Large Scale SfM with the Distributed Camera Model

We introduce the distributed camera model, a novel model for Structure-from-Motion (SfM). This model describes image observations in terms of light rays with ray origins and directions rather than pixels. As such, the proposed model is capable of describing a single camera or multiple cameras simultaneously as the collection of all light rays observed. We show how the distributed camera model is a generalization of the standard camera model and describe a general formulation and solution to the absolute camera pose problem that works for standard or distributed cameras. The proposed method computes a solution that is up to 8 times more efficient and robust to rotation singularities in comparison with gDLS. Finally, this method is used in an novel large-scale incremental SfM pipeline where distributed cameras are accurately and robustly merged together. This pipeline is a direct generalization of traditional incremental SfM; however, instead of incrementally adding one camera at a time to grow the reconstruction the reconstruction is grown by adding a distributed camera. Our pipeline produces highly accurate reconstructions efficiently by avoiding the need for many bundle adjustment iterations and is capable of computing a 3D model of Rome from over 15,000 images in just 22 minutes.Comment: Published at 2016 3DV Conferenc

On Deciding Local Theory Extensions via E-matching

Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently encountered is that verification problems are often not fully expressible in the theories supported natively by the solvers. Many solvers allow the specification of application-specific theories as quantified axioms, but their handling is incomplete outside of narrow special cases. In this work, we show how SMT solvers can be used to obtain complete decision procedures for local theory extensions, an important class of theories that are decidable using finite instantiation of axioms. We present an algorithm that uses E-matching to generate instances incrementally during the search, significantly reducing the number of generated instances compared to eager instantiation strategies. We have used two SMT solvers to implement this algorithm and conducted an extensive experimental evaluation on benchmarks derived from verification conditions for heap-manipulating programs. We believe that our results are of interest to both the users of SMT solvers as well as their developers

Lifelong Multi-Agent Path Finding in Large-Scale Warehouses

Multi-Agent Path Finding (MAPF) is the problem of moving a team of agents to their goal locations without collisions. In this paper, we study the lifelong variant of MAPF, where agents are constantly engaged with new goal locations, such as in large-scale automated warehouses. We propose a new framework Rolling-Horizon Collision Resolution (RHCR) for solving lifelong MAPF by decomposing the problem into a sequence of Windowed MAPF instances, where a Windowed MAPF solver resolves collisions among the paths of the agents only within a bounded time horizon and ignores collisions beyond it. RHCR is particularly well suited to generating pliable plans that adapt to continually arriving new goal locations. We empirically evaluate RHCR with a variety of MAPF solvers and show that it can produce high-quality solutions for up to 1,000 agents (= 38.9\% of the empty cells on the map) for simulated warehouse instances, significantly outperforming existing work.Comment: Published at AAAI 202

Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file

Stress-Minimizing Orthogonal Layout of Data Flow Diagrams with Ports

We present a fundamentally different approach to orthogonal layout of data flow diagrams with ports. This is based on extending constrained stress majorization to cater for ports and flow layout. Because we are minimizing stress we are able to better display global structure, as measured by several criteria such as stress, edge-length variance, and aspect ratio. Compared to the layered approach, our layouts tend to exhibit symmetries, and eliminate inter-layer whitespace, making the diagrams more compact