scholarly journals COMPUTATIONAL AND STRUCTURAL ADVANTAGES OF CIRCULAR BOUNDARY REPRESENTATION

2011 ◽  
Vol 21 (01) ◽  
pp. 47-69 ◽  
Author(s):  
OSWIN AICHHOLZER ◽  
FRANZ AURENHAMMER ◽  
THOMAS HACKL ◽  
BERT JÜTTLER ◽  
MARGOT RABL ◽  
...  
Keyword(s):  
Convex Hull ◽  
Medial Axis ◽  
Boundary Representation ◽  
Line Segments ◽  
Circular Boundary ◽  
Original Shape ◽  
Circular Arcs ◽  
Straight Line ◽  
Planar Shapes ◽  
Boundary Approximation

Boundary approximation of planar shapes by circular arcs has quantitative and qualitative advantages compared to using straight-line segments. We demonstrate this by way of three basic and frequent computations on shapes – convex hull, decomposition, and medial axis. In particular, we propose a novel medial axis algorithm that beats existing methods in simplicity and practicality, and at the same time guarantees convergence to the medial axis of the original shape.

scholarly journals On the generation of spiral-like paths within planar shapes

2017 ◽  
Vol 5 (3) ◽  
pp. 348-357 ◽  
Author(s):  
Martin Held ◽  
Stefan de Lorenzo
Keyword(s):  
Simple Algorithm ◽  
Basic Algorithm ◽  
Line Segments ◽  
Spiral Path ◽  
Curvature Variation ◽  
Circular Arcs ◽  
Straight Line ◽  
Planar Shapes ◽  
Double Spiral ◽  
Step Over

Abstract We simplify and extend prior work by Held and Spielberger [CAD 2009, CAD&A 2014] to obtain spiral-like paths inside of planar shapes bounded by straight-line segments and circular arcs: We use a linearization to derive a simple algorithm that computes a continuous spiral-like path which (1) consists of straight-line segments, (2) has no self-intersections, (3) respects a user-specified maximum step-over distance, and (4) starts in the interior and ends at the boundary of the shape. Then we extend this basic algorithm to double-spiral paths that start and end at the boundary, and show how these double spirals can be used to cover complicated planar shapes by composite spiral paths. We also discuss how to improve the smoothness and reduce the curvature variation of our paths, and how to boost them to higher levels of continuity. Highlights The algorithm computes a spiral path within planar shapes with and without islands. It respects a user-specified maximum step-over distance. Double spirals and composite spiral paths can be computed. Heuristics for smoothing the spirals are discussed. The algorithm is simple and easy to implement, and suitable for various applications.

Grouping of Straight Line Segments and Circular Arcs for Scene Analysis

1995 ◽  
pp. 163-185
Author(s):  
Jean-Luc Arseneault ◽  
Robert Bergevin ◽  
Denis Laurendeau
Keyword(s):  
Scene Analysis ◽  
Line Segments ◽  
Circular Arcs ◽  
Straight Line

Stable Computation of the 2D Medial Axis Transform

1998 ◽  
Vol 08 (05n06) ◽  
pp. 577-598 ◽  
Author(s):  
Guy Evans ◽  
Alan Middleditch ◽  
Nick Miles
Keyword(s):  
Medial Axis ◽  
Medial Axis Transform ◽  
Element Mesh ◽  
Alternative Representation ◽  
Circular Arcs ◽  
Straight Line ◽  
Key Points ◽  
Stable Computation ◽  
Mathematical Definitions ◽  
Biological Shape

The medial axis transform of a 2D region was introduced by Blum in the 1960's as an aid to the description of biological shape. It is an alternative representation of a region which is often more amenable to analysis. This property has led to its use in diverse fields including pattern recognition and automatic finite element mesh generation. There are two widely agreed mathematical definitions for the medial axis transform which are closely related. It is shown that these definitions are not in general equivalent, despite being so far many types of region. In this paper, precise mathematical definitions of the medial axis transform and its key points (atoms) are given, and an O(n2) algorithm for its computation via those atoms presented. This algorithm is described in terms of simple polygons whose sole boundary consists of circular arcs and straight line segments, then extended to polygons with holes. It is shown how more complex edges could be accommodated. In comparison with existing algorithms it is simple to implement and stable in the presence of geometric degeneracy.

scholarly journals TOPOLOGY-PRESERVING WATERMARKING OF VECTOR GRAPHICS

2014 ◽  
Vol 24 (01) ◽  
pp. 61-86 ◽  
Author(s):  
STEFAN HUBER ◽  
MARTIN HELD ◽  
PETER MEERWALD ◽  
ROLAND KWITT
Keyword(s):  
Input Data ◽  
Two Dimensional ◽  
Statistical Features ◽  
Embedding Capacity ◽  
Vector Graphics ◽  
Line Segments ◽  
Circular Arcs ◽  
Straight Line ◽  
Watermark Embedding ◽  
Topological Correctness

Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques.

