Topology of vector fields based on Morse decompositions has been a more numerically stable representation than the conventional trajectory-based topology. The refinement for Morse decompositions means to get the optimal results with lower computations. To address the problems in the already existing refinement methods, which contain too many empirical parameters and vague refinement objectives, this paper proposes a novel refinement method for Morse decompositions of vector fields based on a new refinement criterion using robust critical simplexes. Firstly, the critical simplexes are defined and detected by a robust manner. Secondly, the Morse sets can be classified by their regions and the detected critical simplexes. And a new refinement criterion for identifying Morse sets to refine based on the classification of Morse sets is built. Finally, the refinement flow of the proposed method is presented. Experimental results demonstrate the availability and effectiveness of the proposed method.
Clustering is an effective mean for of marine environment data analysis. This paper proposes a clustering algorithm
based on the “Velocity-Direction” histogram. First of all, the “Velocity-Direction” histogram is constructed based on the
characteristics of marine environment vector field data. Secondly, the exact surface of histogram is reconstructed by the
Gaussian kernel function to eliminate the contaminated data points in “Velocity-Direction” histogram. Finally, the FCM
algorithm is introduced and modified for the “Velocity-Direction” histogram clustering. The initial number and
clustering centers for the FCM algorithm are set as the local extremum in the constructed histogram surfaces. The
experiment results based on the simulation and the NOAA marine environment vector field data verifies the
effectiveness of the proposed algorithm.