We consider the problem of estimating the sparse initial condition of a solution to the advection-diffusion equation based on line integrals of the solution at a later time. We propose models for locating single and multiple point sources. We also propose new algorithms for the efficient implementation of these models. In practice, the models are relevant also for reconstructing the solution of the PDE at the observation time from a very sparse Radon transform; in this case, our models improve on more standard Radon inversion techniques by utilizing the specialized information about how the observed function was generated.

Fast deformable objects are very useful in robotics applications such as haptic rendering, where high simulation update rates (e.g., 1000 simulation steps per second) are required to maintain device stability. However, in order to simulate two rigid or deformable objects in contact with 6-DoF haptic feedback, it is also necessary to resolve contact between the two objects at haptic rates. With complex **deforming** geometry, this problem is difficult due to very short computation times (e.g., 1 millisec) of each simulation cycle. I will present an algorithm which can perform deformable object simulation, deformable collision detection and contact force and torque computation between two objects, at millisecond simulation rates. The algorithm scales well to both objects having complex geometry, and produces stable contact forces and torques, even at stiffness levels close to haptic device hardware limits.

Joint work with Sira Ferradans, Edoardo Provenzi, and Vicent Caselles.

Tone Mapping is the problem of compressing the range of a High Dynamic Range image so that it can be displayed in a Low Dynamic Range screen, without losing or introducing novel details: the final image should produce in the observer a sensation as close as possible to the perception produced by the real world scene. We propose a tone mapping operator with two stages. The first stage is a global method that implements visual adaptation, based on experiments on human perception, in particular we point out the importance of cone saturation. The second stage performs local contrast enhancement, based on a variational model inspired by color vision phenomenology. We evaluate this method with a metric validated by psychophysical experiments, and in terms of this metric our method compares very well with the state of the art.

The accumulation of photon impacts on a surface is the essence of photography. We will investigate the use of acumulation for both image and video fusion/restoration. Registration and patch based methods will be compared for several applications.

Existing image based CAPTCHAs can only transcribe words in an image that contains ASCII characters. In this poster, we are describing a system for transcribing words in an image that contains Unicode characters. Such a system will be useful in transcribing scanned documents from many European languages like Spanish, German, French etc. We will be demonstrating the methods for extracting the individual words from documents using adaptive thresholding, projection and morphological operations. We will also demonstrate a web site for solving the CAPTCHA.

Practice is the single most important determinant of a surgeon’s skills. In an effort to significantly improve the trajectory of surgical training, virtual reality (VR) based systems (so-called “surgical simulators”) are being developed to select, train, credential, and retrain physicians, much like flight simulators are used today to train aviation pilots with great success. Such systems, equipped with visual as well as haptic (touch) interfaces, provide an immersive “virtual environment” that enables the trainee to touch, feel, and manipulate virtual tissues and organs through surgical tool handles used in actual surgery, while seeing high-quality images as in real surgery. In this talk we will present some of our recent work in the development and clinical validation of virual surgical systems.

Joint work with Dr. Christophe Leglent (Radiology Dept, UoM).

Registration of Diffusion-Weighted Magnetic Resonance Images (DW-MRI) is a key step in motion correction, intra and multi-group analysis of brain connectivity, or construction of white matter tracts atlases, among other important tasks. Given the high dimensionality of the data, the registration is usually performed using a single scalar 3D image, which does not optimally represent the full directional information available in the complete diffusion data. Alternatively, tensor-based registration algorithms have been proposed to account for the preferred orientation of diffusion at each voxel. However, tensor-based registration methods impose a diffusion model that might not completely capture the information contained in the raw image. They also depend on the accurate estimation of the tensors, which is known to be sensitive to the Riccian noise, always present in DW-MR images. A new algorithm, based on angular interpolation (AI) of the DW-MRI, has previously been proposed to perform affine registration using the raw DW-MR images, without estimating the diffusion tensors. In this work, we improve and extend this framework and extensively compare it with single volume (using the b0 image) and tensor-based registration techniques. The performance of AI is improved in terms of speed (using kd-trees and parallelism) and accuracy (using sinc interpolation). We show how our technique circumvents the need to re-align the diffusion gradients. We also propose a new algorithm for non-linear registration based on AI and provide a publicly available implementation of the algorithms presented here, extending the FMRIB Software Library (FSL), a well-known open source library for analysis of brain imaging data. Finally, we compare the proposed technique with well known tensor-based registration algorithms such as dti-tk and MedINRIA.

