Preface On the Semilocal Convergence of Newton's Method Under Unifying Conditions Inequalities and Fixed Points in Menger Convex Metric Spaces Applications of the Perov's Fixed Point Theorem to Delay Integro-Differential Equations On Vector Equilibrium Problems with Multifunctions Fixed Points in Generalised Metric Spaces and the Stability of a Cubic Functional Equation Continuous Selection and Coincidence Theorems on Product G-Convex Space Sensitivity Analysis of Solution Set for a New Class of Generalised Implicit Quasi-Variational Inclusions Fixed Points in Probabilistic-Quasi-Metric Spaces Common Fixed Point Theorems for Condensed Mappings The Strongly Convergence Theorems of Fixed Points for Local Strictly F-Pseudocontractive On Generalised Non-linear Variational Inequalities A Note on a Paper of Hadic and Pap The Ishiwaka and Mann Iteration Methods On Certain Applications of Leray-Schauder Alternate Remarks on Concepts of Generalised Convex Spaces Generic Existence and Non-Existence of Approximate Fixed Points General System of Relaxed g-?-r-Pseudococoercive Non-linear Variational Inequalities and Projection Methods Three-Step Iteration Methods with Errors for Non-expansive Mappings in Uniformly Convex Banach Spaces On Nonnegative Linear Composite Games of NTU-Game Probabilistic Contractor and Non-linear Operator Equations with Set-Valued Operator in Probabilistic Normed Spaces Index.

Fixed Point Theory and Applications

This paper presents the first attempt at fusing data from inertial and vision depth sensors within the framework of a hidden Markov model for the application of hand gesture recognition. The data fusion approach introduced in this paper is general purpose in the sense that it can be used for recognition of various body movements. It is shown that the fusion of data from the vision depth and inertial sensors act in a complementary manner leading to a more robust recognition outcome compared with the situations when each sensor is used individually on its own. The obtained recognition rates for the single hand gestures in the Microsoft MSR data set indicate that our fusion approach provides improved recognition in real-time and under realistic conditions.

Fusion of Inertial and Depth Sensor Data for Robust Hand Gesture Recognition

Scene texts contain rich semantic information which may be used in many vision-based applications, and consequently detecting and recognizing scene texts have received increasing attention in recent years. In this paper, we first introduce the history and progress of scene text detection and recognition, and classify conventional methods in detail and point out their advantages as well as disadvantages. After that, we study these methods and illustrate the corresponding key issues and techniques, including loss function, multi-orientation, language model and sequence labeling. Finally, we describe commonly used benchmark datasets and evaluation protocols, based on which the performance of representative scene text detection and recognition methods are analyzed and compared.

Review of Scene Text Detection and Recognition

Vision-based unstructured road following is a challenging task due to the nature of the scene. This paper describes a novel algorithm to improve the accuracy and robustness of vanishing point estimation with very low computational cost. The novelties of this paper are three aspects: 1) We use joint activities of four Gabor filters and confidence measure for speeding up the process of texture orientation estimation. 2) Misidentification chances and computational complexity of the algorithm are reduced by using a particle filter. It limits vanishing point search range and reduces the number of pixels to be voted. The algorithm combines the peakedness measure of vote accumulator space with the displacements of moving average of observations to regulate the distribution of vanishing point candidates. 3) Attributed to the design of a noise-insensitive observation model, the proposed system still has high detection accuracy even when less than 60 sparsely distributed vanishing point candidates are used for voting as the influence introduced by the stochastic measurement noise of vote function and the sparsity of the vanishing point candidates is reduced. The method has been implemented and tested over 20 000 video frames. Experimental results demonstrate that the algorithm achieves better performance than some state-of-the-art texture-based vanishing point detection methods in terms of detection accuracy and speed.

Fast and Robust Vanishing Point Detection for Unstructured Road Following

In order to track the moving objects in long range against occlusion, interruption, and background clutter, this paper proposes a unified approach for global trajectory analysis. Instead of the traditional frame-by-frame tracking, our method recovers target trajectories based on a short sequence of video frames, e.g. $15$ frames. We initially calculate a foreground map at each frame, as obtained from a state-of-the-art background model. An attribute graph is then extracted from the foreground map, where the graph vertices are image primitives represented by the composite features. With this graph representation, we pose trajectory analysis as a joint task of spatial graph partitioning and temporal graph matching. The task can be formulated by maximizing a posteriori under the Bayesian framework, in which we integrate the spatio-temporal contexts and the appearance models. The probabilistic inference is achieved by a data-driven Markov Chain Monte Carlo (MCMC) algorithm. Given a peroid of observed frames, the algorithm simulates a ergodic and aperiodic Markov Chain, and it visits a sequence of solution states in the joint space of spatial graph partitioning and temporal graph matching. In the experiments, our method is tested on several challenging videos from the public datasets of visual surveillance, and it outperforms the state-of-the-art methods.

