An Optimization Based Empirical Mode Decomposition Scheme for Images

Bidimensional empirical mode decompositions (BEMD) have been developed to decompose any bivariate function or image additively into multiscale components, so-called intrinsic mode functions (IMFs), which are approximately orthogonal to each other with respect to the $\ell_2$ inner product. In this paper, a novel optimization problem is designed to achieve this decomposition which takes into account important features desired of the BEMD. Specifically, we propose a data-adapted iterative method which we call Opt-BEMD which minimizes in each iteration a smoothness functional subject to inequality constraints involving the strictly local extrema of the image. In this way, the method constructs a sparse data-adapted basis for the input function as well as an envelope in a mathematically stringent sense. Moreover, we propose an ensemble version of Opt-BEMD to strengthen its performance when applied to noise-contaminated images or images with only few extrema

Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform

Fringe pattern analysis is the central aspect of numerous optical measurement methods, e.g., interferometry, fringe projection, digital holography, quantitative phase microscopy. Experimental fringe patterns always contain significant features originating from fluctuating environment, optical system and illumination quality, and the sample itself that severely affect analysis outcome. Before the stage of phase retrieval (information decoding) interferogram needs proper filtering, which minimizes the impact of mentioned issues. In this paper we propose fully automatic and adaptive fringe pattern pre-processing technique - improved period guided bidimensional empirical mode decomposition algorithm (iPGBEMD). It is based on our previous work about PGBEMD which eliminated the mode-mixing phenomenon and made the empirical mode decomposition fully adaptive. In present work we overcame key problems of original PGBEMD – we have considerably increased algorithm’s application range and shortened computation time several-fold. We proposed three solutions to the problem of erroneous decomposition for very low fringe amplitude images, which limited original PGBEMD significantly and we have chosen the best one among them after comprehensive analysis. Several acceleration methods were also proposed and merged to ensure the best results. We combined our improved pre-processing algorithm with the Hilbert Spiral Transform to receive complete, consistent, and versatile fringe pattern analysis path. Quality and effectiveness evaluation, in comparison with selected reference methods, is provided using numerical simulations and experimental fringe data

Serial-EMD: Fast Empirical Mode Decomposition Method for Multi-dimensional Signals Based on Serialization

Empirical mode decomposition (EMD) has developed into a prominent tool for adaptive, scale-based signal analysis in various fields like robotics, security and biomedical engineering. Since the dramatic increase in amount of data puts forward higher requirements for the capability of real-time signal analysis, it is difficult for existing EMD and its variants to trade off the growth of data dimension and the speed of signal analysis. In order to decompose multi-dimensional signals at a faster speed, we present a novel signal-serialization method (serial-EMD), which concatenates multi-variate or multi-dimensional signals into a one-dimensional signal and uses various one-dimensional EMD algorithms to decompose it. To verify the effects of the proposed method, synthetic multi-variate time series, artificial 2D images with various textures and real-world facial images are tested. Compared with existing multi-EMD algorithms, the decomposition time becomes significantly reduced. In addition, the results of facial recognition with Intrinsic Mode Functions (IMFs) extracted using our method can achieve a higher accuracy than those obtained by existing multi-EMD algorithms, which demonstrates the superior performance of our method in terms of the quality of IMFs. Furthermore, this method can provide a new perspective to optimize the existing EMD algorithms, that is, transforming the structure of the input signal rather than being constrained by developing envelope computation techniques or signal decomposition methods. In summary, the study suggests that the serial-EMD technique is a highly competitive and fast alternative for multi-dimensional signal analysis.Fil: Zhang, Jin. Nankai University; ChinaFil: Feng, Fan. Nankai University; ChinaFil: Marti Puig, Pere. Central University of Catalonia; EspañaFil: Caiafa, César Federico. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Instituto Argentino de Radioastronomía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto Argentino de Radioastronomía; ArgentinaFil: Sun, Zhe. RIKEN; JapónFil: Duan, Feng. Nankai University; ChinaFil: Sole Casals, Jordi. Central University of Catalonia; Españ

