Analysis and Comparative Evaluation of Discrete Tangent Estimators

Abstract

Abstract. This paper presents a comparative evaluation of tangent estimators based on digital line recognition on digital curves. The comparison is carried out with a comprehensive set of criteria: accuracy on smooth or polygonal shapes, behaviour on convex/concave parts, computation time, isotropy, asymptotic convergence. We further propose a new estimator mixing the qualities of existing ones and outperforming them on most mentioned points.

Binomial Convolutions and Derivatives Estimation from Noisy Discretizations

“…Regarding the order of convergence, we have proved that our approach is as good as the one proposed in [6], that is, in O(h 2/3 ) for first order derivatives. Besides, this order of convergence is uniform.…”

“…The asymptotic computational complexity is worst case O( − ln(h)/h) for first order derivatives which is similar to [6].…”

“…This complexity is not as good as the one induced by tangent estimators from discrete geometry which is in O(h) for the best ( [6]). However, it is possible to reduce the complexity of our estimator by considering that values at extremities of the smoothing kernel H n are negligible.…”

“…This problem has been investigated through finite difference methods ( [1]), scale-space ( [4,8]) and discrete geometry ( [6,7,5]). …”

“…However, our approach is oriented toward integer-only models and algorithms and is based on a discrete point of view of analysis. Unlike estimators proposed in [6], our method still works on noisy data. Moreover, we are able to estimate higher order derivatives.…”