I will describe joint work with Matt Elsey and Peter Smereka on large scale simulations of mean curvature and related geometric motions for networks of curves in 2D and surfaces in 3D. These motions arise as gradient flow for variational models encountered in image processing (Mumford-Shah model of image segmentation) and materials science (grain boundary motion in polycrystals). Our methods allow simulations with hundreds of thousands of regions, both in 2D and 3D, on uniform grids, achieve good accuracy, and require modest hardware.

Joint work with Sergio Aguirre (Echopixel, USA).

We introduce a CAD algorithm for candidate polyp flagging based on new geometric and texture features. Both the segmentation and classification problems are addressed. The main novelties of this work are the smoothing scheme, which is a surface motion adapted to this application, the incorporation of Haralick texture features, the consideration of the surrounding area for each candidate polyp (we compute context-based features instead of absolute ones), and the strategy of testing regions of multiple sizes. Differential or context-based features are significantly more discriminative than absolute features, as they emphasize local deviations of the geometry and texture over the colon. Testing regions of different sizes allows to precisely delimitate polyps. The proposed algorithm was tested with ground truth data. Results are very promising, detecting 100% of the true-polyps, including flat and small ones, with an average of less than three false positive detections per study.

In this talk we will describe the derivation of mathematical and numerical models for the simulation of high performance rowing boats. Rowing boats are a complex dynamical system strongly affected by the rowers action and movements. Indeed a rowing boat hardly moves with constant speed, but it is instead subject to a complex system of secondary movements: horizontal and vertical accelerations as well as pitching are the main ones. These in turn generate gravity waves which dissipates part of the rowers power.

A numerical model may help a boat manufacturer to foresee the behaviour of new a boat design, and a trainer to better understand how crew composition and rowing style may affect performance. We present the results of several years of collaboration with an important rowing boat manufacturer for the development of a complete mathematical model of the boat dynamics and of its interaction with the free surface flow.

Most of my work is focused around a single (broad) question: How can we use our understanding of human perception and artistic traditions to improve our tools for communicating and data understanding? In problems ranging from molecular biology to video editing, we are faced with a deluge of data. In this talk, I'll survey some of the ways we've tried to turn this problem into solutions. I'll discuss our efforts in data visualization and multimedia, showing how we can use an understanding of art and perception to create novel tools for a range of problems. I'll also speculate on some of new directions including the use of visual simulation for home healthcare development.

The development of new sports equipment, the optimization of performance or the enjoyment of the spectator has been enhanced in recent years through the rapid in computing power. In general, the anlysis of sport requires three things; (1) the experimental measurement of athlete and equipment in 3 dimensions (the reality); (2) mathematical approximation of the motion in the form of analytical or numerical simulation (the analysis); and (3) the visualization of the results in a meaningful way (the virtual reality).

This presentation will describe how mathematics and computing has contributed to the work of sports engineers to allow them to measure the effects of new interventions designed to improve performance. Examples will be given of pragmatic systems to measure the athlete 'in the field' in professional sports such as soccer and tennis, and Olympic sports such as diving and swimming. The use of finite-element analysis and computation fluid dynamics of tennis and cycling will be described as will the integration of their results with analytical models to determine how to improve performance.

The results from experimentation and simulation have used more and more complex graphics as computing power has increased. A glimpse of the future can be had with the use of low-cost 3-dimensional cameras used in devices such as the Kinect controller. Such systems link together the possiblity of performing complex biomechanical on mobile devices with feedback in the virtual world.

Joint work with Moritz Allmaras (Texas A&M University), David P. Darrow (University of Texas Medical Branch), Guido Kanschat (Texas A&M University), and Peter Kuchment (Texas A&M University).

In this talk, we introduce the segmentation method which incorporates the global convex segmentation method and the split Bregman technique into the region-scalable fitting energy model. The new proposed method based on the region-scalable model can draw upon intensity information in local regions at a controllable scale, so that it can segment images with intensity inhomogeneity. Furthermore, with the application of the global convex segmentation method and the split Bregman technique, the method is very robust and efficient. By using a non-negative edge detector function to the proposed method, the algorithm can detect the boundaries more easily and achieve results that are very similar to those obtained through the classical geodesic active contour model. Experimental results for synthetic and real images have shown the robustness and efficiency of our method and also demonstrated the desirable advantages of the proposed method.

