Recurrence plot statistics and the effect of embedding

Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot. A single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots. If the correlation sum scales exponentially with embedding dimension, we show that these statistics are determined entirely by the exponent of the exponential. This explains the results of Iwanski and Bradley (Chaos 8 [1998] 861-871) who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low-dimensional systems. We also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots. This allows time-localized contributions to mutual information to be visualized. This technique is demonstrated using geomagnetic index data; we show that the AU and AL geomagnetic indices share half their information, and find the timescale on which mutual features appear

Globally-Coordinated Locally-Linear Modeling of Multi-Dimensional Data

This thesis considers the problem of modeling and analysis of continuous, locally-linear, multi-dimensional spatio-temporal data. Our work extends the previously reported theoretical work on the global coordination model to temporal analysis of continuous, multi-dimensional data. We have developed algorithms for time-varying data analysis and used them in full-scale, real-world applications. The applications demonstrated in this thesis include tracking, synthesis, recognitions and retrieval of dynamic objects based on their shape, appearance and motion. The proposed approach in this thesis has advantages over existing approaches to analyzing complex spatio-temporal data. Experiments show that the new modeling features of our approach improve the performance of existing approaches in many applications. In object tracking, our approach is the first one to track nonlinear appearance variations by using low-dimensional representation of the appearance change in globally-coordinated linear subspaces. In dynamic texture synthesis, we are able to model non-stationary dynamic textures, which cannot be handled by any of the existing approaches. In human motion synthesis, we show that realistic synthesis can be performed without using specific transition points, or key frames

Real-time Immersive human-computer interaction based on tracking and recognition of dynamic hand gestures

With fast developing and ever growing use of computer based technologies, human-computer interaction (HCI) plays an increasingly pivotal role. In virtual reality (VR), HCI technologies provide not only a better understanding of three-dimensional shapes and spaces, but also sensory immersion and physical interaction. With the hand based HCI being a key HCI modality for object manipulation and gesture based communication, challenges are presented to provide users a natural, intuitive, effortless, precise, and real-time method for HCI based on dynamic hand gestures, due to the complexity of hand postures formed by multiple joints with high degrees-of-freedom, the speed of hand movements with highly variable trajectories and rapid direction changes, and the precision required for interaction between hands and objects in the virtual world. Presented in this thesis is the design and development of a novel real-time HCI system based on a unique combination of a pair of data gloves based on fibre-optic curvature sensors to acquire finger joint angles, a hybrid tracking system based on inertia and ultrasound to capture hand position and orientation, and a stereoscopic display system to provide an immersive visual feedback. The potential and effectiveness of the proposed system is demonstrated through a number of applications, namely, hand gesture based virtual object manipulation and visualisation, hand gesture based direct sign writing, and hand gesture based finger spelling. For virtual object manipulation and visualisation, the system is shown to allow a user to select, translate, rotate, scale, release and visualise virtual objects (presented using graphics and volume data) in three-dimensional space using natural hand gestures in real-time. For direct sign writing, the system is shown to be able to display immediately the corresponding SignWriting symbols signed by a user using three different signing sequences and a range of complex hand gestures, which consist of various combinations of hand postures (with each finger open, half-bent, closed, adduction and abduction), eight hand orientations in horizontal/vertical plans, three palm facing directions, and various hand movements (which can have eight directions in horizontal/vertical plans, and can be repetitive, straight/curve, clockwise/anti-clockwise). The development includes a special visual interface to give not only a stereoscopic view of hand gestures and movements, but also a structured visual feedback for each stage of the signing sequence. An excellent basis is therefore formed to develop a full HCI based on all human gestures by integrating the proposed system with facial expression and body posture recognition methods. Furthermore, for finger spelling, the system is shown to be able to recognise five vowels signed by two hands using the British Sign Language in real-time

Real-time immersive human-computer interaction based on tracking and recognition of dynamic hand gestures

With fast developing and ever growing use of computer based technologies, human-computer interaction (HCI) plays an increasingly pivotal role. In virtual reality (VR), HCI technologies provide not only a better understanding of three-dimensional shapes and spaces, but also sensory immersion and physical interaction. With the hand based HCI being a key HCI modality for object manipulation and gesture based communication, challenges are presented to provide users a natural, intuitive, effortless, precise, and real-time method for HCI based on dynamic hand gestures, due to the complexity of hand postures formed by multiple joints with high degrees-of-freedom, the speed of hand movements with highly variable trajectories and rapid direction changes, and the precision required for interaction between hands and objects in the virtual world. Presented in this thesis is the design and development of a novel real-time HCI system based on a unique combination of a pair of data gloves based on fibre-optic curvature sensors to acquire finger joint angles, a hybrid tracking system based on inertia and ultrasound to capture hand position and orientation, and a stereoscopic display system to provide an immersive visual feedback. The potential and effectiveness of the proposed system is demonstrated through a number of applications, namely, hand gesture based virtual object manipulation and visualisation, hand gesture based direct sign writing, and hand gesture based finger spelling. For virtual object manipulation and visualisation, the system is shown to allow a user to select, translate, rotate, scale, release and visualise virtual objects (presented using graphics and volume data) in three-dimensional space using natural hand gestures in real-time. For direct sign writing, the system is shown to be able to display immediately the corresponding SignWriting symbols signed by a user using three different signing sequences and a range of complex hand gestures, which consist of various combinations of hand postures (with each finger open, half-bent, closed, adduction and abduction), eight hand orientations in horizontal/vertical plans, three palm facing directions, and various hand movements (which can have eight directions in horizontal/vertical plans, and can be repetitive, straight/curve, clockwise/anti-clockwise). The development includes a special visual interface to give not only a stereoscopic view of hand gestures and movements, but also a structured visual feedback for each stage of the signing sequence. An excellent basis is therefore formed to develop a full HCI based on all human gestures by integrating the proposed system with facial expression and body posture recognition methods. Furthermore, for finger spelling, the system is shown to be able to recognise five vowels signed by two hands using the British Sign Language in real-time.EThOS - Electronic Theses Online ServiceGBUnited Kingdo