Geometirc Model Based EMD Algorithm And Its Application

Empirical mode decomposition(EMD)is a time-frequency analysis method for processing non-linear and non-stationary signals.EMD decomposes an input signal into several intrinsic mode functions(IMF)and a residual function adaptively.By operating on the intrinsic mode functions,many signal processing operations can be achieved,such as filter design and signal denoising.Since the classical EMD algorithm is a scalar function form method,we need to define signal function firstly while processing geo-metric models.While the classic EMD algorithm works well for signals of scalar func-tions,it deals with signals of planar models by separately decomposing each coordinate function of the models,which generally produces inferior results.Radial distance,coor-dinate function and mean curvature can be used as the signal function while processing three-dimensional mesh models.Although mean curvature works best among them,the most serious drawback is that the mesh need to be reconstructed according to the mean curvature at last.In this paper,we proposed a vector form EMD algorithm for geometric models,the plate geometric model and the three-dimensional mesh model were discussed respectively.Our algorithm decomposes a geometric object into sev-eral levels of offsets plus a residual shape,where each offset represents different scale feature of the geometric object and the residual represents the overall shape of the input geometric object.We use a closed discrete curve to represent a two-dimensional shape and utilize the curvature of discrete curve to extract extremum points.Once the extremum points are identified,all the extremum points are connected by a cubic B-spline curve as the extremum envelope.The core of our algorithm is achieving multi-scale decomposition result which is realized by adding two parameters in the process of extraction of ex-tremum points.We apply the algorithm in the fields of denoising,feature editing and feature transfer and verify the effectiveness of the proposed method by comparison with classical methods and coordinate component based EMD algorithm.With regard to the three-dimensional surface model which is topologically home-omorphic to a disk,the extremum points of surface are extracted according to discrete gaussian curvature and the extremum envelope surface is fitted by a uniform knot tensor-product B-spline.In order to fit the extremum envelope surface better,we use the free boundary parameterization method to obtain the plane parameterization results of the model with low distortion.The multi-scale decomposition effect of the model is achieved by controlling the extraction extremum points.We apply the EMD algo-rithm in the field of surface deno(?)sing and feature edgting.Compared with classical methods and mean curvature based EMD algorithm,the effectiveness of our method is verified.