Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Dense active appearance models using a bounded diameter minimum spanning tree

We present a method for producing dense Active Appearance Models (AAMs), suitable for video-realistic synthesis. To this end we estimate a joint alignment of all training images using a set of pairwise registrations and ensure that these pairwise registrations are only calculated between similar images. This is achieved by defining a graph on the image set whose edge weights correspond to registration errors and computing a bounded diameter minimum spanning tree (BDMST). Dense optical flow is used to compute pairwise registration and we introduce a flow refinement method to align small scale texture. Once registration between training images has been established we propose a method to add vertices to the AAM in a way that minimises error between the observed flow fields and a flow field interpolated between the AAM mesh points. We demonstrate a significant improvement in model compactness using the proposed method and show it dealing with cases that are problematic for current state-of-the-art approaches.