2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

How we got Here? A Methodology to Study the Evolution of Economies

This paper proposes a methodology to analyze the evolution of the economic development of countries. Our approach is based upon the definition of temporal trajectories of countries in a common bidimensional space yielded by a High-Order Singular Value Decomposition (HOSVD). These trajectories are defined with respect to a pre-selected set of macroeconomic indicators and are appropriate for comparison purposes. To show the applicability of the proposed methodology we have used data from the World Bank concerning the economic and financial development of EU-27 over a 14-year span, that goes from 1995 to 2008. Based on this data we group the EU-27 state members according to their economic development, which is indicated by the position of their trajectories on the plane. We further perform individual analyses of the trajectories of Luxembourg, Germany and Portugal, aiming to both detect and interpret trends and changes in these economies. The results show that this methodology is of importance for economic studies, since it can help the design, monitoring and evaluation of specific economic policies, as well as provide an overview of the evolution of the studied economic phenomenon.European Union, HOSVD, International Comparisons, Temporal Trajectories

Empirical mode decomposition-based facial pose estimation inside video sequences

We describe a new pose-estimation algorithm via integration of the strength in both empirical mode decomposition (EMD) and mutual information. While mutual information is exploited to measure the similarity between facial images to estimate poses, EMD is exploited to decompose input facial images into a number of intrinsic mode function (IMF) components, which redistribute the effect of noise, expression changes, and illumination variations as such that, when the input facial image is described by the selected IMF components, all the negative effects can be minimized. Extensive experiments were carried out in comparisons to existing representative techniques, and the results show that the proposed algorithm achieves better pose-estimation performances with robustness to noise corruption, illumination variation, and facial expressions

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

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

The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of AM–FM images

The synchrosqueezing method aims at decomposing 1D functions into superpositions of a small number of “Intrinsic Modes”, supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its reconstruction properties, the synchrosqueezing transform provides a powerful representation of multicomponent signals in the time–frequency plane, together with a reconstruction of each mode. In this paper, a bidimensional version of the synchrosqueezing transform is defined, by considering a well-adapted extension of the concept of analytic signal to images: the monogenic signal. We introduce the concept of “Intrinsic Monogenic Mode”, that is the bidimensional counterpart of the notion of Intrinsic Mode. We also investigate the properties of its associated Monogenic Wavelet Decomposition. This leads to a natural bivariate extension of the Synchrosqueezed Wavelet Transform, for decomposing and processing multicomponent images. Numerical tests validate the effectiveness of the method on synthetic and real images

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

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