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.

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.

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.