Improved grid map layout by point set matching

2013 ◽  
Author(s):  
David Eppstein ◽  
Marc van Kreveld ◽  
Bettina Speckmann ◽  
Frank Staals
Keyword(s):  
Grid Map ◽  
Point Set

Improved Grid Map Layout by Point Set Matching

2015 ◽  
Vol 25 (02) ◽  
pp. 101-122 ◽  
Author(s):  
David Eppstein ◽  
Marc van Kreveld ◽  
Bettina Speckmann ◽  
Frank Staals
Keyword(s):  
Previous Method ◽  
Experimental Comparison ◽  
Manhattan Distance ◽  
Basic Operation ◽  
Matching Problem ◽  
Grid Map ◽  
Main Challenge ◽  
Directional Relation ◽  
Global Matching ◽  
Point Set

Associating the regions of a geographic subdivision with the cells of a grid is a basic operation that is used in various types of maps, like spatially ordered treemaps and Origin-Destination maps (OD maps). In these cases the regular shapes of the grid cells allow easy representation of extra information about the regions. The main challenge is to find an association that allows a user to find a region in the grid quickly. We call the representation of a set of regions as a grid a grid map. We introduce a new approach to solve the association problem for grid maps by formulating it as a point set matching problem: Given two sets [Formula: see text] (the centroids of the regions) and [Formula: see text] (the grid centres) of [Formula: see text] points in the plane, compute an optimal one-to-one matching between [Formula: see text] and [Formula: see text]. We identify three optimisation criteria that are important for grid map layout: maximise the number of adjacencies in the grid that are also adjacencies of the regions, minimise the sum of the distances between matched points, and maximise the number of pairs of points in [Formula: see text] for which the matching preserves the directional relation (SW, NW, etc.). We consider matchings that minimise the [Formula: see text]-distance (Manhattan-distance), the ranked [Formula: see text]-distance, and the [Formula: see text]-distance, since one can expect that minimising distances implicitly helps to fulfill the other criteria. We present algorithms to compute such matchings and perform an experimental comparison that also includes a previous method to compute a grid map. The experiments show that our more global, matching-based algorithm outperforms previous, more local approaches with respect to all three optimisation criteria.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
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.

Modified K-means clustering algorithm based on good point set and Leader method

2011 ◽  
Vol 31 (5) ◽  
pp. 1359-1362
Author(s):  
Yan-ping ZHANG ◽  
Juan ZHANG ◽  
Cheng-gang HE ◽  
Wei-cui CHU ◽  
Li-na ZHANG
Keyword(s):  
Clustering Algorithm ◽  
Good Point ◽  
Point Set ◽  
Good Point Set

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

Multi-View Image Color Correction Using 3D Point Set Registration

2021 ◽  
Author(s):  
Hyeonwoo Jeong ◽  
Byunghyun Yoon ◽  
Honggu Jeong ◽  
Kang-Sun Choi
Keyword(s):  
Color Correction ◽  
Point Set Registration ◽  
Point Set
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