Computational-geometric methods for polygonal approximations of a curve
Computer Vision, Graphics, and Image Processing
On the Detection of Dominant Points on Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Contour codes of isothetic polygons
Computer Vision, Graphics, and Image Processing
Isothetic polygon representation for contours
CVGIP: Image Understanding
Optimum polygonal approximation of digitized curves
Pattern Recognition Letters
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Techniques for Assessing Polygonal Approximations of Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curve-drawing algorithms for Raster displays
ACM Transactions on Graphics (TOG)
A new method for polygonal approximation using genetic algorithms
Pattern Recognition Letters
Introduction to Algorithms
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Inner and outer rounding of set operations on lattice polygonal regions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Digital Straight Line Segments
IEEE Transactions on Computers
Isothetic polygonal approximations of a 2d object on generalized grid
PReMI'05 Proceedings of the First international conference on Pattern Recognition and Machine Intelligence
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
TIPS: on finding a tight isothetic polygonal shape covering a 2d object
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
An optimal polygonal boundary encoding scheme in the rate distortion sense
IEEE Transactions on Image Processing
Construction of isothetic covers of a digital object: A combinatorial approach
Journal of Visual Communication and Image Representation
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A novel algorithm to derive an approximate cellular envelope of an arbitrarily thick digital curve on a 2D grid is proposed in this paper. The concept of “cellular envelope” is newly introduced in this paper, which is defined as the smallest set of cells containing the given curve, and hence bounded by two tightest (inner and outer) isothetic polygons on the grid. Contrary to the existing algorithms that use thinning as preprocessing for a digital curve with changing thickness, in our work, an optimal cellular envelope (smallest in the number of constituent cells) that entirely contains the given curve is constructed based on a combinatorial technique. The envelope, in turn, is further analyzed to determine polygonal approximation of the curve as a sequence of cells using certain attributes of digital straightness. Since a real-world curve/curve-shaped object with varying thickness and unexpected disconnectedness is unsuitable for the existing algorithms on polygonal approximation, the curve is encapsulated by the cellular envelope to enable the polygonal approximation. Owing to the implicit Euclidean-free metrics and combinatorial properties prevailing in the cellular plane, implementation of the proposed algorithm involves primitive integer operations only, leading to fast execution of the algorithm. Experimental results including CPU time reinforce the elegance and efficacy of the proposed algorithm.