Dynamic Decomposition of Spatiotemporal Neural Signals

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals

Adaptive image vectorisation and brushing using mesh colours

We propose the use of curved triangles and mesh colours as a vector primitive for image vectorisation. We show that our representation has clear benefits for rendering performance, texture detail, as well as further editing of the resulting vector images. The proposed method focuses on efficiency, but it still leads to results that compare favourably with those from previous work. We show results over a variety of input images ranging from photos, drawings, paintings, all the way to designs and cartoons. We implemented several editing workflows facilitated by our representation: interactive user-guided vectorisation, and novel raster-style feature-aware brushing capabilities

QualityAdaptive sharpness enhancement and noise removal of a colour images based on the bilateral filtering

In this paper, we present the Adaptive Bilateral Filter (ABF) for sharpness enhancement and noise removal of a colour images. The ABF sharpens an image by increasing the slope of the edges without producing overshoot or undershoot. It is an approach to sharpness enhancement that is fundamentally different from the unsharp mask (USM). This new approach to slope restoration also differs significantly from previous slope restoration algorithms. Compared with an USM based sharpening method, the optimal unsharp mask (OUM), In terms of noise removal, ABF will outperform the bilateral filter and the OUM. ABF works well for both gray images and color images. Due to operation of sharpening of colour images along the edge slope tend to poseterize the image using ABF by pulling up or pulling down the colour images. The proposed method is effective at removing signal noise while enhancing the experimental results in perceptual quality both quantatively and qualitatively

Simulation of micro-flow dynamics at low capillary numbers using adaptive interface compression

A numerical framework for modelling micro-scale multiphase flows with sharp interfaces has been developed. The suggested methodology is targeting the efficient and yet rigorous simulation of complex interface motion at capillary dominated flows (low capillary number). Such flows are encountered in various configurations ranging from micro-devices to naturally occurring porous media. The methodology uses as a basis the Volume-of-Fluid (VoF) method combined with additional sharpening smoothing and filtering algorithms for the interface capturing. These algorithms help the minimisation of the parasitic currents present in flow simulations, when viscous forces and surface tension dominate inertial forces, like in porous media. The framework is implemented within a finite volume code (OpenFOAM) using a limited Multidimensional Universal Limiter with Explicit Solution (MULES) implicit formulation, which allows larger time steps at low capillary numbers to be utilised. In addition, an adaptive interface compression scheme is introduced for the first time in order to allow for a dynamic estimation of the compressive velocity only at the areas of interest and thus has the advantage of avoiding the use of a-priori defined parameters. The adaptive method is found to increase the numerical accuracy and to reduce the sensitivity of the methodology to tuning parameters. The accuracy and stability of the proposed model is verified against five different benchmark test cases. Moreover, numerical results are compared against analytical solutions as well as available experimental data, which reveal improved solutions relative to the standard VoF solver

Fast space-variant elliptical filtering using box splines

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based on a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using pre-integration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based on the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.Comment: 12 figures; IEEE Transactions on Image Processing, vol. 19, 201

SurfelMeshing: Online Surfel-Based Mesh Reconstruction

We address the problem of mesh reconstruction from live RGB-D video, assuming a calibrated camera and poses provided externally (e.g., by a SLAM system). In contrast to most existing approaches, we do not fuse depth measurements in a volume but in a dense surfel cloud. We asynchronously (re)triangulate the smoothed surfels to reconstruct a surface mesh. This novel approach enables to maintain a dense surface representation of the scene during SLAM which can quickly adapt to loop closures. This is possible by deforming the surfel cloud and asynchronously remeshing the surface where necessary. The surfel-based representation also naturally supports strongly varying scan resolution. In particular, it reconstructs colors at the input camera's resolution. Moreover, in contrast to many volumetric approaches, ours can reconstruct thin objects since objects do not need to enclose a volume. We demonstrate our approach in a number of experiments, showing that it produces reconstructions that are competitive with the state-of-the-art, and we discuss its advantages and limitations. The algorithm (excluding loop closure functionality) is available as open source at https://github.com/puzzlepaint/surfelmeshing .Comment: Version accepted to IEEE Transactions on Pattern Analysis and Machine Intelligenc

Geometric Surface Processing and Virtual Modeling

In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance