Recognizing straight lines on raster display with a type of convex hull

2001 ◽  
Author(s):  
Shuping Chen ◽  
Yongfa Xia ◽  
Mingshun Wang ◽  
Xin Mao
Keyword(s):  
Convex Hull ◽  
Straight Lines

scholarly journals Set estimation under biconvexity restrictions

2020 ◽  
Vol 24 ◽  
pp. 770-788
Author(s):  
Alejandro Cholaquidis ◽  
Antonio Cuevas
Keyword(s):  
Convex Hull ◽  
Convex Sets ◽  
Optimization Theory ◽  
Minimal Set ◽  
Set Estimation ◽  
Convex Case ◽  
Natural Notion ◽  
Inclination Angles ◽  
Definition Of ◽  
Straight Lines

A set in the Euclidean plane is said to be biconvex if, for some angle θ ∈ [0, π∕2), all its sections along straight lines with inclination angles θ and θ + π∕2 are convex sets (i.e., empty sets or segments). Biconvexity is a natural notion with some useful applications in optimization theory. It has also be independently used, under the name of “rectilinear convexity”, in computational geometry. We are concerned here with the problem of asymptotically reconstructing (or estimating) a biconvex set S from a random sample of points drawn on S. By analogy with the classical convex case, one would like to define the “biconvex hull” of the sample points as a natural estimator for S. However, as previously pointed out by several authors, the notion of “hull” for a given set A (understood as the “minimal” set including A and having the required property) has no obvious, useful translation to the biconvex case. This is in sharp contrast with the well-known elementary definition of convex hull. Thus, we have selected the most commonly accepted notion of “biconvex hull” (often called “rectilinear convex hull”): we first provide additional motivations for this definition, proving some useful relations with other convexity-related notions. Then, we prove some results concerning the consistent approximation of a biconvex set S and the corresponding biconvex hull. An analogous result is also provided for the boundaries. A method to approximate, from a sample of points on S, the biconvexity angle θ is also given.

Domain Formation in Synthetic Quartz

1971 ◽  
Vol 29 ◽  
pp. 156-157
Author(s):  
Joseph J. Comer
Keyword(s):  
Electron Beam ◽  
Room Temperature ◽  
Domain Formation ◽  
Synthetic Quartz ◽  
Transmission Electron ◽  
Black Spots ◽  
Diffraction Mode ◽  
Domain Boundaries ◽  
Kikuchi Lines ◽  
Straight Lines

Domains visible by transmission electron microscopy, believed to be Dauphiné inversion twins, were found in some specimens of synthetic quartz heated to 680°C and cooled to room temperature. With the electron beam close to parallel to the [0001] direction the domain boundaries appeared as straight lines normal to <100> and <410> or <510> directions. In the selected area diffraction mode, a shift of the Kikuchi lines was observed when the electron beam was made to traverse the specimen across a boundary. This shift indicates a change in orientation which accounts for the visibility of the domain by diffraction contrast when the specimen is tilted. Upon exposure to a 100 KV electron beam with a flux of 5x 1018 electrons/cm2sec the boundaries are rapidly decorated by radiation damage centers appearing as black spots. Similar crystallographio boundaries were sometimes found in unannealed (0001) quartz damaged by electrons.

Convex hull of chain-coded blob

1989 ◽  
Vol 136 (6) ◽  
pp. 530
Author(s):  
G.R. Wilson ◽  
B.G. Batchelor
Keyword(s):  
Convex Hull

Automatic Tread Gaging Machine

1979 ◽  
Vol 7 (1) ◽  
pp. 31-39
Author(s):  
G. S. Ludwig ◽  
F. C. Brenner
Keyword(s):  
Experimental Tests ◽  
Automatic Machine ◽  
Wear Rates ◽  
Handling Device ◽  
Straight Line ◽  
Component Systems ◽  
Before And After ◽  
Good Repeatability ◽  
The Difference ◽  
Straight Lines

Abstract An automatic tread gaging machine has been developed. It consists of three component systems: (1) a laser gaging head, (2) a tire handling device, and (3) a computer that controls the movement of the tire handling machine, processes the data, and computes the least-squares straight line from which a wear rate may be estimated. Experimental tests show that the machine has good repeatability. In comparisons with measurements obtained by a hand gage, the automatic machine gives smaller average groove depths. The difference before and after a period of wear for both methods of measurement are the same. Wear rates estimated from the slopes of straight lines fitted to both sets of data are not significantly different.

Saliency Detection Based on Improved Manifold Ranking via Convex Hull

2019 ◽  
Vol 31 (5) ◽  
pp. 761
Author(s):  
Xiao Lin ◽  
Zuxiang Liu ◽  
Xiaomei Zheng ◽  
Jifeng Huang ◽  
Lizhuang Ma
Keyword(s):  
Convex Hull ◽  
Saliency Detection ◽  
Manifold Ranking

scholarly journals Properties of galaxies with an offset between the position angles of the major kinematic and photometric axes

2020 ◽  
Vol 634 ◽  
pp. A26 ◽  
Author(s):  
L. S. Pilyugin ◽  
E. K. Grebel ◽  
I. A. Zinchenko ◽  
J. M. Vílchez ◽  
F. Sakhibov ◽  
...  
Keyword(s):  
Star Formation ◽  
Surface Brightness ◽  
Star Formation Rate ◽  
Formation Rate ◽  
Velocity Fields ◽  
Oxygen Abundance ◽  
Star Forming ◽  
Measured Position ◽  
Central Oxygen ◽  
Straight Lines

We derive the photometric, kinematic, and abundance characteristics of 18 star-forming MaNGA galaxies with fairly regular velocity fields and surface brightness distributions and with a large offset between the measured position angles of the major kinematic and photometric axes, ΔPA ≳ 20°. The aim is to examine if there is any other distinctive characteristic common to these galaxies. We found morphological signs of interaction in some (in 11 out of 18) but not in all galaxies. The observed velocity fields show a large variety; the maps of the isovelocities vary from an hourglass-like appearance to a set of straight lines. The position angles of the major kinematic axes of the stellar and gas rotations are close to each other. The values of the central oxygen abundance, radial abundance gradient, and star formation rate are distributed within the intervals defined by galaxies with small (no) ΔPA of similar mass. Thus, we do not find any specific characteristic common to all galaxies with large ΔPA. Instead, the properties of these galaxies are similar to those of galaxies with small (no) ΔPA. This suggests that either the reason responsible for the large ΔPA does not influence other characteristics or the galaxies with large ΔPA do not share a common origin, they can, instead, originate through different channels.

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