scholarly journals Polar Transforms for ITK

2006 ◽  
Author(s):  
Jakub Bican
Keyword(s):  
Image Processing ◽  
Coordinate System ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Cartesian Coordinates ◽  
Polar Coordinate ◽  
2D Space

Polar transform is a geometric transform, that transforms points form cartesian coordinates to so-called polar coordinates. In case of 2D space, a point in polar coordinate system is addressed by radius and angle. In image processing, polar transform is usually used to convert rotations around the origin of polar coordinate system to translations.This submission contains the implementation of forward and inverse polar transforms in two very simple classes for the Insight Toolkit.

scholarly journals Determination of Ship Approach Parameters in the Polar Coordinates System

2014 ◽  
Vol 96 (1) ◽  
pp. 1-8
Author(s):  
Andrzej Banachowicz ◽  
Adam Wolski
Keyword(s):  
Coordinate System ◽  
Target Position ◽  
Geometric Interpretation ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Polar Coordinate ◽  
Radar Measurements ◽  
Cartesian Coordinate ◽  
Radar Antenna

Abstract An essential aspect of the safety of navigation is avoiding collisions with other vessels and natural or man made navigational obstructions. To solve this kind of problem the navigator relies on automatic anti-collision ARPA systems, or uses a geometric method and makes radar plots. In both cases radar measurements are made: bearing (or relative bearing) on the target position and distance, both naturally expressed in the polar coordinates system originating at the radar antenna. We first convert original measurements to an ortho-Cartesian coordinate system. Then we solve collision avoiding problems in rectangular planar coordinates, and the results are transformed to the polar coordinate system. This article presents a method for an analysis of a collision situation at sea performed directly in the polar coordinate system. This approach enables a simpler geometric interpretation of a collision situation

The Shape of Space: Evidence for Spontaneous but Flexible Use of Polar Coordinates in Visuospatial Representations

2021 ◽  
pp. 095679762097237
Author(s):  
Sami R. Yousif ◽  
Frank C. Keil
Keyword(s):  
Spatial Representation ◽  
Spatial Scales ◽  
Human Mind ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Coordinate Systems ◽  
Spatial Tasks ◽  
Polar Coordinate ◽  
Visual Matching ◽  
2D Space

What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing 2D space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which capture angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments, using a simple visual-matching paradigm, show that (a) representational format is recoverable from the errors that observers make in simple spatial tasks, (b) human-made errors spontaneously favor a polar coordinate system of representation, and (c) observers are capable of using other coordinate systems when acting in highly structured spaces (e.g., grids). We discuss these findings in relation to classic work on dimension independence as well as work on spatial representation at other spatial scales.

Outlier detection by the EM algorithm for laser scanning in rectangular and polar coordinate systems

2015 ◽  
Vol 9 (3) ◽  
Author(s):  
Karl-Rudolf Koch ◽  
Boris Kargoll
Keyword(s):  
Em Algorithm ◽  
Coordinate System ◽  
Linear Model ◽  
Laser Scanning ◽  
Local Coordinate System ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Coordinate Systems ◽  
The Em Algorithm ◽  
Polar Coordinate

AbstractTo visualize the surface of an object, laser scanners determine the rectangular coordinates of points of a grid on the surface of the object in a local coordinate system. Vertical angles, horizontal angles and distances of a polar coordinate system are measured with the scanning. Outliers generally occur as gross errors in the distances. It is therefore investigated here whether rectangular or polar coordinates are better suited for the detection of outliers. The parameters of a surface represented by a polynomial are estimated in the nonlinear Gauss Helmert (GH) model and in a linear model. Rectangular and polar coordinates are used, and it is shown that the results for both coordinate systems are identical. It turns out that the linear model is sufficient to estimate the parameters of the polynomial surface. Outliers are therefore identified in the linear model by the expectation maximization (EM) algorithm for the variance-inflation model and are confirmed by the EM algorithm for the mean-shift model. Again, rectangular and polar coordinates are used. The same outliers are identified in both coordinate systems.

Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions

1991 ◽  
Author(s):  
C. Rajalingham ◽  
R. B. Bhat ◽  
G. D. Xistris
Keyword(s):  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Polar Coordinate System ◽  
Free Boundaries ◽  
Natural Modes ◽  
Polar Coordinate ◽  
Boundary Characteristic

Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

scholarly journals Aerosol Plume Detection Algorithm Based on Image Segmentation of Scanning Atmospheric Lidar Data

2016 ◽  
Vol 33 (4) ◽  
pp. 697-712 ◽  
Author(s):  
R. Andrew Weekley ◽  
R. Kent Goodrich ◽  
Larry B. Cornman
Keyword(s):  
Coordinate System ◽  
Original Data ◽  
Detection Algorithm ◽  
Polar Coordinate System ◽  
Lidar Data ◽  
Image Processing Algorithm ◽  
Polar Coordinate ◽  
Scanning Lidar ◽  
Performance Statistics ◽  
Background Fields

AbstractAn image-processing algorithm has been developed to identify aerosol plumes in scanning lidar backscatter data. The images in this case consist of lidar data in a polar coordinate system. Each full lidar scan is taken as a fixed image in time, and sequences of such scans are considered functions of time. The data are analyzed in both the original backscatter polar coordinate system and a lagged coordinate system. The lagged coordinate system is a scatterplot of two datasets, such as subregions taken from the same lidar scan (spatial delay), or two sequential scans in time (time delay). The lagged coordinate system processing allows for finding and classifying clusters of data. The classification step is important in determining which clusters are valid aerosol plumes and which are from artifacts such as noise, hard targets, or background fields. These cluster classification techniques have skill since both local and global properties are used. Furthermore, more information is available since both the original data and the lag data are used. Performance statistics are presented for a limited set of data processed by the algorithm, where results from the algorithm were compared to subjective truth data identified by a human.

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