Integrating Graph Partitioning and Matching for Trajectory Analysis in Video Surveillance

In this letter, we extend the first-order Markov chain model commonly used in visual tracking and present a novel framework of visual tracking using high-order Monte Carlo Markov chain By using graphical models to obtain conditional independence properties, we derive a general expression for the posterior density function of an m th-order hidden Markov model We subsequently use Sequential Importance Sampling (SIS) to estimate the posterior density and obtain the high-order particle filtering algorithm for visual object tracking Experimental results demonstrate that the performance of our proposed algorithm is superior to traditional first-order particle filtering (ie, particle filtering derived based on first-order Markov chain)

Visual Tracking Using High-Order Particle Filtering

In this paper, we develop a novel solution for particle filtering on general graphs. We provide an exact solution for particle filtering on directed cycle-free graphs. The proposed approach relies on a partial-order relation in an antichain decomposition that forms a high-order Markov chain over the partitioned graph. We subsequently derive a closed-form sequential updating scheme for conditional density propagation using particle filtering on directed cycle-free graphs. We also provide an approximate solution for particle filtering on general graphs by splitting graphs with cycles into multiple directed cycle-free subgraphs. We then use the sequential updating scheme by alternating among the directed cycle-free subgraphs to obtain an estimate of the density propagation. We rely on the proposed method for particle filtering on general graphs for two video tracking applications: 1) object tracking using high-order Markov chains; and 2) distributed multiple object tracking based on multi-object graphical interaction models. Experimental results demonstrate the improved performance of the proposed approach to particle filtering on graphs compared with existing methods for video tracking.

Video Tracking Based on Sequential Particle Filtering on Graphs

Many important problems in statistical signal processing can be formulated as function estimation from randomly scattered sensors in a multidimensional space, e.g., image reconstruction from photon-limited images and field estimation from scattered sensors. We present a novel approach to the study of signal reconstruction from random samples in a multidimensional space. In particular, we study a classical iterative reconstruction method and demonstrate that it forms a sequence of unbiased estimates for band-limited signals, which converge to the true function in the mean-square sense. We subsequently rely on the iterative estimation method for multidimensional image reconstruction and field estimation from sensors scattered according to a multidimensional Poisson and uniform distribution. Computer simulation experiments are used to demonstrate the efficiency of the iterative estimation method in image reconstruction and field estimation from randomly scattered sensors.

Image Reconstruction and Multidimensional Field Estimation From Randomly Scattered Sensors

In this paper, we develop novel solutions for particle filtering on graphs. An exact solution of particle filtering for conditional density propagation on directed cycle-free graphs is performed by a sequential updating scheme in a predetermined order. We also provide an approximate solution for particle filtering on general graphs by splitting the graphs with cycles into multiple directed cycle-free subgraphs. We utilize the proposed solution for distributed multiple object tracking. Experimental results show the improved performance of our method compared with existing methods for multiple object tracking.

Sequential particle filtering for conditional density propagation on graphs

This paper presents a novel approach to particle filtering which minimizes the total tracking distortion by considering dynamic variance of proposal density and optimal number of particles for each frame. Traditionally, particle filters use fixed variance of proposal density and fixed number of particles per frame. We propose a tracking distortion measurement and use rate distortion theory to obtain the optimal memory size and particle number allocation equations under different two constraints. We subsequently propose the dynamic proposal variance and optimal particle number allocation algorithm for video tracking systems. Simulation results show the improved performance of our proposed algorithm in comparison to traditional particle filters. To the best of our knowledge, our approach is the first to consider variant numbers of particles for each frame.

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Papers

Visual Tracking Using High-Order Particle Filtering

Video Tracking Based on Sequential Particle Filtering on Graphs

Image Reconstruction and Multidimensional Field Estimation From Randomly Scattered Sensors

Sequential particle filtering for conditional density propagation on graphs

Adaptive Particle-Distortion Tradeoff Control in Particle Filtering for Video Tracking