The art of fitting p-mode spectra: Part II. Leakage and noise covariance matrices

In Part I we have developed a theory for fitting p-mode Fourier spectra assuming that these spectra have a multi-normal distribution. We showed, using Monte-Carlo simulations, how one can obtain p-mode parameters using 'Maximum Likelihood Estimators'. In this article, hereafter Part II, we show how to use the theory developed in Part I for fitting real data. We introduce 4 new diagnostics in helioseismology: the $(m,\nu)$ echelle diagramme, the cross echelle diagramme, the inter echelle diagramme, and the ratio cross spectrum. These diagnostics are extremely powerful to visualize and understand the covariance matrices of the Fourier spectra, and also to find bugs in the data analysis code. These diagrammes can also be used to derive quantitative information on the mode leakage and noise covariance matrices. Numerous examples using the LOI/SOHO and GONG data are given.Comment: 17 pages with tex and ps files, submitted to A&A, [email protected]

The art of fitting p-mode spectra: Part I. Maximum Likelihood Estimation

In this article we present our state of the art of fitting helioseismic p-mode spectra. We give a step by step recipe for fitting the spectra: statistics of the spectra both for spatially unresolved and resolved data, the use of Maximum Likelihood estimates, the statistics of the p-mode parameters, the use of Monte-Carlo simulation and the significance of fitted parameters. The recipe is applied to synthetic low-resolution data, similar to those of the LOI, using Monte-Carlo simulations. For such spatially resolved data, the statistics of the Fourier spectrum is assumed to be a multi-normal distribution; the statistics of the power spectrum is \emph{not} a $\chi^{2}$ with 2 degrees of freedom. Results for $l=1$ shows that all parameters describing the p modes can be obtained without bias and with minimum variance provided that the leakage matrix is known. Systematic errors due to an imperfect knowledge of the leakage matrix are derived for all the p-mode parameters.Comment: 13 pages, ps file gzipped. Submitted to A&

Gait recognition in the wild using shadow silhouettes

Gait recognition systems allow identification of users relying on features acquired from their body movement while walking. This paper discusses the main factors affecting the gait features that can be acquired from a 2D video sequence, proposing a taxonomy to classify them across four dimensions. It also explores the possibility of obtaining users’ gait features from the shadow silhouettes by proposing a novel gait recognition system. The system includes novel methods for: (i) shadow segmentation, (ii) walking direction identification, and (iii) shadow silhouette rectification. The shadow segmentation is performed by fitting a line through the feet positions of the user obtained from the gait texture image (GTI). The direction of the fitted line is then used to identify the walking direction of the user. Finally, the shadow silhouettes thus obtained are rectified to compensate for the distortions and deformations resulting from the acquisition setup, using the proposed four-point correspondence method. The paper additionally presents a new database, consisting of 21 users moving along two walking directions, to test the proposed gait recognition system. Results show that the performance of the proposed system is equivalent to that of the state-of-the-art in a constrained setting, but performing equivalently well in the wild, where most state-of-the-art methods fail. The results also highlight the advantages of using rectified shadow silhouettes over body silhouettes under certain conditions.info:eu-repo/semantics/acceptedVersio

View-invariant gait recognition exploiting spatio-temporal information and a dissimilarity metric

In gait recognition, when subjects do not follow a known walking trajectory, the comparison against a database may be rendered impossible. Some proposed solutions rely on learning and mapping the appearance of silhouettes along various views, with some limitations caused for instance by appearance changes (e.g. coats or bags). The present paper discusses this problem and proposes a novel solution for automatic viewing angle identification, using minimal information computed from the walking person silhouettes, while being robust against appearance changes. The proposed method is more efficient and provides improved results when compared to the available alternatives. Moreover, unlike most state-of-the- art methods, it does not require a training stage. The paper also discusses the use of a dissimilarity metric for the recognition stage. Dissimilarity metrics have shown interesting results in several recognition systems. This paper also attests the strength of a dissimilarity-based approach for gait recognition.info:eu-repo/semantics/acceptedVersio

View-invariant gait recognition system using a gait energy image decomposition method

