simple points deletion, that we call guided homotopic thinning (Davies and Plummer (1981); Couprie et al (2007)), may be described as follows. The input data consists of a set X of points in the grid (called object), and a subset K ⊂ X (called constraint set).…”
Section: Introductionmentioning
confidence: 99%
“…The idea is to reduce this set while both preserving its topology and respecting facts (a) and (b). To this aim, we use a constrained ultimate homotopic skeleton [12]. Roughly speaking, an ultimate homotopic skeleton of a set X constrained by a set C, has the same topology as X, contains C, and cannot be reduced (by point removal) while keeping these two invariants.…”
Section: Bmentioning
confidence: 99%
“…Implement a new "exact medial axis" algorithm (Couprie et al 2007, Saúde et al 2006) for creating a 3-D skeleton, based on Remy and Thiel (2005). This will avoid having to choose along which axis a skeletal slice-stack should be constructed, avoid skeletal artifacts such as those arising from folds lying along a slice, increase accuracy and reduce inconsistencies across acquisitions and orientations, and result in much faster processing times.…”
Section: Student Projectmentioning
confidence: 99%