Gradient-Based Feature Extraction Operators for the Segmentation of Image Curves
Shigeru Ando, Kenji Nagao · Transactions of the Society of Instrument and Control Engineers · 1990
In this paper, a set of curve descriptors for representing and classifying very short curve segments according to their circularity are proposed. First, we show a degenerative gradient covariance matrix of a curve segment indicates it can be fitted by some circular arcs without knowing its radius. After deriving dimensionless and normalized equations and adding a noise suppressing characteristic to them, we obtain two basic operators which evaluate the desimilarities to 1) arcs whose centers are locating at an origin (NON-CIRCLE) and 2) arcs of arbitrary locations (NON-ARC). Their complementary operators which respond to 3) centered arcs (CIRCLE) and 4) non-centered arcs (ARC) are also defined. Basically, they are seen to measure the similarities between a given line segment and two types of circles noted above. By a theoretical analysis, however, the NON-CIRCLE and NON-ARC operators are shown to act as the singularity detecting operators which respond maximally on tangential and/or curvature discontinuities in an invariant manner to their strength. By using computer generated curves and actual TV image data, the proposed operators are examined under noiseless and noisy conditions.