We present an approach to learning features that represent the local geometry around a point in an unstructured point cloud. Such features play a central role in geometric registration, which supports diverse applications in robotics and 3D vision. Current state-of-the-art local features for unstructured point clouds have been manually crafted and none combines the desirable properties of precision, compactness, and robustness. We show that features with these properties can be learned from data, by optimizing deep networks that map high-dimensional histograms into low-dimensional Euclidean spaces. The presented approach yields a family of features, parameterized by dimension, that are both more compact and more accurate than existing descriptors.

BackgroundThe immune system behaves like a complex, dynamic network with interacting elements including leukocytes, cytokines, and chemokines. While the immune system is broadly distributed, leukocytes must communicate effectively to respond to a pathological challenge. The Basic Immune Simulator 2010 contains agents representing leukocytes and tissue cells, signals representing cytokines, chemokines, and pathogens, and virtual spaces representing organ tissue, lymphoid tissue, and blood. Agents interact dynamically in the compartments in response to infection of the virtual tissue. Agent behavior is imposed by logical rules derived from the scientific literature. The model captured the agent-to-agent contact history, and from this the network topology and the interactions resulting in successful versus failed viral clearance were identified. This model served to integrate existing knowledge and allowed us to examine the immune response from a novel perspective directed at exploiting complex dynamics, ultimately for the design of therapeutic interventions.ResultsAnalyzing the evolution of agent-agent interactions at incremental time points from identical initial conditions revealed novel features of immune communication associated with successful and failed outcomes. There were fewer contacts between agents for simulations ending in viral elimination (win) versus persistent infection (loss), due to the removal of infected agents. However, early cellular interactions preceded successful clearance of infection. Specifically, more Dendritic Agent interactions with TCell and BCell Agents, and more BCell Agent interactions with TCell Agents early in the simulation were associated with the immune win outcome. The Dendritic Agents greatly influenced the outcome, confirming them as hub agents of the immune network. In addition, unexpectedly high frequencies of Dendritic Agent-self interactions occurred in the lymphoid compartment late in the loss outcomes.ConclusionsAn agent-based model capturing several key aspects of complex system dynamics was used to study the emergent properties of the immune response to viral infection. Specific patterns of interactions between leukocyte agents occurring early in the response significantly improved outcome. More interactions at later stages correlated with persistent inflammation and infection. These simulation experiments highlight the importance of commonly overlooked aspects of the immune response and provide insight into these processes at a resolution level exceeding the capabilities of current laboratory technologies.

Optimizing a stress model is a natural technique for drawing graphs: one seeks an embedding into R d which best preserves the induced graph metric. Current approaches to solving the stress model for a graph with |V| nodes and |E| edges require the full all-pairs shortest paths (APSP) matrix, which takes O(|V| 2 log |E| + |V||E|) time and O(|V| 2 ) space. We propose a novel algorithm based on a low-rank approximation to the required matrices. The crux of our technique is an observation that it is possible to approximate the full APSP matrix, even when only a small subset of its entries are known. Our algorithm takes time O(k|V| + |V| log |V| + |E|) per iteration with a preprocessing time of O(k 3 + k(|E| + |V| log |V|) + k 2 |V|) and memory usage of O(k|V|), where a user-defined parameter k trades off quality of approximation with running time and space. We give experimental results which show, to the best of our knowledge, the largest (albeit approximate) full stress model based layouts to date.