平面几何模型的EMD分解算法及其应用

EMD Algorithm of Planar Models and Its Applications

经验模态分解(Empirical mode decomposition,简称EMD)算法是一种处理非线性非平稳信号的时频分析方法.该方法可以自适应地将输入信号分解成若干层本征模函数(Intrinsic mode function,简称IMF)和一层余项函数,通过对IMF的特定操作可以实现信号的滤波和去噪等功能.经典的EMD算法主要针对标量形式的函数信号,对于平面几何图形,EMD则按每一个坐标分量分别处理,其效果往往较差.文章提出一种向量形式的平面几何模型EMD算法,该算法将一个平面几何模型分解成若干层偏置向量和一个残差模型,其中偏置向量表示几何体不同尺度的特征,残差模型表示输入模型的大致形状.通过在极值点的定义中施加特征尺度的限制从而保证每次分解只分离出特定尺度的特征.实验表明,该方法可以有效地实现平面几何模型的分解,并应用在去噪、特征编辑以及特征迁移的领域.通过与经典方法以及标量函数信号EMD算法的比较,文章方法的有效性得到验证.

Empirical mode decomposition(EMD) algorithm is a time-frequency analysis method to process non-linear and non-stationary signals.This method can decompose the input signal into several intrinsic mode functions(IMF) and a residual function adaptively.By operating on the intrinsic mode function,many signal processing operations can be achieved,such as filter design and signal denoising.While the classic EMD algorithm works well for signals of scalar functions,it deals with signals of planar models by separately decomposing each coordinate function of the models,which generally produces inferior results.This paper proposes an EMD analogous algorithm for two dimensional models.The algorithm decomposes a geometric object into several 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.In order to extract features of specific scales,we add scale constraints in the definition of extreme points.Experiments show that the proposed method can effectively decompose the two-dimensional geometric model and apply it in the fields of denoising,feature editing and feature transferring.The effectiveness of the proposed method is verified by comparison with classical methods and scalar function EMD algorithm.