Nonholonomic path planning among obstacles subject to curvature restrictions

Robotica ◽  
2002 ◽  
Vol 20 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Wilson D. Esquivel ◽  
Luciano E. Chiang
Keyword(s):  
Path Planning ◽  
Shortest Path ◽  
Autonomous Navigation ◽  
Line Segments ◽  
Circular Arcs ◽  
Straight Line ◽  
Smoothing Process ◽  
Planning Methodology ◽  
Final Orientation ◽  
Complete Path

This paper addresses the problem of finding a nonholonomic path subject to a curvature restriction, to be tracked by a wheeled autonomous navigation vehicle. This robot is able to navigate in a structured environment, with obstacles modeled as polygons, thus constituting a model based system. The path planning methodology begins with the conditioning of the polygonal environment by offsetting each polygon in order to avoid the possibility of collision with the mobile. Next, the modified polygonal environment is used to compute a preliminary shortest path (PA) between the two extreme positions of the trajectory in the plane (x, y). This preliminary path (PA) does not yet consider the restrictions on the curvature and is formed only by straight line segments. A smoothing process follows in order to obtain a path (PS) that satisfies curvature restrictions which consist basically of joining the straight line segments by circular arcs of minimum radius R (filleting). Finally, the initial and final orientation of the vehicle are accounted for. This is done using a technique we have called the Star Algorithm, because of the geometric shape of the resulting maneuvers. A final complete path (PC) is thus obtained.

A New and Efficient Method for Curve Drawing using Circular Arcs and Straight Line Segments

1989 ◽  
Vol 6 (5) ◽  
pp. 365-371 ◽  
Author(s):  
S N Biswas ◽  
D Dutta Majumder ◽  
B B Chaudhuri
Keyword(s):  
Efficient Method ◽  
Line Segments ◽  
Circular Arcs ◽  
Straight Line

scholarly journals Use of otoliths to estimate size at sexual maturity in fish

2000 ◽  
Vol 43 (4) ◽  
pp. 437-440 ◽  
Author(s):  
Carlos Sérgio Agostinho
Keyword(s):  
Sexual Maturity ◽  
Line Segments ◽  
Alternative Method ◽  
Straight Line ◽  
Size At Sexual Maturity

The viability of an alternative method for estimating the size at sexual maturity of females of Plagioscion squamosissimus (Perciformes, Sciaenidae) was analyzed. This methodology was used to evaluate the size at sexual maturity in crabs, but has not yet been used for this purpose in fishes. Separation of young and adult fishes by this method is accomplished by iterative adjustment of straight-line segments to the data for length of the otolith and length of the fish. The agreement with the estimate previously obtained by another technique and the possibility of calculating the variance indicates that in some cases, the method analyzed can be used successfully to estimate size at sexual maturity in fish. However, additional studies are necessary to detect possible biases in the method.

scholarly journals An Automatic Measurement Method for Absolute Depth of Objects in Two Monocular Images Based on SIFT Feature

2017 ◽  
Author(s):  
Lixin He ◽  
Jing Yang ◽  
Bin Kong ◽  
Can Wang
Keyword(s):  
Automatic Measurement ◽  
Depth Estimation ◽  
Depth Information ◽  
Scale Invariant ◽  
Line Segments ◽  
Sift Feature ◽  
Novel Approach ◽  
Straight Line ◽  
Object Depth ◽  
Scale Invariant Feature

It is one of very important and basic problem in compute vision field that recovering depth information of objects from two-dimensional images. In view of the shortcomings of existing methods of depth estimation, a novel approach based on SIFT (the Scale Invariant Feature Transform) is presented in this paper. The approach can estimate the depths of objects in two images which are captured by an un-calibrated ordinary monocular camera. In this approach, above all, the first image is captured. All of the camera parameters remain unchanged, and the second image is acquired after moving the camera a distance d along the optical axis. Then image segmentation and SIFT feature extraction are implemented on the two images separately, and objects in the images are matched. Lastly, an object depth can be computed by the lengths of a pair of straight line segments. In order to ensure that the best appropriate a pair of straight line segments are chose and reduce the computation, the theory of convex hull and the knowledge of triangle similarity are employed. The experimental results show our approach is effective and practical.

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