Two-dimensional multi-pixel anisotropic Gaussian filter for edge-line segment (ELS) detection

This article presents a novel line segment extraction algorithm using two-dimensional (2D) laser data, which is composed of four main procedures: seed-segment detection, region growing, overlap region processing, and endpoint generation. Different from existing approaches, the proposed algorithm borrows the idea of seeded region growing in the field of image processing, which is more efficient with more precise endpoints of the extracted line segments. Comparative experimental results with respect to the well-known Split-and-Merge algorithm are presented to show superior performance of the proposed approach in terms of efficiency, correctness, and precision, using real 2D data taken from our hallway and laboratory.

Download Full-text

A lower bound for electrostatic capacity in the plane

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500020114 ◽

1981 ◽

Vol 88 (3-4) ◽

pp. 267-273 ◽

Cited By ~ 13

Author(s):

L. E. Fraenkel

Keyword(s):

Lower Bound ◽

Line Segment ◽

Diameter Ratio ◽

Two Dimensional ◽

Steiner Symmetrization

SynopsisThis note presents a lower bound, in terms of the diameter ratio of the inner and outer conductors, for the electrostatic capacity of certain two-dimensional condensers. We use double Steiner symmetrization to prove that the minimizing condenser consists of a line segment placed symmetrically within a circle; the capacity of this condenser is known explicitly.

Download Full-text

Two-dimensional Unwrapped Phase Inversion with Damping and a Gaussian Filter

Proceedings 76th EAGE Conference and Exhibition 2014 ◽

10.3997/2214-4609.20140702 ◽

2014 ◽

Author(s):

Y. Choi ◽

T. Alkhalifah

Keyword(s):

Phase Inversion ◽

Gaussian Filter ◽

Two Dimensional

Download Full-text

Transition Probabilities for Markov Process on a Line Segment Located within a Quarter-Plane

Herald of the Bauman Moscow State Technical University Series Natural Sciences ◽

10.18698/1812-3368-2021-2-4-24 ◽

2021 ◽

pp. 4-24

Author(s):

A.V. Kalinkin

Keyword(s):

Markov Process ◽

Random Process ◽

Generating Function ◽

Line Segment ◽

Transition Probabilities ◽

Special Functions ◽

Transition Probability ◽

Separation Of Variables ◽

Two Dimensional ◽

Quarter Plane

The paper considers a quadratic birth-death Markov process. The points on a line segment located within a quarter-plane represent the states of the random process. We designate the set of vectors that have integer non-negative coordinates as our quarter plane. The process is defined by infinitesimal characteristics, or transition probability densities. These characteristics are determined by a quadratic function of the coordinates at the segment points with integer coordinates. The boundary points of the segment are absorbing; at these points, the random process stops. We investigated a critical case when process jumps are equally probable at the moment of exiting a point. We derived expressions describing transition probabilities of the Markov process as a spectral series. We used a two-dimensional exponential generating function of transition probabilities and a two-dimensional generating function of transition probabilities. The first and second systems of ordinary differential Kolmogorov equations for Markov process transition probabilities are reduced to second-order mixed type partial differential equations for a double generating function. We solve the resulting system of linear equations using separation of variables. The spectrum obtained is discrete. The eigen-functions are expressed in terms of hypergeometric functions. The particular solution constructed is a Fourier series, whose coefficients are derived by means of expo-nential expansion. We employed sums of functional series known in the theory of special functions to construct the exponential expansion required

Download Full-text