On the application of projection methods for computing optical flow fields

Detecting optical flow means to find the apparent displacement field in a sequence of images. As starting point for many optical flow methods serves the so called optical flow constraint (OFC), that is the assumption that the gray value of a moving point does not change over time. Variational methods are amongst the most popular tools to compute the optical flow field. They compute the flow field as minimizer of an energy functional that consists of a data term to comply with the OFC and a smoothness term to obtain uniqueness of this underdetermined problem. In this article we replace the smoothness term by projecting the solution to a finite dimensional, affine subspace in the spatial variables which leads to a smoothing and gives a unique solution as well. We explain the mathematical details for the quadratic and nonquadratic minimization framework, and show how alternative model assumptions such as constancy of the brightness gradient can be incorporated. As basis functions we consider tensor products of B-splines. Under certain smoothness assumptions for the global minimizer in Sobolev scales, we prove optimal convergence rates in terms of the energy functional. Experiments are presented that demonstrate the feasibility of our approach

A TV flow based local scale estimate and its application to texture discrimination

This paper presents a local region based scale measure, which exploits properties of a certain type of nonlinear diffusion, the so-called total variation (TV) flow. During the signal evolution by means of TV flow, pixels change their value with a speed that is inversely proportional to the size of the region they belong to. From this evolution speed one can derive a local scale estimate based on regions instead of derivative filters. Main motivation for such a scale measure is its application to texture discrimination, in particular the construction of an alternative to Gabor filters. When the scale estimate is combined with the components of the structure tensor, which provides orientation information, it yields a texture feature space of only four dimensions. Like Gabor features, this sparse feature space discriminates textures by means of their orientation and scale, yet the representation of orientation and scale is less redundant. The quality of the feature space containing the new scale measure is evaluated in texture segmentation experiments by comparing results to those achieved with Gabor filters. It turns out that one can gain a total speedup of factor 2 without loosing any quality concerning the discrimination of textures

Level set segmentation with multiple regions

The popularity of level sets for segmentation is mainly based on the sound and convenient treatment of regions and their boundaries. Unfortunately, this convenience is so far not known from level set methods when applied to images with more than two regions. This paper introduces a comparatively simple way how to extend active contours to multiple regions keeping the familiar quality of the two-phase case. We further suggest a strategy to determine the optimum number of regions as well as initializations for the contours

Colour, texture, and motion in level set based segmentation and tracking

This paper introduces an approach for the extraction and combination of different cues in a level set based image segmentation framework. Apart from the image grey value or colour, we suggest to add its spatial and temporal variations, which may provide important further characteristics. It often turns out that the combination of colour, texture, and motion permits to distinguish object regions that cannot be separated by one cue alone. We propose a two-step approach. In the first stage, the input features are extracted and enhanced by applying coupled nonlinear diffusion. This ensures coherence between the channels and deals with outliers. We use a nonlinear diffusion technique, closely related to total variation flow, but being strictly edge enhancing. The resulting features are then employed for a vector-valued front propagation based on level sets and statistical region models that approximate the distributions of each feature. The application of this approach to two-phase segmentation is followed by an extension to the tracking of multiple objects in image sequences

Obesity : novel and unusual predisposing factors

To tackle the complexity of the global obesity epidemic, it is important to consider the many predisposing factors that underlie progressive and sustained weight gain. Some of the biological drivers for weight gain following initial weight loss include persistent changes in appetite hormones [including ghrelin and postprandial plasma peptide YY (PYY)], and ‘persistent metabolic adaptation’. However, many factors within our busy, stressful modern-day environment seem to conspire towards promotion of weight gain. These include the effects of sleep deprivation on appetite regulation, and the effects of modern-day technology on ‘attention competition’. These factors, combined with cultural and societal factors can result in a ‘mindless’ attitude regarding eating-related behaviour that is likely to predispose to weight gain. In addition to the external environment, our internal environment within the gut has also changed radically within the last few decades, resulting from changes in fibre intake, and increased ingestion of highly refined, sterilised and processed foods. Although contentious, these dietary changes have implications for our gut microbiota, and possible downstream effects on control of appetite and metabolism. In this brief review, we consider some of the novel predisposing factors for weight gain within our modern-day 21st century environments (both external and internal), and explore how legal terminology can help to conceptualise the numerous factors that contribute towards weight gain, and, ultimately the global obesity epidemic

