A Continuous Framework of Morse-Smale Complex Segmentation for Two-Dimensional Scalar Fields

Mining topology structure is an effective way of obtaining key information of data fields, and MorseSmale(MS) complex is an important topology of two dimensional scalar fields. The traditional methods were all based on PL models and discrete Morse theory. The results generated from a discrete frame have lower accuracy, zigzag integral lines and much redundant feature information, which have to be cut repeatedly. This article introduced a new method of MS complex segmentation for two dimensional scalar data fields. Firstly, we reconstruct a quasi-interpolation model based on double ZP splines for the data field; Then we use the continuous Morse theory to extract feature points, to compute Hessian matrix for classifying features accurately; Finally, we calculate gradient information to build integral lines and MS complex. Double ZP splines adopted in this paper have higher order of continuity and satisfy the condition of at least C²-continuity of Morse theory. The continuous framework is mathematically completeness, on which all differential computations are exact. It can extract high accurate feature points, and obey a strict standard of classification and generate smooth integral lines without massive post-processing. The experiments show that the flow of the method is simpler than any of traditional methods. Its MS complex results are more accuracy and smoother, which can demonstrate key feature structures contained in the data field more clearly.