Automated Real-time Anomaly Detection in Human Trajectories using Sequence to Sequence Networks

Detection of anomalous trajectories is an important problem with potential applications to various domains, such as video surveillance, risk assessment, vessel monitoring and high-energy physics. Modeling the distribution of trajectories with statistical approaches has been a challenging task due to the fact that such time series are usually non stationary and highly dimensional. However, modern machine learning techniques provide robust approaches for data-driven modeling and critical information extraction. In this paper, we propose a Sequence to Sequence architecture for real-time detection of anomalies in human trajectories, in the context of risk-based security. Our detection scheme is tested on a synthetic dataset of diverse and realistic trajectories generated by the ISL iCrowd simulator. The experimental results indicate that our scheme accurately detects motion patterns that deviate from normal behaviors and is promising for future real-world applications.Comment: AVSS 201

The Sylvester Resultant Matrix and Image Deblurring

This paper describes the application of the Sylvester resultant matrix to image deblurring. In particular, an image is represented as a bivariate polynomial and it is shown that operations on polynomials, specifically greatest common divisor (GCD) computations and polynomial divisions, enable the point spread function to be calculated and an image to be deblurred. The GCD computations are performed using the Sylvester resultant matrix, which is a structured matrix, and thus a structure-preserving matrix method is used to obtain a deblurred image. Examples of blurred and deblurred images are presented, and the results are compared with the deblurred images obtained from other methods

Computer Graphics Techniques in Military Applications

The determination of intersection points of plane curves is a problem of Computer Graphics with many applications in Applied Mathematics, Numerical Analysis and many other scientific fields. More precisely, in military applications, the trajectories of two flying objects such as missiles, aircrafts etc, can be interpreted by two plane curves. Our scope is to find the intersection points of the given curves. The number of floating point operations (flops) of many classical methods is not satisfactory, since they demand over O(n 4) operations. Conversely, many algorithms that are fast enough, have serious problems with their numerical stability. The main objective here is to develop fast and stable algorithms computing the intersection points of plane curves. The error analysis and the computation of complexity of all the proposed methods are analysed and demonstrated through various examples. © 2012, Springer Science+Business Media New York

Effective Descriptors for Human Action Retrieval from 3D Mesh Sequences

Two novel methods for fully unsupervised human action retrieval using 3D mesh sequences are presented. The first achieves high accuracy but is suitable for sequences consisting of clean meshes, such as artificial sequences or highly post-processed real sequences, while the second one is robust and suitable for noisy meshes, such as those that often result from unprocessed scanning or 3D surface reconstruction errors. The first method uses a spatio-temporal descriptor based on the trajectories of 6 salient points of the human body (i.e. the centroid, the top of the head and the ends of the two upper and two lower limbs) from which a set of kinematic features are extracted. The resulting features are transformed using the wavelet transformation in different scales and a set of statistics are used to obtain the descriptor. An important characteristic of this descriptor is that its length is constant independent of the number of frames in the sequence. The second descriptor consists of two complementary sub-descriptors, one based on the trajectory of the centroid of the human body across frames and the other based on the Hybrid static shape descriptor adapted for mesh sequences. The robustness of the second descriptor derives from the robustness involved in extracting the centroid and the Hybrid sub-descriptors. Performance figures on publicly available real and artificial datasets demonstrate our accuracy and robustness claims and in most cases the results outperform the state-of-the-art. © 2019 World Scientific Publishing Company

Survey of automated multiple sclerosis lesion segmentation techniques on magnetic resonance imaging

Multiple sclerosis (MS) is a chronic disease. It affects the central nervous system and its clinical manifestation can variate. Magnetic Resonance Imaging (MRI) is often used to detect, characterize and quantify MS lesions in the brain, due to the detailed structural information that it can provide. Manual detection and measurement of MS lesions in MRI data is time-consuming, subjective and prone to errors. Therefore, multiple automated methodologies for MRI-based MS lesion segmentation have been proposed. Here, a review of the state-of-the-art of automatic methods available in the literature is presented. The current survey provides a categorization of the methodologies in existence in terms of their input data handling, their main strategy of segmentation and their type of supervision. The strengths and weaknesses of each category are analyzed and explicitly discussed. The positive and negative aspects of the methods are highlighted, pointing out the future trends and, thus, leading to possible promising directions for future research. In addition, a further clustering of the methods, based on the databases used for their evaluation, is provided. The aforementioned clustering achieves a reliable comparison among methods evaluated on the same databases. Despite the large number of methods that have emerged in the field, there is as yet no commonly accepted methodology that has been established in clinical practice. Future challenges such as the simultaneous exploitation of more sophisticated MRI protocols and the hybridization of the most promising methods are expected to further improve the performance of the segmentation

A hybrid method for computing the intersection and tangency points of plane curves

In this paper we present a symbolic-numeric (hybrid) method for computing the intersection and tangency points of given plane curves. The whole procedure involves three phases: (i) implicitization, (ii) root specification, and (iii) inversion. For each one of these phases we propose an appropriate algorithm fully documented regarding its complexity and stability. A comparison with other existing methods is also provided. All the proposed methods are illustrated through examples. © 2012 Elsevier Inc. All rights reserved