Shapes Recognition Using the Straight Line Hough Transform: Theory and Generalization

A shape matching technique based on the straight line Hough transform (SLHT) is presented. In the θ-p space, the transform can be expressed as the sum of two terms, namely, the translation term and the intrinsic term. This formulation allows the translation, rotation, and intrinsic parameters of the curve be easily decoupled. A shape signature, called the scalable translation invariant rotation-to-shifting (STIRS) signature, is obtained from the θ-p space by computing the distances between pairs of points having the same θ value. This is equivalent to computing the perpendicular distances between pairs of parallel tangents to the curves. This signature has the following properties: 1) It is invariant to translation; 2) rotation in the image space corresponds to circular shifting of the signature; 3) the signature can be easily normalized. Matching two signatures only amounts to computing a 1-D correlation. The height and location of a peak (if it exists) indicates the similarity and orientation of the test object with respect to the reference object. Knowing the orientation, the location of the test object is obtained by an inverse transform (voting) from the θ-p space to the x-y plane. Examples demonstrating the feasibility of these techniques are presented. The shape matching technique assumes that the shape is characterized by its set of tangent lines. It is proved, based on curve reconstruction, that a continuous closed smooth curve is indeed uniquely characterized by its complete set of tangents. This result serves as the theoretical foundation of the shape recognition methodology based on SLHT. © 1992 IEEE