Highly accurate optic flow computation with theoretically justified warping

In this paper, we suggest a variational model for optic flow computation based on non-linearised and higher order constancy assumptions. Besides the common grey value constancy assumption, also gradient constancy, as well as the constancy of the Hessian and the Laplacian are proposed. Since the model strictly refrains from a linearisation of these assumptions, it is also capable to deal with large displacements. For the minimisation of the rather complex energy functional, we present an efficient numerical scheme employing two nested fixed point iterations. Following a coarse-to-fine strategy it turns out that there is a theoretical foundation of so-called warping techniques hitherto justified only on an experimental basis. Since our algorithm consists of the integration of various concepts, ranging from different constancy assumptions to numerical implementation issues, a detailed account of the effect of each of these concepts is included in the experimental section. The superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques. Further experiments also confirm excellent robustness under noise and insensitivity to parameter variations

On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and SIDEs

Soft wavelet shrinkage, total variation (TV) diffusion, total variation regularization, and a dynamical system called SIDEs are four useful techniques for discontinuity preserving denoising of signals and images. In this paper we investigate under which circumstances these methods are equivalent in the 1-D case. First we prove that Haar wavelet shrinkage on a single scale is equivalent to a single step of space-discrete TV diffusion or regularization of two-pixel pairs. In the translationally invariant case we show that applying cycle spinning to Haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of TV diffusion. We prove that space-discrete TV difusion and TV regularization are identical, and that they are also equivalent to the SIDEs system when a specific force function is chosen. Afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the Laplacian pyramid of the signal. We analyse possibilities to avoid Gibbs-like artifacts for multiscale Haar wavelet shrinkage by scaling the thesholds. Finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and PDE / variational approaches. These methods are based on iterated shift-invariant wavelet shrinkage at multiple scales with scaled thresholds

The health benefits of dietary fibre

Background: Dietary fibre consists of non-digestible forms of carbohydrate, usually as polysaccharides that originate from plant-based foods. Over recent decades, our diet within Westernised societies has changed radically from that of our hominid ancestors, with implications for our co-evolved gut microbiota. This includes increased ingestion of ultra-processed foods that are typically impoverished of dietary fibre, and associated reduction in the intake of fibre-replete plant-based foods. Over recent decades, there has been a transformation in our understanding of the health benefits of dietary fibre. Objective: To explore the current medical literature on the health benefits of dietary fibre, with a focus on overall metabolic health. Data Sources: We performed a narrative review, based on relevant articles written in English from a PubMed search, using the terms ‘dietary fibre and metabolic health’. Results: In the Western world, our diets are impoverished of fibre. Dietary fibre intake associates with overall metabolic health (through key pathways that include insulin sensitivity) and a variety of other pathologies that include cardiovascular disease, colonic health, gut motility and risk for colorectal carcinoma. Dietary fibre intake also correlates with mortality. The gut microflora functions as an important mediator of the beneficial effects of dietary fibre, including the regulation of appetite, metabolic processes and chronic inflammatory pathways. Conclusions: Multiple factors contribute to our fibre-impoverished modern diet. Given the plethora of scientific evidence that corroborate the multiple and varied health benefits of dietary fibre, and the risks associated with a diet that lacks fibre, the optimization of fibre within our diets represents an important public health strategy to improve both metabolic and overall health. If implemented successfully, this strategy would likely result in substantial future health benefits for the population. View Full-Tex

Rule-based PI controller autotuning for drive systems

Tuning a PI controller can be quite cumbersome for the non-expert as the closed-loop control system has to meet various requirements while the influence and interaction of the two degrees of freedom are not always clear. This paper addresses the design of an iterative PI controller autotuning for drive systems with the idea of imitating a human expert. In contrast to existing concepts, a new approach with multiple tuning strategies is applied which gives a compact rule base that is easy to modify. The performance of the proposed algorithm is illustrated through motion control testbench trials