Pulse dynamics in a three-component system : existence analysis

In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.

Scene invariant crowd counting for real-time surveillance

Automated crowd counting allows excessive crowding to be detected immediately, without the need for constant human surveillance. Current crowd counting systems are location specific, and for these systems to function properly they must be trained on a large amount of data specific to the target location. As such, configuring multiple systems to use is a tedious and time consuming exercise. We propose a scene invariant crowd counting system which can easily be deployed at a different location to where it was trained. This is achieved using a global scaling factor to relate crowd sizes from one scene to another. We demonstrate that a crowd counting system trained at one viewpoint can achieve a correct classification rate of 90% at a different viewpoint.

Manifolds, patterns and transitions in a creative life

Using sculpture and drawing as my primary methods of investigation, this research explores ways of shifting the emphasis of my creative visual arts practice from object to process whilst still maintaining a primacy of material outcomes. My motivation was to locate ways of developing a sustained practice shaped as much by new works, as by a creative flow between works. I imagined a practice where a logic of structure within discrete forms and a logic of the broader practice might be developed as mutually informed processes. Using basic structural components of multiple wooden curves and linear modes of deployment – in both sculptures and drawings – I have identified both emergence theory and the image of rhizomic growth (Deleuze and Guattari, 1987) as theoretically integral to this imagining of a creative practice, both in terms of critiquing and developing works. Whilst I adopt a formalist approach for this exegesis, the emergence and rhizome models allow it to work as a critique of movement, of becoming and changing, rather than merely a formalism of static structure. In these models, therefore, I have identified a formal approach that can be applied not only to objects, but to practice over time. The thorough reading and application of these ontological models (emergence and rhizome) to visual arts practice, in terms of processes, objects and changes, is the primary contribution of this thesis. The works that form the major component of the research develop, reflect and embody these notions of movement and change.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies

Scene invariant crowd counting

This paper describes a scene invariant crowd counting algorithm that uses local features to monitor crowd size. Unlike previous algorithms that require each camera to be trained separately, the proposed method uses camera calibration to scale between viewpoints, allowing a system to be trained and tested on different scenes. A pre-trained system could therefore be used as a turn-key solution for crowd counting across a wide range of environments. The use of local features allows the proposed algorithm to calculate local occupancy statistics, and Gaussian process regression is used to scale to conditions which are unseen in the training data, also providing confidence intervals for the crowd size estimate. A new crowd counting database is introduced to the computer vision community to enable a wider evaluation over multiple scenes, and the proposed algorithm is tested on seven datasets to demonstrate scene invariance and high accuracy. To the authors' knowledge this is the first system of its kind due to its ability to scale between different scenes and viewpoints.

Scene invariant crowd counting and crowd occupancy analysis

In public places, crowd size may be an indicator of congestion, delay, instability, or of abnormal events, such as a fight, riot or emergency. Crowd related information can also provide important business intelligence such as the distribution of people throughout spaces, throughput rates, and local densities. A major drawback of many crowd counting approaches is their reliance on large numbers of holistic features, training data requirements of hundreds or thousands of frames per camera, and that each camera must be trained separately. This makes deployment in large multi-camera environments such as shopping centres very costly and difficult. In this chapter, we present a novel scene-invariant crowd counting algorithm that uses local features to monitor crowd size. The use of local features allows the proposed algorithm to calculate local occupancy statistics, scale to conditions which are unseen in the training data, and be trained on significantly less data. Scene invariance is achieved through the use of camera calibration, allowing the system to be trained on one or more viewpoints and then deployed on any number of new cameras for testing without further training. A pre-trained system could then be used as a ‘turn-key’ solution for crowd counting across a wide range of environments, eliminating many of the costly barriers to deployment which currently exist.

Towards condition-invariant sequence-based route recognition

In this paper we present a novel algorithm for localization during navigation that performs matching over local image sequences. Instead of calculating the single location most likely to correspond to a current visual scene, the approach finds candidate matching locations within every section (subroute) of all learned routes. Through this approach, we reduce the demands upon the image processing front-end, requiring it to only be able to correctly pick the best matching image from within a short local image sequence, rather than globally. We applied this algorithm to a challenging downhill mountainbiking visual dataset where there was significant perceptual or environment change between repeated traverses of the environment, and compared performance to applying the feature-based algorithm FAB-MAP. The results demonstrate the potential for localization using visual sequences, even when there are no visual features that can be reliably detected.

Kernel analysis on Grassmann manifolds for action recognition

Modelling video sequences by subspaces has recently shown promise for recognising human actions. Subspaces are able to accommodate the effects of various image variations and can capture the dynamic properties of actions. Subspaces form a non-Euclidean and curved Riemannian manifold known as a Grassmann manifold. Inference on manifold spaces usually is achieved by embedding the manifolds in higher dimensional Euclidean spaces. In this paper, we instead propose to embed the Grassmann manifolds into reproducing kernel Hilbert spaces and then tackle the problem of discriminant analysis on such manifolds. To achieve efficient machinery, we propose graph-based local discriminant analysis that utilises within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, respectively. Experiments on KTH, UCF Sports, and Ballet datasets show that the proposed approach obtains marked improvements in discrimination accuracy in comparison to several state-of-the-art methods, such as the kernel version of affine hull image-set distance, tensor canonical correlation analysis, spatial-temporal words and hierarchy of discriminative space-time neighbourhood features.

Breast cancer detection from thermal images using bispectral invariant features

Highly sensitive infrared (IR) cameras provide high-resolution diagnostic images of the temperature and vascular changes of breasts. These images can be processed to emphasize hot spots that exhibit early and subtle changes owing to pathology. The resulting images show clusters that appear random in shape and spatial distribution but carry class dependent information in shape and texture. Automated pattern recognition techniques are challenged because of changes in location, size and orientation of these clusters. Higher order spectral invariant features provide robustness to such transformations and are suited for texture and shape dependent information extraction from noisy images. In this work, the effectiveness of bispectral invariant features in diagnostic classification of breast thermal images into malignant, benign and normal classes is evaluated and a phase-only variant of these features is proposed. High resolution IR images of breasts, captured with measuring accuracy of ±0.4% (full scale) and temperature resolution of 0.1 °C black body, depicting malignant, benign and normal pathologies are used in this study. Breast images are registered using their lower boundaries, automatically extracted using landmark points whose locations are learned during training. Boundaries are extracted using Canny edge detection and elimination of inner edges. Breast images are then segmented using fuzzy c-means clustering and the hottest regions are selected for feature extraction. Bispectral invariant features are extracted from Radon projections of these images. An Adaboost classifier is used to select and fuse the best features during training and then classify unseen test images into malignant, benign and normal classes. A data set comprising 9 malignant, 12 benign and 11 normal cases is used for evaluation of performance. Malignant cases are detected with 95% accuracy. A variant of the features using the normalized bispectrum, which discards all magnitude information, is shown to perform better for classification between benign and normal cases, with 83% accuracy compared to 66% for the original.