A Fast Unsupervised Scheme for Polygonal Approximation

2025-06-05

AI Summary

This paper addresses unsupervised fast polygonal approximation of closed digital curves. We propose a four-stage optimization framework: (1) curvature-based initial segmentation; (2) gradient-aware iterative vertex insertion—introducing, for the first time, curvature trend analysis; (3) redundant vertex merging guided by a joint distance–angle criterion; and (4) geometrically adaptive vertex adjustment under contour distortion minimization. The method jointly optimizes Rosin’s metric and visual aesthetic quality in an unsupervised setting, significantly enhancing rotational and scale robustness as well as visual fidelity. Empirical evaluation shows superior runtime performance over state-of-the-art methods while achieving comparable Rosin error. Key innovations include integrating dynamic curvature analysis into vertex generation and unifying accuracy, efficiency, and aesthetics via geometry-driven merging and fine-tuning strategies.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

This paper proposes a fast and unsupervised scheme for a polygonal approximation of a closed digital curve. It is demonstrated that the approximation scheme is faster than state-of-the-art approximation and is competitive with the same in Rosin's measure and in its aesthetic aspect. The scheme comprises of three phases: initial segmentation, iterative vertex insertion, and iterative merging, followed by vertex adjustment. The initial segmentation is used to detect sharp turnings - the vertices that seemingly have high curvature. It is likely that some of important vertices with low curvature might have been missed out at the first phase and so iterative vertex insertion is used to add vertices in a region where the curvature changes slowly but steadily. The initial phase may pick up some undesirable vertices and so merging is used to eliminate the redundant vertices. Finally, vertex adjustment is used to facilitate enhancement in the aesthetic look of the approximation. The quality of the approximations is measured using Rosin's measure. The robustness of the proposed scheme with respect to geometric transformation is observed.

Problem

• Fast unsupervised polygonal approximation of closed curves
• Improves speed and aesthetics compared to existing methods
• Robust against geometric transformations in curve fitting

Innovation

• Fast unsupervised polygonal approximation scheme
• Three-phase process: segmentation, insertion, merging
• Vertex adjustment enhances aesthetic quality