A ROTATION - INVARIANT PATTERN SIGNATUREEero

We propose a \signature" for rotation-invariant representation of local image structure. The signature is a complex-valued vector constructed analytically from the projections of the image onto a set of oriented basis kernels. The components of the signature form an over-complete set of algebraic invariants, but are chosen to avoid instabilities associated with previously developed algebraic invariants. We demonstrate the use of this signature for representing and classifying junctions in grayscale imagery. Local image symmetry provides important cues for visual interpretation. In particular, the local arrangement of oriented contours is a powerful source of information in applications ranging from optical character recognition, to texture-based segmentation, to occlu-sion boundaries detection. It is typically the relative orientation of such contours that carries the important information: the absolute orientation is often irrelevant. It is thus of interest to develop stable, unique, rotation-invariant representations of such structures. Many authors begin by projecting the image structure onto a local rotation-invariant basis (e. Examples of such decompositions are various types of local moment, derivative operators (which are moments in the Fourier domain), or angular harmonics. These decompositions are closely related, often diiering only by a linear transformation. Consider the problem of matching an observed local image intensity pattern against a set of candidate patterns. A brute-force solution, in which one rotates the image pattern through a set of discretized orientations searching for an optimal match is inelegant, ineecient, and highly susceptible to local minima. A number of authors have taken the approach of rst estimating a \dominant" orientation from the projection onto low-order basis functions (e.g., the gradient), and using this estimate to align the two patterns for compari-strongly dominant orientation. More generally, one can use the theory of algebraic in-variants to construct rotation-invariant representations of image content 1, 12, 13, 14]. The theory allows one to construct a complete set of such invariants. But the set is non-unique, and depends on the initial choice of basis. Many such invariants are highly noise-sensitive, and thus unsuitable for applications. In the present paper, we propose a simple, stable, unique, rotation-invariant signature, consisting of a set of invariants of the angular Fourier decomposition.