Detecting zero curvature points for the direction-dependent tangent on discrete curves

Many techniques in machine vision require tangent estimation. The direction-dependent tangent (DDT) is introduced. The representation makes explicit the direction of curve following and the concavity, hence facilitating shape matching. The scheme is a simple but powerful enhancement to the standard tangent notation. However, discrete tangent and curvature estimations are very sensitive to noise and quantization errors, and the original DDT formulation is difficult to apply directly to digital curves. Based on the geometric property of DDT, we propose to detect zero curvature points to determine the DDT values. Traditional approaches to zero curvature detection rely heavily on discrete tangent and curvature estimations, which are difficult to approximate accurately. Hence, most researchers adopted the multi-scale solutions, which are costly to compute. In this paper, we put forth a new measure, which we called `turning angle', for zero curvature detection. Based on this measure, we develop an efficient conditioning algorithm to tackle the zero curvature detection problem. Although the conditioning algorithm is quite straightforward, the zero curvature points detected are quite stable across scales.