Abstract
Empirical mode decomposition (EMD) is a fully data-driven technique designed for multi-scale decomposition of signals into their natural scale components, called intrinsic mode functions (IMFs). When EMD is directly applied to perform fusion of multivariate data from multiple and heterogeneous sources, the problem of uniqueness, that is, different numbers of decomposition levels for different sources, is likely to occur, due to the empirical nature of EMD. Although the multivariate EMD (MEMD) has been proposed for temporal data, which employs real-valued projections along multiple directions on a unit hypersphere in the $n$ -dimensional space to calculate the envelope and the local mean of multivariate signals, in order to guarantee the uniqueness of the scales, its direct usefulness in 2D multi-scale image fusion is still limited, due to its inability to maintain the spatial information. To address this issue, we propose a novel bidimensional MEMD (BMEMD) which directly projects a bidimensional multivariate signal, which is composed of multiple images, on the unit hypersphere in the $n$ -dimensional space. This is achieved via real-valued surface projections and the mean surface is estimated by interpolating the multivariate scatter data so as to extract common spatio-temporal scales across multiple images. Case studies involving texture analysis and multi-focus image fusion are presented to demonstrate the effectiveness of the proposed method.
Highlights
Image fusion is a process of gathering salient features from multiple images to produce a single ‘‘fused’’ image, which is especially important in situations where optical cameras, due to the limited depth of focus, cannot be focused simultaneously on all objects at different distances to gain a clear image [1]
We propose a bidimensional multivariate Empirical mode decomposition (EMD) (BMEMD) method, which possesses both the capability of multivariate EMD (MEMD) to address the problems of uniqueness and mode-mixing and the 2D processing nature of bidimensional EMD (BEMD), by directly projecting a bidimensional multivariate signal, e.g., composed of multiple images, on the unit hypersphere in the multidimensional space via novel real-valued surface projections and estimating the mean surface by interpolating the multivariate scatter data to extract intrinsic mode functions (IMFs) with matched scales across data channels
ORIGINAL MEMD The key issue to implement EMD is the computation of local mean of the original signal, a step which critically depends on finding local maxima and minima
Summary
Image fusion is a process of gathering salient features from multiple images to produce a single ‘‘fused’’ image, which is especially important in situations where optical cameras, due to the limited depth of focus, cannot be focused simultaneously on all objects at different distances to gain a clear image [1]. Multivariate extensions of EMD based data fusion schemes aim to address the problem of uniqueness within the original EMD by considering a multichannel signal as a whole and using multiple real-valued projections to find the local mean of the original signal, a key issue to find physically meaningful IMFs [16]–[20] This is important, given that univariate EMD processes multichannel signals componentwise, it cannot guarantee that decompositions of different data sources are matched, either in number or properties of local scales, making a multi-scale comparison often difficult. Simulations involving texture analysis and multi-focus image fusion demonstrate the effectiveness of the proposed method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
