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

A new view of nonlinear water waves: the Hilbert spectrum

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes

A scale-space approach with wavelets to singularity estimation

This paper is concerned with the problem of determining the typical features of a curve when it is observed with noise. It has been shown that one can characterize the Lipschitz singularities of a signal by following the propagation across scales of the modulus maxima of its continuous wavelet transform. A nonparametric approach, based on appropriate thresholding of the empirical wavelet coefficients, is proposed to estimate the wavelet maxima of a signal observed with noise at various scales. In order to identify the singularities of the unknown signal, we introduce a new tool, "the structural intensity", that computes the "density" of the location of the modulus maxima of a wavelet representation along various scales. This approach is shown to be an effective technique for detecting the significant singularities of a signal corrupted by noise and for removing spurious estimates. The asymptotic properties of the resulting estimators are studied and illustrated by simulations. An application to a real data set is also proposed

Feature extraction using extrema sampling of discrete derivatives for spike sorting in implantable upper-limb neural prostheses

Next generation neural interfaces for upper-limb (and other) prostheses aim to develop implantable interfaces for one or more nerves, each interface having many neural signal channels that work reliably in the stump without harming the nerves. To achieve real-time multi-channel processing it is important to integrate spike sorting on-chip to overcome limitations in transmission bandwidth. This requires computationally efficient algorithms for feature extraction and clustering suitable for low-power hardware implementation. This paper describes a new feature extraction method for real-time spike sorting based on extrema analysis (namely positive peaks and negative peaks) of spike shapes and their discrete derivatives at different frequency bands. Employing simulation across different datasets, the accuracy and computational complexity of the proposed method are assessed and compared with other methods. The average classification accuracy of the proposed method in conjunction with online sorting (O-Sort) is 91.6%, outperforming all the other methods tested with the O-Sort clustering algorithm. The proposed method offers a better tradeoff between classification error and computational complexity, making it a particularly strong choice for on-chip spike sorting

Multi-Oriented Multi-Resolution Edge Detection

In order to build an edge detector that provides information on the degree of importance spatial features represent in the visual field, I used the wavelet transform applied to two-dimensional signals and performed a multi-resolution multi-oriented edge detection. The wavelets are functions well-localized in spatial domain and in frequency domain. Thus the wavelet decomposition of a signal or an image provides outputs in which you can still extract spatial features and not only frequency components. In order to detect edges the wavelet I chose is the first derivative of a smoothing function. I decompose the images as many times as I have directions of detection. I decided to work for the moment on the X-direction and the Y-direction only. Each step of the decomposition corresponds to a different scale. I use a discrete scale s = 2j (dyadic wavelet) and a finite number of decomposed images. Instead of scaling the filters at each step I sample the image by 2 (gain in processing time). Then, I extract the extrema, track and link them from the coarsest scale to the finest one. I build a symbolic image in which the edge-pixels are not only localized but labelled too, according to the number of appearances in the different scales and according to the contrast range of the edge. Without any arbitrary threshold I can subsequently classify the edges according to their physical properties in the scene and their degree of importance. This process is subsequently intended to be part of more general perceptual learning procedures. The context should be: none or as little as possible a priori knowledge, and the ultimate goal is to integrate this detector in a feedback system dealing with color information, texture and smooth surfaces extraction. Then decisions must be taken on symbolic levels in order to make new interpretation or even new edge detection on ambiguous areas of the visual field

Facial Emotion Recognition Based on Empirical Mode Decomposition and Discrete Wavelet Transform Analysis

This paper presents a new framework of using empirical mode decomposition (EMD) and discrete wavelet transform (DWT) with an application for facial emotion recognition. EMD is a multi-resolution technique used to decompose any complicated signal into a small set of intrinsic mode functions (IMFs) based on sifting process. In this framework, the EMD was applied on facial images to extract the informative features by decomposing the image into a set of IMFs and residue. The selected IMFs was then subjected to DWT in which it decomposes the instantaneous frequency of the IMFs into four sub band. The approximate coefficients (cA1) at first level decomposition are extracted and used as significant features to recognize the facial emotion. Since there are a large number of coefficients, hence the principal component analysis (PCA) is applied to the extracted features. The k-nearest neighbor classifier is adopted as a classifier to classify seven facial emotions (anger, disgust, fear, happiness, neutral, sadness and surprise). To evaluate the effectiveness of the proposed method, the JAFFE database has been employed. Based on the results obtained, the proposed method demonstrates the recognition rate of 80.28%, thus it is converging

An Intelligent Multi-Resolutional and Rotational Invariant Texture Descriptor for Image Retrieval Systems

To find out the identical or comparable images from the large rotated databases with higher retrieval accuracy and lesser time is the challenging task in Content based Image Retrieval systems (CBIR). Considering this problem, an intelligent and efficient technique is proposed for texture based images. In this method, firstly a new joint feature vector is created which inherits the properties of Local binary pattern (LBP) which has steadiness regarding changes in illumination and rotation and discrete wavelet transform (DWT) which is multi-resolutional and multi-oriented along with higher directionality. Secondly, after the creation of hybrid feature vector, to increase the accuracy of the system, classifiers are employed on the combination of LBP and DWT. The performance of two machine learning classifiers is proposed here which are Support Vector Machine (SVM) and Extreme learning machine (ELM). Both proposed methods P1 (LBP+DWT+SVM) and P2 (LBP+DWT+ELM) are tested on rotated Brodatz dataset consisting of 1456 texture images and MIT VisTex dataset of 640 images. In both experiments the results of both the proposed methods are much better than simple combination of DWT +LBP and much other state of art methods in terms of precision and accuracy when different number of images is retrieved.  But the results obtained by ELM algorithm shows some more improvement than SVM. Such as when top 25 images are retrieved then in case of Brodatz database the precision is up to 94% and for MIT VisTex database its value is up to 96% with ELM classifier which is very much superior to other existing texture retrieval methods