Visualizing concave and convex partitioning of 2D contours

Abstract

A new method based on parsing the concavity code is used to partition a digital contour into concave and convex sections. Innovative features of the technique include: (1) coerced two-state classification of every point into a concavity or a convexity; (2) linguistic explanation for each point’s classification; (3) curvature validation via the residue (that portion of the boundary remaining after curvature extraction); (4) preservation of original contour shape; (5) symbolic logic methodology (no floating point operations); (6) parameter-free implementation; (7) linear time and space complexity. No other currently available contour partitioning method exhibits all of these features. The parser achieves two-state partitioning by implementing simple notions of cumulative curvature, vertex adjacency, shallow curvature absorption, and residue sharing. Concavities and convexities are color-coded to help disambiguate complex images such as topographic contour maps and radio frequency propagation plots. To gauge product quality, the observer may appeal visually to the residue for validation.