Dan C. Popescu

A nonlinear model for fractal image coding

After a very promising start, progress in fractal image coding has been relatively slow recently. Most improvements have been concentrating on better adaptive coding algorithms and on search strategies to reduce the encoding time. Very little has been-done to challenge the linear model of the fractal transformations used so far in practical applications. In this paper, we explain why effective nonlinear transformations are not easy to find and propose a model based on conformal mappings in the geometric domain that are a natural extension of the affine model. Our compression results show improvements over the linear model and support the hope that a deeper understanding of the notion of self-similarity would further advance fractal image coding.

A model for efficient and accurate interaction with elastic objects in haptic virtual environments

This paper describes a method of modelling real-time interactions with elastic 3D objects represented by finite element models, which is particularly suitable for haptic virtual environments. The assumption we make is that the area of interaction of the external forces on the object is small. Our method provides a physically based solution and only requires the precomputation of the inverse of the stiffness matrix. It can be naturally coupled with a technique of local multiresolution collision detection, in order to increase geometrical accuracy while maintaining a low cost computation.Our model shows that under reasonable constraints, it is possible to meet the generally hard to reconcile requirements of having both a real-time and physically accurate simulation in a haptic virtual environment.

Contact Modelling Based on Displacement Field Redistribution for Surgical Simulation

We present a novel method of contact modelling for discrete deformable models. Our algorithm is used to simulate contact between rigid surgical tools of arbitrary shape and deformable virtual organs bounded by triangular mesh surfaces. It uses a divide and conquer strategy to redistribute an arbitrary field of displacements on organ surfaces into an equivalent field of displacements at the nodes. The computational complexity depends on the size of the touch field, but not on the size of the mesh representing the organ. Our algorithm results in accurate modelling and can be used in real-time applications requiring haptic feedback.

A manifold flattening approach for anchorless localization

We present a new method for anchorless localization of mobile nodes in wireless networks using only measured distances between pairs of nodes. Our method relies on the completion of the Euclidean distance matrix, followed by multidimensional scaling in order to compute the relative locations of the nodes. The key element of novelty of our algorithm is the method of completing the Euclidean distance matrix, which consists of gradually inferring the unknown distances, such as to align all nodes on a k-hyperplane, where typically k is 2 or 3. Our method leads to perfect anchorless localization for noise-free range measurements, if the network is sufficiently connected. We introduce refinements to the algorithm to make it robust to noisy and outlier range measurements. We present results from several localization tests, using both simulated data and experimental results measured using a large indoor network deployment of our WASP platform. Our results show improvements in localization using our algorithm over previously published techniques.

Point spread function estimation for a terahertz imaging system

We present a method for estimating the point spread function of a terahertz imaging system designed to operate in reflection mode. The method is based on imaging phantoms with known geometry, which have patterns with sharp edges at all orientations. The point spread functions are obtained by a deconvolution technique in the Fourier domain. We validate our results by using the estimated point spread functions to deblur several images of natural scenes and by direct comparison with a point source response. The estimations turn out to be robust and produce consistent deblurring quality over the entire depth of the focal region of the imaging system.

Range Data Correction for Improved Localization

We present a method to correct noisy range data to improve localization performance in wireless sensor networks. Mutual ranges between nodes are determined by node positions, and in typical deployments the communication links over which range is measured greatly exceeds the number of unknown node coordinates. We exploit this redundancy to reduce range error. A remarkable feature of our method is that redundancy is exploited strictly in the space of measured ranges, without requiring the construction of a coordinate system. Experimental results in indoor and outdoor environments using our proposed technique show reductions in location error between 35% and 60%.

Topology modification for surgical simulation using precomputed finite element models based on linear elasticity.

Surgical simulators provide another tool for training and practising surgical procedures, usually restricted to the use of cadavers. Our surgical simulator utilises Finite Element (FE) models based on linear elasticity. It is driven by displacements, as opposed to forces, allowing for realistic simulation of both deformation and haptic response at real-time rates. To achieve demanding computational requirements, the stiffness matrix K, which encompasses the geometrical and physical properties of the object, is precomputed, along with K⁻¹. Common to many surgical procedures is the requirement of cutting tissue. Introducing topology modifications, such as cutting, into these precomputed schemes does however come as a challenge, as the precomputed data needs to be modified, to reflect the new topology. In particular, recomputing K⁻¹ is too costly to be performed during the simulation. Our topology modification method is based upon updating K⁻¹ rather than entirely recomputing the matrix. By integrating condensation, we improve efficiency to allow for interaction with larger models. We can further enhance this by redistributing computational load to improve the systems real-time response. We exemplify our techniques with results from our surgical simulation system.

Real-time topology modification for finite element models with haptic feedback

We propose a real-time procedure for performing topology modifications on finite element models of objects with linear elastic behaviour. For a 3D tetrahedral model, it requires the inversion of a 6 × 6 matrix and the weighted multiplication of a thin matrix with its transpose. We exemplify with an implementation in our surgical simulator, where we impose the tight computational constraints of haptic feedback. Our experimental results show that we can obtain response times of under one second for objects represented by tetrahedral meshes with more than 2000 nodes.

Posterior Cramér–Rao Bound for Anchorless Tracking

We derive the posterior Cramer-Rao bound (PCRB) for tracking in anchorless dynamic networks consisting of static nodes at unknown locations and mobile nodes. We show that this is a type of PCRB under parametric constraints where the parameter space cannot be modeled by equation constraints. We propose a novel framework for modeling the constrained parameter manifold, as a factor manifold under the actions of a group. The approach we propose is generic, and can be used to derive lower error bounds for other parameter estimation problems where the parametric constraints cannot be optimally described by equation constraints.

Anchorless localization with local manifold flattening

We present a new method for anchorless localization of mobile nodes in wireless networks using only measured distances between pairs of nodes. The novelty of the algorithm lies in the method to complete the Euclidean distance matrix by inferring the unknown distances such as to align all nodes on a k-hyperplane, where typically k is 2 or 3. The relative locations of the nodes are then computed using multidimensional scaling. We also present experimental results with data collected using our WASP platform to verify the improvement in localization using our algorithm over previously published techniques.