Fourier Features Research Articles

Stable myoelectric control of a hand prosthesis using non-linear incremental learning

Stable myoelectric control of hand prostheses remains an open problem. The only successful human–machine interface is surface electromyography, typically allowing control of a few degrees of freedom. Machine learning techniques may have the potential to remove these limitations, but their performance is thus far inadequate: myoelectric signals change over time under the influence of various factors, deteriorating control performance. It is therefore necessary, in the standard approach, to regularly retrain a new model from scratch. We hereby propose a non-linear incremental learning method in which occasional updates with a modest amount of novel training data allow continual adaptation to the changes in the signals. In particular, Incremental Ridge Regression and an approximation of the Gaussian Kernel known as Random Fourier Features are combined to predict finger forces from myoelectric signals, both finger-by-finger and grouped in grasping patterns. We show that the approach is effective and practically applicable to this problem by first analyzing its performance while predicting single-finger forces. Surface electromyography and finger forces were collected from 10 intact subjects during four sessions spread over two different days; the results of the analysis show that small incremental updates are indeed effective to maintain a stable level of performance. Subsequently, we employed the same method on-line to teleoperate a humanoid robotic arm equipped with a state-of-the-art commercial prosthetic hand. The subject could reliably grasp, carry and release everyday-life objects, enforcing stable grasping irrespective of the signal changes, hand/arm movements and wrist pronation and supination.

Automatic EEG seizure detection using dual-tree complex wavelet-Fourier features

Epilepsy is one of the most common neurological disorders with 0.8% of the world population. The epilepsy is unpredictable and recurrent, so it is very difficult to treat. In this paper, we propose a new Electroencephalography (EEG) seizure detection method by using the dual-tree complex wavelet (DTCWT) – Fourier features. These features achieve perfect classification rates (100%) for the EEG database from the University of Bonn. These classification rates outperform a number of existing EEG seizure detection methods published in the literature. However, it should be mentioned that several recent works also achieved this perfect classification rate (100%). Our proposed method should be as good as these works since our method only performs the DTCWT transform for up to 5 scales and our method only conducts the FFT to the 4th and 5th scales of the DTCWT decomposition. In addition, we could replace the conventional FFT in our method by sparse FFT so that our method could be even faster.

Nonlinear spectral management: Linearization of the lossless fiber channel

Using the integrable nonlinear Schrödinger equation (NLSE) as a channel model, we describe the application of nonlinear spectral management for effective mitigation of all nonlinear distortions induced by the fiber Kerr effect. Our approach is a modification and substantial development of the so-called "eigenvalue communication" idea first presented in A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993). The key feature of the nonlinear Fourier transform (inverse scattering transform) method is that for the NLSE, any input signal can be decomposed into the so-called scattering data (nonlinear spectrum), which evolve in a trivial manner, similar to the evolution of Fourier components in linear equations. We consider here a practically important weakly nonlinear transmission regime and propose a general method of the effective encoding/modulation of the nonlinear spectrum: The machinery of our approach is based on the recursive Fourier-type integration of the input profile and, thus, can be considered for electronic or all-optical implementations. We also present a novel concept of nonlinear spectral pre-compensation, or in other terms, an effective nonlinear spectral pre-equalization. The proposed general technique is then illustrated through particular analytical results available for the transmission of a segment of the orthogonal frequency division multiplexing (OFDM) formatted pattern, and through WDM input based on Gaussian pulses. Finally, the robustness of the method against the amplifier spontaneous emission is demonstrated, and the general numerical complexity of the nonlinear spectrum usage is discussed.

Small bowel image classification based on Fourier-Zernike moment features and canonical discriminant analysis

In this paper, we propose a novel method for the classification of small bowel images into normal or abnormal class for automatic detection of cancers. We extract the Fourier features from the input small bowel image, and then the Zernike moment features are computed from the Fourier features. We then use the canonical discriminant analysis (CDA) to classify the small bowel images to normal or abnormal class. Experimental results show that the proposed method achieves the highest correct classification rate 100% for this problem. Our method is computationally very efficient. It can be used to automate the classification of capsule endoscopic images and to reduce the cost of interpreting those images that are acquired in clinical setting.

