EMD Based Smoothing Algorithm Reseach For Digital Curves And Surfaces

Digital geometry signal is nonlinear and non-stationary. Traditional signal analysis tools such as Fourier transform, Wavelet transform can't decompose the geometry signal efficiently. Empirical mode decomposition (EMD) is a new self-adaptive method for non-stationary signal analysis. It decomposes a complex non-stationary signal into several stationary data levels and remained data level to shows the final trend, localizes the time-frequency at the same time. EMD method can also reduce the pollution of singularity signal.In this thesis, a novel method for digital curve and surface smoothing based on EMD is presented. The method for digital curve based on EMD contains simple curve, closed curve and random curve smoothing. The algorithm is composed of following steps: Firstly, parameterized the digital curve into 1D, transform the curve into 1D signal. Secondly, decompose the 1D signal into a collection of intrinsic mode functions (IMF) by using EMD. Thirdly, remove the high frequency IMFs and reconstructing the signal. Finally, mapping the reconstructed signal to 2D and the smoothing curve is obtained; the method for digital surface based on EMD contains regular surface and non- regular surface smoothing is more complex. Regular surface smoothing for image is composed of following steps: Firstly, decomposing the horizontal and vertical signal by using curve EMD. Secondly, mapping the reconstructed signal into 2D and the smoothing surface is obtained. It dose not only reduce the complexity but also gain excellent result; non-regular surface smoothing namely free scanning surface, we use Delaunay triangulation to fit the envelope surface and get the average value, then remove the high frequency IMFs and reconstructing the signal.Experiments show that good results are obtained by using the smoothing method. We get a specific application in the shoe last surface reconstruction, 3D-restrucion on Medical Image and foot modeling and get good results.