Intuitively, one of the best ways to understand motion is to see it, but how can we picture the large multidimensional databases of motion collected today in surgical training or biomechanical studies? In this talk, I will present recent research that begins to address this question through developing novel methods for interactively querying and visualizing motion data. I will describe motivating problems and initial tools developed to support data analysis in two application areas: (1) surgical training, and (2) biomechanical experiments in humans and animals.

In MREIT, the harmonic Bz algorithm has been successfully applied to Bz data from phantoms and animals. The algorithm is, however, sensitive to measurement noise in Bz data. In addition, MR signal void in outer l ayers of bones and gas-filled organs, for example, produces salt-pepper noise in MR phase and consequently Bz images. The Bz images typically present areas of sloped transitions, which can be assimilated to ramps. Conductivity contrasts change ramp slopes in Bz images and it is critical to preserve positions of those ramps to correctly recover edges in conductivity images. Here, we propose a ramp-preserving denoising method utilizing a structure tensor. Using an eigenvalue analysis, we identified local regions of salt-pepper noise. Outside the identified local regions, we applied an anisotropic smoothing to reduce noise while preserving their ramp structures. Inside the local regions of salt-pepper noise, we used an isotropic smoothing.

The numerical simulation of free-surface flows around sailing boats is a complex topic that addresses multiple mathematical tasks: the correct study of the flow field around a rigid hull, the numerical simulation of the hull dynamics, the deformation of the sails and appendages under transient external conditions like gusts of wind or wave patterns and, overall, the coupling among all these components. In this work, we present some recent advances that have been achieved in different research topics related to yacht design and performance prediction. In particular, we describe the numerical algorithms that have been developed in the framework of open-source libraries for the simulation of free-surface hydrodynamics and boat dynamics, as well as for the analysis of the fluid-structure interaction between wind and sails. Theoretical and methodological aspects are described and the first preliminary results are reported.

I will survey what has been done in the last years on the inpainting problem, both for still images and video, and give an account of what remains to do.

In this talk we will presents the results concerning different aspects of the performance optimization of a swimsuit. The influence of the sewing on the performance has been analyzed: the results have proved a relevant improvements (in term of drag reduction and course time gain) when sewings are not present on the surface of the swimsuit. We will also analyze the stroke: in order to be able to simulate such kind of phenomena the development of a new set of simulation tools able to treat moving domain problems has been developed. A complete reconstruction of the swimmer kinematics is an extremely complex problem. Even the motion of a single arm is hard to be reproduced accurately without considering complex kinematics: in this respect, we have considered and implemented different stroke kinematics with increasing level of complexity.

This is the brief introduction to the level set formulation for spirals evolving by the geometric flow equation in the plane. Here we consider evolution of spirals with multiple centers and curves. The crucial difficulty is that a spiral does not divide a domain into interior and exterior, and thus the usual level set formulation does not work well. To overcome this difficulty, we consider a curve is on the covering space like as Riemannian surface. For our formulation and equation we obtain the existence and uniqueness of solutions in viscosity sense, and uniqueness of level sets.

The past few years have seen an incredible explosion of new (or revival of old) fast and effective algorithms for various imaging and information science applications. These include: nonloca; means, compressive sensing, Bregman iteration, as well as relatively old favorites such as the level set method and PDE based image restoration. I'll give my view of where we are and where we are going.

In this talk, I will present an overview of the numerical models that have been developed during the last few years for the performance prediction of America's Cup yachts. Different aspects which characterize the behaviour of racing boats will be discussed, such as the role of the yacht appendages, the dynamical response of the yacht in calm and wavy seas and the fluid-structure interaction between wind and sails. A selection of the large scale numerical simulations that were performed to support an America's Cup design team during the last three campaigns will be presented, highlighting the role played by the numerical simulations in the overall yacht design process.

To broaden the use of simulation for surgical training, in particular of new procedures and of low-volume procedures, we propose an environment and workflow that lets surgeon-educators create the teaching modules. Our challenge is to make the simulation tools accessible, modifiable and sharable by users with moderate computer and VR experience. Our contribution is a workflow that promotes consistency between instructional material and measured criteria; and that makes the authoring process efficient, both for the surgeon, and for computer scientists supporting the simulation environment.

The role of mathematics in understanding and simulating fluid dynamics and biochemical processes in the physiological and pathological functioning of the human cardiovascular system is becoming more and more crucial. These phenomena are indeed correlated with the origin of some major cardiovascular pathologies, and influence the efficacy of the treatments to heal the arteries from their diseases.