Parallel computing for efficient time‐frequency feature extraction of power quality disturbances

Fast signal processing implementation techniques for detection and classification of power quality (PQ) disturbances are the need of the hour. Hence in this work, a parallel computing approach has been proposed to speed up the feature extraction of PQ signals to facilitate rapid building of classifier models. Considering that the Fourier, the one-dimensional discrete wavelet, the time-time and the Stockwell transforms have been used extensively to extract pertinent time-frequency features from non-stationary and multi-frequency PQ signals, acceleration approaches using data and task parallelism have been employed for parallel implementation of the above time-frequency transforms. In the first approach, data parallelism was applied to the Stockwell transform and the time-time transform-based feature extraction methods separately to alleviate capability problems. Also, data parallelism was applied to Fourier and wavelet-based feature extraction methods independently to alleviate capacity problems. Secondly, a combination of task and data parallelism was applied to speed up S-transform based three-phase sag feature extraction. Experiments were conducted using shared-memory and distributed memory architectures to try out the effectiveness of the proposed parallel approaches. The performances of these parallel implementations were analysed in terms of computational speed and efficiency in comparison with the sequential approach.

Learning with infinitely many features

We propose a principled framework for learning with infinitely many features, situations that are usually induced by continuously parametrized feature extraction methods. Such cases occur for instance when considering Gabor-based features in computer vision problems or when dealing with Fourier features for kernel approximations. We cast the problem as the one of finding a finite subset of features that minimizes a regularized empirical risk. After having analyzed the optimality conditions of such a problem, we propose a simple algorithm which has the flavour of a column-generation technique. We also show that using Fourier-based features, it is possible to perform approximate infinite kernel learning. Our experimental results on several datasets show the benefits of the proposed approach in several situations including texture classification and large-scale kernelized problems (involving about 100 thousand examples).

Sidebands in Fourier transform ion cyclotron resonance mass spectra

Sidebands in mass spectra are an intrinsic feature of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). Appearance of the sidebands there is detrimental for the analytical performance, especially in case of complex mixtures analyzed at high resolution. Yet, the sidebands have a practical potential as well. Specifically, they can be applied for fine tuning of ICR cells and were previously employed to improve mass measurement accuracy for small molecules and atoms in fundamental physics experiments. Moreover, experimental characteristics of sidebands allow evaluating the theory of the ICR signal, which provides the metrological basis in FT-ICR MS. Here, we revisit the sidebands phenomenon in the conventional FT-ICR MS, specifically applied to macromolecules. We extend the previous reports on sidebands by examining the appearance of sidebands as functions of ICR cell trapping potentials, resolution, and number of charges for the first three harmonics of the reduced cyclotron frequency. Next, we develop an analytical model of sidebands that contributes to the existing theory of the ICR signal by showing the origin of sidebands to be the result of the broadband amplitude-phase modulation occurring in the ICR signal. Finally, we evaluate the theory of the ICR signal on the basis of the obtained experimental sidebands. Further progress in the theory of the ICR signal shall outline the way for further improvements in FT-ICR MS performance.

Several Face Images Recognition in Uncontrolled Illumination Variation Images

This paper to study and present a face recognition system under uncontrolled illumination images. It consists of pre-processing method, a hybrid Fourier feature extraction and a score fusion. In the pre-processing stage a face image is transformed in to an illumination-insensitive image, called an “integral normalized gradient image”. The hybrids Fourier feature are extracted from different Fourier domains in different frequency bandwidth. In this paper the multiple Face Models are generated by plural normalized face images that have different eye distances. Finally to combine the scores from multiple complementary classifiers, a log likelihood ratio-based score fusion scheme is applied. This system using the Face recognition Grand Challenge (FRGC) experimental protocols is evaluated. it shows the average verification rate on 2-D face images under various environmental variations such as illumination changes, expression changes, and time elapses.

Static and dynamic features of Fourier transform profilometry: A review

Fringe projection techniques are very popular among the several profilometry methods proposed in literature. One of their main advantages is that most of them require one image of the object to retrieve its surface. From a theoretical point of view these techniques are based on a simple mathematical model which is at the base of the conversion of the measured quantity (usually the phase map of the image of the grid projected onto an object surface) into the height distribution of the object. However, the practical implementation of the system is not an easy task to be achieved. The mathematical models are often a simplification of the reality and it is valid only under some conditions. These discrepancies between the theory and the practice deal to a series of discussions about the quality of the measure of fringe projection techniques. This paper proposes a wide argumentation about the measurement uncertainty and the source of error which is influenced by. After a concise description of the triangulation model and of the basic idea of the system working, the measurement techniques are analyzed both from a static and a dynamic point of view, with a special attention to the uncertainty sources in the two measurement conditions and the possible improvements that may be applied to reduce their influence.

