Natural morphological extraction based on the nonlinear manifold pursuit (NMP) algorithm

A manifold defined as a smooth curve passing through the middle of data points can be a good morphological representation for the data feature extraction. In this paper, a new algorithm called nonlinear manifold pursuit (NMP) is introduced to find an ID nonlinear manifold embedded in the 2D Euclidean space. Based on virtual principal direction, the algorithm constructs the global topology from the continuous increment of the local topology. The corresponding nonlinear manifold is, then, developed by a set of piecewise lines passing through the middle of global topology. NMP is applied to both synthetic and real data in many applications such as skeletonization, object detection, and curve fitting