Localized Components Analysis (LoCA) is a new method for describing surface shape variation in an ensemble of objects using a linear subspace of spatially localized shape components. In contrast to earlier methods, LoCA optimizes explicitly for localized components and allows a flexible trade-off between localized and concise representations, and the formulation of locality is flexible enough to incorporate properties such as symmetry. This paper demonstrates that LoCA can provide intuitive presentations of shape differences associated with sex, disease state, and species in a broad range of biomedical specimens, including human brain regions and monkey crania.

We demonstrate an efficient data-parallel algorithm for building large hash tables of millions of elements in real-time. We consider two parallel algorithms for the construction: a classical sparse perfect hashing approach, and cuckoo hashing, which packs elements densely by allowing an element to be stored in one of multiple possible locations. Our construction is a hybrid approach that uses both algorithms. We measure the construction time, access time, and memory usage of our implementations and demonstrate real-time performance on large datasets: for 5 million key-value pairs, we construct a hash table in 35.7 ms using 1.42 times as much memory as the input data itself, and we can access all the elements in that hash table in 15.3 ms. For comparison, sorting the same data requires 36.6 ms, but accessing all the elements via binary search requires 79.5 ms. Furthermore, we show how our hashing methods can be applied to two graphics applications: 3D surface intersection for moving data and geometric hashing for image matching.

We introduce a volumetric space-time technique for the reconstruction of moving and deforming objects from point data. The output of our method is a four-dimensional space-time solid, made up of spatial slices, each of which is a three-dimensional solid bounded by a watertight manifold. The motion of the object is described as an incompressible flow of material through time. We optimize the flow so that the distance material moves from one time frame to the next is bounded, the density of material remains constant, and the object remains compact. This formulation overcomes deficiencies in the acquired data, such as persistent occlusions, errors, and missing frames. We demonstrate the performance of our flow-based technique by reconstructing coherent sequences of watertight models from incomplete scanner data.