Rotation-Invariant Image and Video Description With Local Binary Pattern Features

In this paper, we propose a novel approach to compute rotation-invariant features from histograms of local noninvariant patterns. We apply this approach to both static and dynamic local binary pattern (LBP) descriptors. For static-texture description, we present LBP histogram Fourier (LBP-HF) features, and for dynamic-texture recognition, we present two rotation-invariant descriptors computed from the LBPs from three orthogonal planes (LBP-TOP) features in the spatiotemporal domain. LBP-HF is a novel rotation-invariant image descriptor computed from discrete Fourier transforms of LBP histograms. The approach can be also generalized to embed any uniform features into this framework, and combining the supplementary information, e.g., sign and magnitude components of the LBP, together can improve the description ability. Moreover, two variants of rotation-invariant descriptors are proposed to the LBP-TOP, which is an effective descriptor for dynamic-texture recognition, as shown by its recent success in different application problems, but it is not rotation invariant. In the experiments, it is shown that the LBP-HF and its extensions outperform noninvariant and earlier versions of the rotation-invariant LBP in the rotation-invariant texture classification. In experiments on two dynamic-texture databases with rotations or view variations, the proposed video features can effectively deal with rotation variations of dynamic textures (DTs). They also are robust with respect to changes in viewpoint, outperforming recent methods proposed for view-invariant recognition of DTs.

High-resolution satellite scene classification using a sparse coding based multiple feature combination

This article presents a new method for high-resolution satellite scene classification. Specifically, we make three main contributions: (1) we introduce the sparse coding method for satellite scene classification; (2) we present local ternary pattern histogram Fourier (LTP-HF) features, an improved rotation invariant texture descriptor based on LTPs; (3) we effectively combine a set of diverse and complementary features to further improve the performance. A two-stage linear support vector machine (SVM) classifier is designed for this purpose. In the first stage, the SVM is used to generate probability images with a scale invariant feature transform (SIFT), LTP-HF and colour histogram features, respectively. The generated probability images with different features are fused in the second stage in order to obtain the final classification results. Experimental results show that the suggested classification method achieves very promising performance.

Shape retrieval using combined Fourier features

Centroid-distance signature is one of the classical shape signatures which are used to derive Fourier descriptors. It has the strong ability of capturing the global features of the shape. However, its ability of characterizing the local shape features is poor. To overcome this limitation, a novel shape signature, perimeter area function (PAF), is proposed in this paper. PAF places all the vertexes of the triangle on the shape boundary. Therefore it can finely capture the local shape boundary information. The Fourier features derived from the proposed PAF are combined with the ones derived from the traditional centroid distance signature for shape retrieval. This hybrid scheme presents an accurate shape description which is more suitable for shape retrieval than the traditional Fourier descriptors. This method is tested on the standard MPEG-7 shape database and the proposed leaf shape database using the standard performance evaluation scheme. All the experimental results indicate that the proposed method outperforms the existing Fourier descriptors and Wavelet Fourier descriptor.

Face Recognition System Using Multiple Face Model of Hybrid Fourier Feature Under Uncontrolled Illumination Variation

The authors present a robust face recognition system for large-scale data sets taken under uncontrolled illumination variations. The proposed face recognition system consists of a novel illumination-insensitive preprocessing method, a hybrid Fourier-based facial feature extraction, and a score fusion scheme. First, in the preprocessing stage, a face image is transformed into an illumination-insensitive image, called an "integral normalized gradient image," by normalizing and integrating the smoothed gradients of a facial image. Then, for feature extraction of complementary classifiers, multiple face models based upon hybrid Fourier features are applied. The hybrid Fourier features are extracted from different Fourier domains in different frequency bandwidths, and then each feature is individually classified by linear discriminant analysis. In addition, multiple face models are generated by plural normalized face images that have different eye distances. Finally, to combine scores from multiple complementary classifiers, a log likelihood ratio-based score fusion scheme is applied. The proposed system using the face recognition grand challenge (FRGC) experimental protocols is evaluated; FRGC is a large available data set. Experimental results on the FRGC version 2.0 data sets have shown that the proposed method shows an average of 81.49% verification rate on 2-D face images under various environmental variations such as illumination changes, expression changes, and time elapses.

An Overview of Infrared Spectroscopy Based on Continuous Wavelet Transform Combined with Machine Learning Algorithms: Application to Chinese Medicines, Plant Classification, and Cancer Diagnosis

Infrared spectroscopy has been a workhorse technique for materials analysis and can result in positively identifying many different types of material. In recent years there have been reports using wavelet analysis and machine learning algorithms to extract features of Fourier transform infrared spectrometry (FTIR). The machine learning algorithms contain back-propagation neural network (BPNN), radial basis function neural network (RBFNN), and support vector machine (SVM). This article reviews the important advances in FTIR analysis employing a continuous wavelet transform (CWT) and machine learning algorithms, especially in the applications of the method for Chinese medicine identification, plant classification, and cancer diagnosis.

