Discrete Representation of Straight Lines

Authors:
Leo Dorst;Arnold W. M. Smeulders
Affiliations:
Laboratorium voor Technische Natuurkunde, Technische Hogeschool Delft, Delft, The Netherlands.;Department of Applied Physics, Delft University of Technology, Delft, The Netherlands/ Department of Pathology and Medical Informatics, Free University, Amsterdam, The Netherlands.
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1984

Citing 0
Cited 18

Digital or analog Hough transform?

Pattern Recognition Letters
Digital planarity-A review

Discrete Applied Mathematics
Reversible vectorisation of 3D digital planar curves and applications

Image and Vision Computing
A generalized preimage for the digital analytical hyperplane recognition

Discrete Applied Mathematics
Discrete-Euclidean operations

Discrete Applied Mathematics
Gift-wrapping based preimage computation algorithm

Pattern Recognition
Supercover model, digital straight line recognition and curve reconstruction on the irregular isothetic grids

Computers and Graphics
On digital plane preimage structure

Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Discrete analytical curve reconstruction without patches

Image and Vision Computing
Patterns for multigrid equidistributed functions: Application to general parabolas and length estimation

Theoretical Computer Science
Duality and geometry straightness, characterization and envelope

DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Two discrete-euclidean operations based on the scaling transform

DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Revisiting digital straight segment recognition

DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
A generalized preimage for the standard and supercover digital hyperplane recognition

DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Supercover model and digital straight line recognition on irregular isothetic grids

DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Linear discrete line recognition and reconstruction based on a generalized preimage

IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Walking in the farey fan to compute the characteristics of a discrete straight line subsegment

DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Two efficient algorithms for computing the characteristics of a subsegment of a digital straight line

Discrete Applied Mathematics

Quantified Score

Hi-index	0.14

Visualization

Abstract

If a continuous straight line segment is digitized on a regular grid, obviously a loss of information occurs. As a result, the discrete representation obtained (e.g., a chaincode string) can be coded more conveniently than the continuous line segment, but measurements of properties (such as line length) performed on the representation have an intrinsic inaccuracy due to the digitization process. In this paper, two fundamental properties of the quantization of straight line segments are treated. 1) It is proved that every ``straight'' chaincode string can be represented by a set of four unique integer parameters. Definitions of these parameters are given. 2) A mathematical expression is derived for the set of all continuous line segments which could have generated a given chaincode string. The relation with the chord property is briefly discussed.