Curve fitting approach for tangent angle and curvature measurements

摘要

The measures of tangent angle and curvature of a digital curve play an important role in image analysis such as corner detection, 1D shape representation and shape signature in the Generalized Hough Transform. Instead of using the discrete measurement approach, the least-squares method is employed to fit known digital points to two cubic polynomial functions, one with y = f(x) that minimizes the sum of the vertical distances and the other with x = g(y) that minimizes the sum of the horizontal distances from the known points to the approximated curve. The tangent angle and curvature are therefore directly computable from the first- and second-order derivatives of the continuous functions. Hybrid procedures are also proposed to select the better curve from f and g for accurate evaluation of tangent angle and curvature. Experimented results on both analytic curves and real-world images are included.