scholarly journals Characterizing optimal point sets determining one distinct triangle

2020 ◽  
Vol 13 (1) ◽  
pp. 91-98
Author(s):  
Hazel N. Brenner ◽  
James S. Depret-Guillaume ◽  
Eyvindur A. Palsson ◽  
Robert Stuckey
Keyword(s):  
Point Sets ◽  
Optimal Point ◽  
Distinct Triangle

scholarly journals Globally Optimal Point Set Registration by Joint Symmetry Plane Fitting

2021 ◽  
Author(s):  
Lan Hu ◽  
Laurent Kneip
Keyword(s):  
State Of The Art ◽  
Symmetry Plane ◽  
Point Sets ◽  
Optimal Point ◽  
Point Set Registration ◽  
Registration Process ◽  
Current State ◽  
Plane Fitting ◽  
Point Set ◽  
Dense 3D Reconstruction

AbstractThe present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of symmetry. By reflecting the points of each set with respect to the plane of symmetry, we can largely increase the overlap between the sets and therefore boost the registration process. However, prior knowledge about the plane of symmetry is generally unavailable or at least very hard to find, especially with limited partial views. Finding this plane could strongly benefit from a prior alignment of the partial point sets. We solve this chicken-and-egg problem by jointly optimizing the relative pose and symmetry plane parameters. We present a globally optimal solver by employing the branch-and-bound paradigm and thereby demonstrate that joint symmetry plane fitting leads to a great improvement over the current state of the art in globally optimal point set registration for common objects. We conclude with an interesting application of our method to dense 3D reconstruction of scenes with repetitive objects.

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.

Modern capabilities for prognosis of postoperative complications in patients with colorectal cancer

2020 ◽  
pp. 36-51
Author(s):  
G. Rodoman ◽  
G. Gendlin ◽  
N. Malgina ◽  
T. Dolgina
Keyword(s):  
Colorectal Cancer ◽  
Postoperative Complications ◽  
Surgical Patients ◽  
Cardiac Complications ◽  
Optimal Point

The article discusses the most frequently used prognostic scales intended to assess the risk of cardiac complications in surgical patients. The choice of optimal point scales for patients with colorectal cancer is justified.

An Algorithm for Extracting and Enhancing Valley-ridge Features from Point Sets

2010 ◽  
Vol 36 (8) ◽  
pp. 1073-1083 ◽  
Author(s):  
Xu-Fang PANG ◽  
Ming-Yong PANG ◽  
Chun-Xia XIAO
Keyword(s):  
Point Sets

Multifractal Analysis of Chaotic Point Sets

1992 ◽  
Author(s):  
L. V. Meisel ◽  
M. A. Johnson
Keyword(s):  
Multifractal Analysis ◽  
Point Sets

ON THE GENERAL THEORY OF POINT SETS, II

1986 ◽  
Vol 12 (1) ◽  
pp. 377 ◽  
Author(s):  
Morgan
Keyword(s):  
General Theory ◽  
Point Sets

scholarly journals Sparse Approximation via Generating Point Sets

2019 ◽  
Vol 15 (3) ◽  
pp. 1-16
Author(s):  
Avrim Blum ◽  
Sariel Har-Peled ◽  
Benjamin Raichel
Keyword(s):  
Sparse Approximation ◽  
Point Sets

Pareto domain: an invaluable source of process information

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Geraldine Cáceres Sepúlveda ◽  
Silvia Ochoa ◽  
Jules Thibault
Keyword(s):  
Case Studies ◽  
Optimal Solution ◽  
Pareto Optimal ◽  
Process Variables ◽  
Optimal Point ◽  
Decision Variables ◽  
Visualization Tools ◽  
Pareto Domain ◽  
And Performance ◽  
Typical Process

AbstractDue to the highly competitive market and increasingly stringent environmental regulations, it is paramount to operate chemical processes at their optimal point. In a typical process, there are usually many process variables (decision variables) that need to be selected in order to achieve a set of optimal objectives for which the process will be considered to operate optimally. Because some of the objectives are often contradictory, Multi-objective optimization (MOO) can be used to find a suitable trade-off among all objectives that will satisfy the decision maker. The first step is to circumscribe a well-defined Pareto domain, corresponding to the portion of the solution domain comprised of a large number of non-dominated solutions. The second step is to rank all Pareto-optimal solutions based on some preferences of an expert of the process, this step being performed using visualization tools and/or a ranking algorithm. The last step is to implement the best solution to operate the process optimally. In this paper, after reviewing the main methods to solve MOO problems and to select the best Pareto-optimal solution, four simple MOO problems will be solved to clearly demonstrate the wealth of information on a given process that can be obtained from the MOO instead of a single aggregate objective. The four optimization case studies are the design of a PI controller, an SO2 to SO3 reactor, a distillation column and an acrolein reactor. Results of these optimization case studies show the benefit of generating and using the Pareto domain to gain a deeper understanding of the underlying relationships between the various process variables and performance objectives.

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