Hierarchical Ensemble of Global and Local Classifiers for Face Recognition

In the literature of psychophysics and neurophysiology, many studies have shown that both global and local features are crucial for face representation and recognition. This paper proposes a novel face recognition method which exploits both global and local discriminative features. In this method, global features are extracted from the whole face images by keeping the low-frequency coefficients of Fourier transform, which we believe encodes the holistic facial information, such as facial contour. For local feature extraction, Gabor wavelets are exploited considering their biological relevance. After that, Fisher's linear discriminant (FLD) is separately applied to the global Fourier features and each local patch of Gabor features. Thus, multiple FLD classifiers are obtained, each embodying different facial evidences for face recognition. Finally, all these classifiers are combined to form a hierarchical ensemble classifier. We evaluate the proposed method using two large-scale face databases: FERET and FRGC version 2.0. Experiments show that the results of our method are impressively better than the best known results with the same evaluation protocol.

Automated classification of duodenal imagery in celiac disease using evolved Fourier feature vectors

Feature extraction techniques based on selection of highly discriminant Fourier filters have been developed for an automated classification of magnifying endoscope images with respect to pit patterns of colon lesions. These are applied to duodenal imagery for diagnosis of celiac disease. Features are extracted from the Fourier domain by selecting the most discriminant features using an evolutionary algorithm. Subsequent classification is performed with various standard algorithms (KNN, SVM, Bayes classifier) and combination of several Fourier filters and classifiers which is called multiclassifier. The obtained results are promising, due to a high specificity for the detection of mucosal damage typical of untreated celiac disease.

Binarized eigenphases applied to limited memory face recognition systems

Most of the algorithms proposed for face recognition involve considerable amount of computations and hence they cannot be used on devices constrained with limited memory. In this paper, we propose a novel solution for efficient face recognition problem for the systems that utilize low memory devices. The new technique applies the principal component analysis to the binarized phase spectrum of the Fourier transform of the covariance matrix constructed from the MPEG-7 Fourier Feature Descriptor vectors of the images. The binarization step that is applied to the phases adds many interesting advantages to the system. It will be shown that the proposed technique increases the face recognition rate and at the same time achieves substantial savings in the computational time, when compared to other known systems. Experiments on two independent databases of face images are reported to demonstrate the effectiveness of the proposed technique.

CONTOUR-BASED FEATURE EXTRACTION USING DUAL-TREE COMPLEX WAVELETS

A contour-based feature extraction method is proposed by using the dual-tree complex wavelet transform and the Fourier transform. Features are extracted from the 1D signals r and θ, and hence the processing memory and time are reduced. The approximate shift-invariant property of the dual-tree complex wavelet transform and the Fourier transform guarantee that this method is invariant to translation, rotation and scaling. The method is used to recognize aircrafts from different rotation angles and scaling factors. Experimental results show that it achieves better recognition rates than that which uses only the Fourier features and Granlund's method. Its success is due to the desirable shift invariant property of the dual-tree complex wavelet transform, the translation invariant property of the Fourier spectrum, and our new complete representation of the outer contour of the pattern.

Face recognition based on discriminant fractional Fourier feature extraction

Developed from the conventional Fourier transform, the fractional Fourier transform is a powerful signal analysis and processing technique. In this paper, we apply it to the field of face recognition. By combining it with the discrimination analysis technique, we propose a new face recognition approach. First, we use a two-dimensional separability judgment to select appropriate value of angle parameter for discrete fractional Fourier transform. Second, we present a reformative Fisherface method to extract discriminative features from the preprocessed images and perform the classification using the nearest neighbor classifier. Experimental results on two public face databases indicate that our approach outperforms four representative discrimination methods. It obtains better and robust classification effects.

Principles and applications of GFT projection NMR spectroscopy

The two defining features of G-matrix Fourier transform (GFT) projection NMR spectroscopy are (i) repeated joint sampling of several indirect chemical shift evolution periods of a multidimensional NMR experiment so that transfer amplitudes are generated which are proportional to all possible permutations of cosine and sine modulations of the individual shifts, and (ii) linear combination of the subspectra resulting from such repeated joint sampling in the time or frequency domain which yields edited subspectra containing signals encoding phase-sensitively detected linear combinations of the jointly sampled shifts. This review sketches the underlying principles of GFT NMR and outlines its relation to further developments such as the reconstruction of multidimensional NMR spectra.