March 5 - 6, 2011
Keywords of the presentation: interfacial motion, variational models, numerical methods, level sets, phase field
Many of the variational models of image processing and computer vision involve optimizing an energy over interfaces. An important example is image segmentation, where the goal is to partition the image domain into regions containing distinct objects. Typically, the models include a geometric penalty term, such as perimeter or Euler's elastica energy. We will discuss some of the popular algorithms for computing these models, including level set, diffuse interface (phase field), and diffusion generated motion-based approaches. However, the emphasis will be on more recent algorithms that convert some of these notoriously hard, non-convex optimizations to equivalent convex optimization problems.
Keywords of the presentation: Computational fluid dynamics; fluid structure interaction
Mathematics in sports covers a wide range of aspects, from the study of dynamical systems (to assess biological response to fatigue, for instance), the mechanics of biological tissues (like in injury studies), game theory (for strategy planing), up to the dynamics of fluids and structures to optimise the performance of sport devices (ski, racing boats etc.). In this lectures we focus most on the last topic, giving an introduction to fluid and structural dynamics and fluid-structure interaction problems.
Keywords of the presentation: finite elements, real time, elasticity, biomechanics, virtual surgery
Elasticity plays a fundamental role in many biomechanics and computer
graphics related problems. I will talk about numerical methods used
for simulating elastic phenomena in soft tissues, skeletal muscles as
well as techniques inspired by imaging for determining elastic
constitutive models. Specifically, I will discuss common difficulties
encountered and my recent algorithm developments to address them. I
will put specific emphasis on applications in computer graphics based
special effects for virtual characters. Topics include robust
resolution of: severe nonlinearity, near incompressibility, extremely
large deformation, collision/contact and solid/fluid coupling. I will
also discuss the impact of multi-core accelerated computation for such
problems and the potentially revolutionary applications it will admit.