Novel optimization-based bidimensional empirical mode decomposition

Despite its rapid advancement in the past two decades, bidimensional empirical mode decomposition (BEMD) still has several limitations in multi-scale feature description of input images. To ameliorate this issue, in this paper we present several optimization-based approaches to BEMD. First, we articulate an improved unconstrained optimization approach to BEMD (IUOA-BEMD). The essential idea is to formulate an optimization model to decompose an input image based on the Delaunay triangulation of its local maxima (minima). Second, we design a scale-guided optimization approach to BEMD (SGO-BEMD) so as to arrive at an improved modal image. SGO-BEMD uses the initial modal image (obtained from the aforementioned proposed IUOA-BEMD) as a necessary guide and can capture much clearer features at various spatial scales of the input image. In addition, an additional edge-preserving property can be obtained with the edge-aware decomposition if an edge-aware scale-guided optimization to BEMD (EASGO-BEMD) is used. The visualization and quantitative results for many artificial amplitude-modulated–frequency-modulated (AM-FM) images and real images have shown that the newly-proposed methods are very competitive with state-of-the-art BEMD methods. Moreover, we further evaluate the performance of BEMD methods according to their applications in image detail enhancement and image contrast & brightness enhancement. It may be noted that image contrast & brightness enhancement represents the first attempt to integrate BEMD with Retinex theory. Collectively, both types of enhancement validate the utility of the novel optimization-based approaches to BEMD proposed herein.