Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body

Fluids real-time rendering

In this thesis the existing methods for realistic visualization of uids in real-time are reviewed. The correct handling of the interaction of light with a uid surface can highly increase the realism of the rendering, therefore method for physically accurate rendering of re ections and refractions will be used. The light- uid interaction does not stop at the surface, but continues inside the uid volume, causing caustics and beams of light. The simulation of uids require extremely time-consuming processes to achieve physical accuracy and will not be explored, although the main concepts will be given. Therefore, the main goals of this work are: Study and review the existing methods for rendering uids in realtime. Find a simpli ed physical model of light interaction, because a complete physically correct model would not achieve real-time. Develop an application that uses the found methods and the light interaction model

Context-based urban terrain reconstruction from uav-videos for geoinformation applications

Urban terrain reconstruction has many applications in areas of civil engineering, urban planning, surveillance and defense research. Therefore the needs of covering ad-hoc demand and performing a close-range urban terrain reconstruction with miniaturized and relatively inexpensive sensor platforms are constantly growing. Using (miniaturized) unmanned aerial vehicles, (M) UAVs, represents one of the most attractive alternatives to conventional large-scale aerial imagery. We cover in this paper a four-step procedure of obtaining georeferenced 3D urban models from video sequences. The four steps of the procedure - orientation, dense reconstruction, urban terrain modeling and geo-referencing - are robust, straight-forward, and nearly fully-automatic. The two last steps - namely, urban terrain modeling from almost-nadir videos and co-registration of models - represent the main contribution of this work and will therefore be covered with more detail. The essential substeps of the third step include digital terrain model (DTM) extraction, segregation of buildings from vegetation, as well as instantiation of building and tree models. The last step is subdivided into quasi-intrasensorial registration of Euclidean reconstructions and intersensorial registration with a geo-referenced orthophoto. Finally, we present reconstruction results from a real data-set and outline ideas for future work

Automatic Aircraft Collision Avoidance System and Method

The invention is a system and method of compressing a DTM to be used in an Auto-GCAS system using a semi-regular geometric compression algorithm. In general, the invention operates by first selecting the boundaries of the three dimensional map to be compressed and dividing the three dimensional map data into regular areas. Next, a type of free-edged, flat geometric surface is selected which will be used to approximate terrain data of the three dimensional map data. The flat geometric surface is used to approximate terrain data for each regular area. The approximations are checked to determine if they fall within selected tolerances. If the approximation for a specific regular area is within specified tolerance, the data is saved for that specific regular area. If the approximation for a specific area falls outside the specified tolerances, the regular area is divided and a flat geometric surface approximation is made for each of the divided areas. This process is recursively repeated until all of the regular areas are approximated by flat geometric surfaces. Finally, the compressed three dimensional map data is provided to the automatic ground collision system for an aircraft

Hallucinating optimal high-dimensional subspaces

Linear subspace representations of appearance variation are pervasive in computer vision. This paper addresses the problem of robustly matching such subspaces (computing the similarity between them) when they are used to describe the scope of variations within sets of images of different (possibly greatly so) scales. A naive solution of projecting the low-scale subspace into the high-scale image space is described first and subsequently shown to be inadequate, especially at large scale discrepancies. A successful approach is proposed instead. It consists of (i) an interpolated projection of the low-scale subspace into the high-scale space, which is followed by (ii) a rotation of this initial estimate within the bounds of the imposed ``downsampling constraint''. The optimal rotation is found in the closed-form which best aligns the high-scale reconstruction of the low-scale subspace with the reference it is compared to. The method is evaluated on the problem of matching sets of (i) face appearances under varying illumination and (ii) object appearances under varying viewpoint, using two large data sets. In comparison to the naive matching, the proposed algorithm is shown to greatly increase the separation of between-class and within-class similarities, as well as produce far more meaningful modes of common appearance on which the match score is based.Comment: Pattern Recognition, 201