Bidimensional Empirical Mode Decomposition And Its Application In Image Analysis

Image analysis has long been a great challenge in computer vision because of the non-stationarity, nonlinearity and multi-resolution property of two dimensional images. Since image intensities change randomly across the spatial field, and there is no rule for the variation of scale and amplitude, image intensities are generally treated as two dimensional nonlinear, non-stationary signals. For these kinds of signals, the locality and adaptiveness of time-frequency analysis are the most important requirements. However, existing methods such as the Fourier spectral analysis and Wavelet analysis rely on a set of pre-defined basis functions. Therefore, they are not adaptive. How to represent the amplitude and frequency as time-varying functions for nonlinear, non-stationary signals is the primary task for analyzing such signals. The AM-FM Representation of two dimensional images tries to represent images as the sum of a set of locally coherent complex-valued components, from which the local amplitude and instantaneous frequency can be further acquired.This thesis explores the application of Bidimensional Empirical Mode Decomposition (BEMD) on image analysis. The BEMD method is the two dimensional extension of Empirical Mode Decomposition (EMD). It decomposes the original image into a series of AM-FM functions and can further derive the amplitude and frequency as time-varying functions, thus localizing image characteristics.The main contribution of this thesis is on the implementation of BEMD and its application in image analysis. The thesis proposed the implementation of several key algorithms in the BEMD framework. Considering the actual property of natural images, extrema point extraction is realized by using 8-neighbor comparison method. The boundary effect is suppressed using mirror symmetry and the upper and lower envelopes of the original image are calculated using triangle based cubic interpolation. Finally, the sifting process is terminated by carrying the iteration a fixed number of times, thus avoiding over-decomposition. In addition, the thesis also proposed the pre-processing method for image filtering after the implementation of BEMD. In fact, the decomposition result of BEMD can be abstracted as a general purpose image filter. Based on the numerical properties and practical desire, corresponding frequency components can be extracted, thus image filtering is realized.Experiments have shown the sound effectiveness and efficiency of our method. Compared with traditional methods, it is more suitable for two dimensional image analysis and also provides new insight for this field.