Mathematical models allow the description of the complex fluid-structure interaction which govern the artery wall deformation under the pressure pulse. Moreover, appropriate reduction strategies can be devised to allow for an effective description of the interaction between large, 3D components, and small 1D branches of the circulatory system, as well as the transfer of drugs and chemicals between the arterial lumen and the vessel wall.

This presentation will address some of these issues, the role of medical imaging and their integration in the numerical process as well as in the validation step.

In this talk I will describe recent work with Guoshen Yu and Stephane Mallat on PCA/GMM/structured-sparsity. I will introduce the framework, show state-of-the-art results for image restoration and matrix completion, and present theoretical results regarding compressed sensing of GMM.

There are many cases where strong vortices shed by parts of a moving body impinge on or come close to other parts of the body that are downwind. These include diverse bodies ranging from aircraft, to race cars to golf balls.

Traditional computation fluid dynamic (CFD) methods solve discretized versions of the governing partial differential equations. In these methods much effort is applied in reducing the local numerical discretization error, such as use of high order discretization schemes or dense computational grids. For thin features, such as shed vortices that propagate over long distances in high Reynolds number flows, this is usually not feasible. Current computers are still not capable of accurately solving the flow equations in these cases.

A relatively new method that is efficient and practical for these problems and that largely overcomes the deficiencies of conventional methods—Vorticity Confinement (VC) —will be described. VC is designed to efficiently capture and convect the important features of flows with thin vortical features without spreading due to numerical diffusion. Effectively, the vortices are treated as multi-dimensional nonlinear discrete solitary waves that “live” on the computational lattice. The basic idea behind VC is similar to shock capturing, where the feature is treated as a weak solution; However, this feature has a structure, which is captured over 2-3 cells on a computational grid with a well defined internal structure, which conserves important quantities such as vorticity and momentum.

Since attached boundary layers are typically also thin vortical regions, Vorticity Confinement can also be used as an implicit no-slip boundary layer model. This implicit boundary layer model thus allows complex bodies to be treated in a simple manner by immersing them in a coarse uniform, Cartesian grid.

Computed shed vortices will be shown for a number of cases, including aircraft, as well as results from blunt body computations ranging from motorcycles to rotorcraft.

I will present a second order accurate, geometrically flexible and easy to implement method for solving the variable coefficient Poisson equation with interfacial discontinuities on an irregular domain. We discretize the equations using an embedded approach on a uniform Cartesian grid employing virtual nodes at interfaces and boundaries. A variational method is used to define numerical stencils near these special virtual nodes and a Lagrange multiplier approach is used to enforce jump conditions and Dirichlet boundary conditions. Our combination of these two aspects yields a symmetric positive definite discretization. In the general case, we obtain the standard 5-point stencil away from the interface. For the specific case of interface problems with continuous coefficients, we present a discontinuity removal technique that admits use of the standard 5-point finite difference stencil everywhere in the domain. Numerical experiments indicate second order accuracy in L-infinty.

The problem of detection of colonic polyps in endoscopic images, obtained by a capsule device, is addressed. A procedure, based on geometric features of the input medical image, is proposed and analyzed. It relies on the assumption that the polyps show up as protrusions, and has proven to efficiently detect and single out the colonic polyps. It essentially uses the curvature information of the images, which are interpreted as the graphs of functions defined over the pixel domain. The procedure involves a curvature based identification (using both the Gaussian and mean curvatures) to the graph of the original input image, and subsequently utilizes a predefined threshold to classify the frames with polyps in videos. Numerical experiments on a data-set of wireless capsule endoscopic images and videos are undertaken for evaluation and validation of the proposed approach.

Joint work with Anton Schiela (Konrad-Zuse-Zentrum für Informationstechnik (ZIB)).

After accidents or inflammations with severe bone traumata, implants are used to restore both functionality and facial appearance of the patients. We consider computing the implant's shape required to match a desired facial shape by optimal control methods. Somewhat surprisingly, the shape optimization problem can be formulated as a quite standard boundary control problem. Function space nonlinear programming algorithms are developed and preliminary numerical results are presented.

This talk overviews a few viable sparse optimization algorithms such as variable splitting L1/TV minimization, compressive sensing edge detection, nonnegative matrix factorization, and Beta-process based Bayesian learning. They allow us to take advantages of structures in both the model and the data to produce state-of-the-art results.

Imaging examples such as edge detection, image deblurring and denoising, MRI reconstruction, background subtraction, as well as hyperspectral image processing will be given.