Gait recognition systems can capture biometrical information from a distance and without the user's active cooperation, making them suitable for surveillance environments. However, there are two challenges for gait recognition that need to be solved, namely when: (i) the walking direction is unknown and/or (ii) the subject's appearance changes significantly due to different clothes being worn or items being carried. This study discusses the problem of gait recognition in unconstrained environments and proposes a new system to tackle recognition when facing the two listed challenges. The system automatically identifies the walking direction using a perceptual hash (PHash) computed over the leg region of the gait energy image (GEI) and then compares it against the PHash values of different walking directions stored in the database. Robustness against appearance changes are obtained by decomposing the GEI into sections and selecting those sections unaltered by appearance changes for comparison against a database containing GEI sections for the identified walking direction. The proposed recognition method then recognises the user using a majority decision voting. The proposed view-invariant gait recognition system is computationally inexpensive and outperforms the state-of-the-art in terms of recognition performance.info:eu-repo/semantics/acceptedVersio

Using transfer learning for classification of gait pathologies

Different diseases can affect an individual’s gait in different ways and, therefore, gait analysis can provide important insights into an individual’s health and well-being. Currently, most systems that perform gait analysis using 2D video are limited to simple binary classification of gait as being either normal or impaired. While some systems do perform gait classification across different pathologies, the reported results still have a considerable margin for improvement. This paper presents a novel system that performs classification of gait across different pathologies, with considerably improved results. The system computes the walking individual’s silhouettes, which are computed from a 2D video sequence, and combines them into a representation known as the gait energy image (GEI), which provides robustness against silhouette segmentation errors. In this work, instead of using a set of handcrafted gait features, feature extraction is done using the VGG-19 convolutional neural network. The network is fine-tuned to automatically extract the features that best represent gait pathologies, using transfer learning. The use of transfer learning improves the classification accuracy while avoiding the need of a very large training set, as the network is pre-trained for generic image description, which also contributes to a better generalization when tested across different datasets. The proposed system performs the final classification using linear discriminant analysis (LDA). Obtained results show that the proposed system outperforms the state-of-the-art, achieving a classification accuracy of 95% on a dataset containing gait sequences affected by diplegia, hemiplegia, neuropathy and Parkinson’s disease, along with normal gait sequences.info:eu-repo/semantics/acceptedVersio

NIR Luminosity Function of Galaxies in Close Major-Merger Pairs and Mass Dependence of Merger Rate

A sample of close major-merger pairs (projected separation ${\rm 5 \leq r \leq 20 h^{-1}}$ kpc, ${\rm K_s}$ band magnitude difference $\delta {\rm K_s} \leq 1$ mag) is selected from the matched 2MASS-2dFGRS catalog of Cole et al. (2001). The pair primaries are brighter than ${\rm K_s} = 12.5$ mag. After corrections for various biases, the comparison between counts in the paired galaxy sample and counts in the parent sample shows that for the local `M* galaxies' sampled by flux limited surveys, the fraction of galaxies in the close major-merger pairs is 1.70$\pm 0.32$. Using 38 paired galaxies in the sample, a ${\rm K_s}$ band luminosity function (LF) is calculated. This is the first unbiased LF for a sample of objectively defined interacting/merging galaxies in the local universe, while all previously determined LFs of paired galaxies are biased by mistreating paired galaxies as singles. A stellar mass function (MF) is translated from the LF. Compared to the LF/MF of 2MASS galaxies, a differential pair fraction function is derived. The results suggest a trend in the sense that less massive galaxies may have lower chance to be involved in close major-merger pairs than more massive galaxies. The algorithm presented in this paper can be easily applied to much larger samples of 2MASS galaxies with redshifts in near future.Comment: Accepted by ApJL, 16 pages, 2 figure

Sparse error gait image: a new representation for gait recognition

The performance of a gait recognition system is very much related to the usage of efficient feature representation and recognition modules. The first extracts features from an input image sequence to represent a user's distinctive gait pattern. The recognition module then compares the features of a probe user with those registered in the gallery database. This paper presents a novel gait feature representation, called Sparse Error Gait Image (SEGI), derived from the application of Robust Principal Component Analysis (RPCA) to Gait Energy Images (GEI). GEIs obtained from the same user at different instants always present some differences. Applying RPCA results in low-rank and sparse error components, the former capturing the commonalities and encompassing the small differences between input GEIs, while the larger differences are captured by the sparse error component. The proposed SEGI representation exploits the latter for recognition purposes. This paper also proposes two simple approaches for the recognition module, to exploit the SEGI, based on the computation of a Euclidean norm or the Euclidean distance. Using these simple recognition methods and the proposed SEGI representation gait recognition, results equivalent to the state-of-the-art are obtained