Level set driven smooth curve approximation from unorganized or noisy point set

Smooth Curve Approximation to the Energy‐Level Distribution for Quantum Harmonic Oscillators

The Journal of Chemical Physics ◽

10.1063/1.1734187 ◽

1963 ◽

Vol 39 (12) ◽

pp. 3258-3262 ◽

Cited By ~ 50

Author(s):

Everett Thiele

Keyword(s):

Energy Level ◽

Smooth Curve ◽

Harmonic Oscillators ◽

Curve Approximation

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B-Spline Curve Approximation with Nearly Arc-Length Parameterization

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.513-517.3372 ◽

2014 ◽

Vol 513-517 ◽

pp. 3372-3376 ◽

Cited By ~ 2

Author(s):

Si Hui Shu ◽

Zi Zhi Lin ◽

Yun Ding

Keyword(s):

Three Dimensional ◽

Smooth Curve ◽

Least Square ◽

Arc Length ◽

Key Factors ◽

B Spline ◽

Spline Curve ◽

Curve Approximation ◽

Fitting Algorithm ◽

Data Points

An algorithm of B-spline curve approximation with the three-dimensional data is presented in this paper. In this algorithm, we will get a smooth curve which is nearly arc-length parameterization. The smoothness and uniform parameterization are key factors of the approximating curve, specifically in skinning surface and surface approximation. Firstly, the data points are fitted using local interpolation, this local fitting algorithm yields n Bezier segments, each segment having speed equal to 1 at their end and midpoints. Then segments are composed of a C1 continuous cubic B-spline curve which named controlling curve. But the controlling curves control points are redundancy, so we find another curve to approximate the controlling curve using least square approximation with smoothness

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Computational Micrograph Registration with Sieve Processes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164660 ◽

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.

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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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