Electrostatic Halftoning

We introduce a new global approach for image dithering, stippling, screening and sampling. It is inspired by the physical principles of electrostatics. Repelling forces between equally charged particles create a homogeneous distribution in flat areas, while attracting forces from the image brightness values ensure a high approximation quality. Our model is transparent and uses only two intuitive parameters: One steers the granularity of our halftoning approach, and the other its regularity. We evaluate two versions of our algorithm: A discrete version for dithering that ties points to grid positions, as well as a continuous one which does not have this restriction, and can thus be used for stippling or sampling density functions. Our methods create very few visual artefacts, reveal favourable blue‐noise behaviour in the frequency domain, and have a lower approximation error under Gaussian convolution than state‐of‐the‐art methods.     

Detecting Regular Visit Patterns

We are given a trajectory T\mathcal{T} and an area A\mathcal{A} . T\mathcal{T} might intersect A\mathcal{A} several times, and our aim is to detect whether T\mathcal{T} visits A\mathcal{A} with some regularity, e.g. what is the longest time span that a GPS-GSM equipped elephant visited a specific lake on a daily (weekly or yearly) basis, where the elephant has to visit the lake most of the days (weeks or years), but not necessarily on every day (week or year).     

Lucas/Kanade Meets Horn/Schunck: Combining Local and Global Optic Flow Methods

Differential methods belong to the most widely used techniques for optic flow computation in image sequences. They can be classified into local methods such as the Lucas–Kanade technique or Bigün's structure tensor method, and into global methods such as the Horn/Schunck approach and its extensions. Often local methods are more robust under noise, while global techniques yield dense flow fields. The goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways; (i) We juxtapose the role of smoothing/regularisation processes that are required in local and global differential methods for optic flow computation. (ii) This discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches: It yields dense flow fields that are robust against noise. (iii) Spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method. (iv) We propose a simple confidence measure for optic flow methods that minimise energy functionals. It allows to sparsify a dense flow field gradually, depending on the reliability required for the resulting flow. Comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure.     

Use of coupled canopy structure dynamic and radiative transfer models to estimate biophysical canopy characteristics

Leaf area index (LAI) is a key variable for the understanding of several eco-physiological processes within a vegetation canopy. The LAI could thus provide vital information for the management of the environment and agricultural practices when estimated continuously over time and space thanks to remote sensing sensors.This study proposed a method to estimate LAI spatial and temporal variation based on multi-temporal remote sensing observations processed using a simple semi-mechanistic canopy structure dynamic model (CSDM) coupled with a radiative transfer model (RTM). The CSDM described the temporal evolution of the LAI as function of the accumulated daily air temperature as measured from classical ground meteorological stations.The retrieval performances were evaluated for two different data sets: first, a data set simulated by the RTM but taking into account realistic measurement conditions and uncertainties resulting from different error sources; second, an experimental data set acquired over maize crops the Blue Earth City area (USA) in 1998. Results showed that the proposed approach improved significantly the retrieval performances for LAI mainly by smoothing the residual errors associated to each individual observation. In addition it provides a way to describe in a continuous manner the LAI time course from a limited number of observations during the growth cycle.     

Mass-spring systems on the GPU

We present and analyze different implementations of mass-spring systems for interactive simulation of deformable surfaces on graphics processing units (GPUs). For the amount of springs we target, numerical time integration of spring displacements needs to be accelerated and the transfer of displaced point positions for rendering must be avoided. To fulfill these requirements, we exploit features of recent graphics accelerators to simulate spring elongation and compression on the GPU, saving displaced point masses in graphics memory, and then sending these positions through the GPU again to render the deformed surface. Two different simulation algorithms implementing scattering and gathering operations on the GPU are compared with respect to performance and numerical accuracy. We discuss GPU specific issues to be considered in simulation techniques showing similar computation and memory access patterns to mass-spring systems.     

Curvature-Driven PDE Methods for Matrix-Valued Images

Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edge-like structures in tensor fields, we first generalise Di Zenzo’s concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts.     

The conformal alpha shape filtration

Conformal alpha shapes are a new filtration of the Delaunay triangulation of a finite set of points in ℝ^d. In contrast to (ordinary) alpha shapes the new filtration is parameterized by a local scale parameter instead of the global scale parameter in alpha shapes. The local scale parameter conforms to the local geometry and is motivated from applications and previous algorithms in surface reconstruction. We show how conformal alpha shapes can be used for surface reconstruction of non-uniformly sampled surfaces, which is not possible with alpha shapes.