Bidimensional empirical mode decomposition for image processing using order-statistics filter based envelope estimation (2009)

Bidimensional empirical mode decomposition (BEMD) method is a relatively new, but potential image processing algorithm. BEMD decomposes an image into multiple hierarchical components known as bidimensional intrinsic mode functions (BIMFs) and a bidimensional residue (BR), based on the local spatial variations or scales of the image. In each iteration of the process, two-dimensional (2D) scattered data surface interpolation is applied to a set of arbitrarily distributed local maxima (minima) points to form the upper (lower) envelope. But, 2D scattered data interpolation methods cause huge computation time and other artifacts in the decomposition. In this dissertation, a novel approach of the BEMD method is proposed to overcome the difficulties of the currently available BEMD approaches. This dissertation suggests a simple, but effective, method of envelope estimation that substitutes the surface interpolation. In this method, order statistics filters are employed to get the upper and lower envelopes, where filter size is derived from the data. The proposed BEMD approach provides extremely fast decomposition compared to other surface interpolation based BEMD (SIBEMD) methods. It also provides various levels of adaptability in the process. Thus, based on the properties of the proposed approach, it is named as a fast and adaptive BEMD (FABEMD). Besides providing extremely fast computation, it removes many decomposition artifacts, otherwise observed in the SIBEMD methods, and makes it practically implementable to the images of any size or resolution. Simulation results with various images using FABEMD and comparison with the results with SIBEMD methods demonstrate the efficacy of this proposed algorithm for image processing. The proposed FABEMD method is significantly different from all other currently existing BEMD methods, and it brings a new insight to this area. 
To further find out the superiority of the FABEMD method over the SIBEMD methods, it is applied for edge detection and noise removal in a simplified manner and compared with the performance of a SIBEMD. However, the proposed edge detection and noise removal approaches of this dissertation utilizing BEMD methods in general, and the FABEMD method in particular, themselves are novel or partly novel. Since the first BIMF provides the highest local spatial variations and/or scales of the image, this BIMF contains all the edge information of an image at the finest scales. Binarization and subsequent morphological operations are applied to the first BIMF to achieve the desired edge map. Because of the properties of FABEMD based decomposition, the edge detection also becomes adaptive, which can result in various edge maps as per chosen parameters and needs. Simulation results with real images using FABEMD based edge detection and comparison with two other standard techniques, namely, Canny and Sobel edge operators, demonstrates the success of the proposed algorithm for edge detection. Additionally, comparison with a SIBEMD based edge detection proves the superiority of the FABEMD over SIBEMD methods. In BEMD based decomposition, the noise is separated into the first or first few BIMFs. Hence, in the proposed noise removal scheme, denoising filters are applied to the noisy BIMFs, and then the BIMFs are combined to get the reconstructed image. This technique provides better noise removal than applying the denoising filters directly to the image. Simulation results again show that the FABEMD performs better than the SIBEMD methods for denoising, using the proposed denoising algorithm. 
Color images are important components in many real life applications. Although currently existing BEMD methods are proposed for gray scale images, there has been no BEMD method for color image analysis. In this dissertation, an approach of the BEMD technique is developed for the first time to incorporate the advantages of BEMD based analysis to color images, employing the FABEMD method. In fact,FABEMD facilitates the extension of the BEMD process for color images in an expedient and usable way, whereas it is difficult to employ/extend the other SIBEMD methods for color images in their current form. The proposed color BEMD (CBEMD) also acts as a major and successful application of the FABEMD method of this dissertation. Simulation results with real images exemplify the potential of the proposed color BEMD (CBEMD) for color image processing.