Cycle-Consistent Adversarial Networks and Fast Adaptive Bi-Dimensional Empirical Mode Decomposition for Style Transfer

Recently, research endeavors have shown the potentiality of Cycle-Consistent Adversarial Networks (CycleGAN) in style transfer. In Cycle-Consistent Adversarial Networks, the consistency loss is introduced to measure the difference between the original images and the reconstructed in both directions, forward and backward. In this work, the combination of Cycle-Consistent Adversarial Networks with Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD) is proposed to perform style transfer on images. In the proposed approach the cycle-consistency loss is modified to include the differences between the extracted Intrinsic Mode Functions (BIMFs) images. Instead of an estimation of pixel-to-pixel difference between the produced and input images, the FABEMD is applied and the extracted BIMFs are involved in the computation of the total cycle loss. This method enriches the computation of the total loss in a content-to-content and style-to-style comparison by connecting the spatial information to the frequency components. The experimental results reveal that the proposed method is efficient and produces qualitative results comparable to state-of-the-art methods

Content based Medical Image Retrieval: use of Generalized Gaussian Density to model BEMD's IMF.

In this paper, we address the problem of medical ddiagnosis aid through content based image retrieval methods. We propose to characterize images without extracting local features, by using global information extracted from the image Bidimensional Empirical Mode Decomposition (BEMD). This method decompose image into a set of functions named Intrinsic Mode Functions (IMF) and a residu. The generalized Gaussian density function (GGD) is used to represent the coefficients derived from each IMF, and the Kullback–Leibler Distance (KLD) compute the similarity between GGDs. Retrieval efficiency is given for different databases including a diabetic retinopathy, and a face database. Results are promising: the retrieval efficiency is higher than 85% for some cases

BEMDEC: An Adaptive and Robust Methodology for Digital Image Feature Extraction

The intriguing study of feature extraction, and edge detection in particular, has, as a result of the increased use of imagery, drawn even more attention not just from the field of computer science but also from a variety of scientific fields. However, various challenges surrounding the formulation of feature extraction operator, particularly of edges, which is capable of satisfying the necessary properties of low probability of error (i.e., failure of marking true edges), accuracy, and consistent response to a single edge, continue to persist. Moreover, it should be pointed out that most of the work in the area of feature extraction has been focused on improving many of the existing approaches rather than devising or adopting new ones. In the image processing subfield, where the needs constantly change, we must equally change the way we think. In this digital world where the use of images, for variety of purposes, continues to increase, researchers, if they are serious about addressing the aforementioned limitations, must be able to think outside the box and step away from the usual in order to overcome these challenges. In this dissertation, we propose an adaptive and robust, yet simple, digital image features detection methodology using bidimensional empirical mode decomposition (BEMD), a sifting process that decomposes a signal into its two-dimensional (2D) bidimensional intrinsic mode functions (BIMFs). The method is further extended to detect corners and curves, and as such, dubbed as BEMDEC, indicating its ability to detect edges, corners and curves. In addition to the application of BEMD, a unique combination of a flexible envelope estimation algorithm, stopping criteria and boundary adjustment made the realization of this multi-feature detector possible. Further application of two morphological operators of binarization and thinning adds to the quality of the operator

Edge-preserving Multiscale Image Decomposition based on Local Extrema

We propose a new model for detail that inherently captures oscillations, a key property that distinguishes textures from individual edges. Inspired by techniques in empirical data analysis and morphological image analysis, we use the local extrema of the input image to extract information about oscillations: We define detail as oscillations between local minima and maxima. Building on the key observation that the spatial scale of oscillations are characterized by the density of local extrema, we develop an algorithm for decomposing images into multiple scales of superposed oscillations. Current edge-preserving image decompositions assume image detail to be low contrast variation. Consequently they apply filters that extract features with increasing contrast as successive layers of detail. As a result, they are unable to distinguish between high-contrast, fine-scale features and edges of similar contrast that are to be preserved. We compare our results with existing edge-preserving image decomposition algorithms and demonstrate exciting applications that are made possible by our new notion of detail