Approximate Matching of Digital Point Sets Using a Novel Angular Tree

P. Bhowmick; R.K. Pradhan; B.B. Bhattacharya

doi:10.1109/tpami.2007.70812

Approximate Matching of Digital Point Sets Using a Novel Angular Tree

IEEE Transactions on Pattern Analysis and Machine Intelligence ◽

10.1109/tpami.2007.70812 ◽

2009 ◽

Vol 31 (5) ◽

pp. 769-782 ◽

Cited By ~ 7

Author(s):

P. Bhowmick ◽

R.K. Pradhan ◽

B.B. Bhattacharya

Keyword(s):

Point Sets ◽

Approximate Matching

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Representation of certain self-similar quasiperiodic tilings with perfect matching rules by discrete point sets

Journal de Physique I ◽

10.1051/jp1:1994234 ◽

1994 ◽

Vol 4 (6) ◽

pp. 893-904 ◽

Cited By ~ 4

Author(s):

Richard Klitzing ◽

Michael Baake

Keyword(s):

Perfect Matching ◽

Discrete Point ◽

Point Sets ◽

Self Similar ◽

Matching Rules ◽

Quasiperiodic Tilings

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Almost empty polygons

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.40.2003.3.1 ◽

2003 ◽

Vol 40 (3) ◽

pp. 269-286 ◽

Cited By ~ 4

Author(s):

H. Nyklová

Keyword(s):

Exact Results ◽

Point Sets ◽

Planar Point ◽

Convex Position ◽

Vertex Set ◽

Point Set ◽

Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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