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

The Right (Angled) Perspective: Improving the Understanding of Road Scenes Using Boosted Inverse Perspective Mapping

Many tasks performed by autonomous vehicles such as road marking detection, object tracking, and path planning are simpler in bird's-eye view. Hence, Inverse Perspective Mapping (IPM) is often applied to remove the perspective effect from a vehicle's front-facing camera and to remap its images into a 2D domain, resulting in a top-down view. Unfortunately, however, this leads to unnatural blurring and stretching of objects at further distance, due to the resolution of the camera, limiting applicability. In this paper, we present an adversarial learning approach for generating a significantly improved IPM from a single camera image in real time. The generated bird's-eye-view images contain sharper features (e.g. road markings) and a more homogeneous illumination, while (dynamic) objects are automatically removed from the scene, thus revealing the underlying road layout in an improved fashion. We demonstrate our framework using real-world data from the Oxford RobotCar Dataset and show that scene understanding tasks directly benefit from our boosted IPM approach.Comment: equal contribution of first two authors, 8 full pages, 6 figures, accepted at IV 201

Efficient motion planning for problems lacking optimal substructure

We consider the motion-planning problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We suggest a natural cost function that balances path length and risk-exposure time. Specifically, we consider the discrete setting where we are given a graph, or a roadmap, and we wish to compute the minimal-cost path under this cost function. Interestingly, paths defined using our cost function do not have an optimal substructure. Namely, subpaths of an optimal path are not necessarily optimal. Thus, the Bellman condition is not satisfied and standard graph-search algorithms such as Dijkstra cannot be used. We present a path-finding algorithm, which can be seen as a natural generalization of Dijkstra's algorithm. Our algorithm runs in $O\left((n_B\cdot n) \log( n_B\cdot n) + n_B\cdot m\right)$ time, where~$n$ and $m$ are the number of vertices and edges of the graph, respectively, and $n_B$ is the number of intersections between edges and the boundary of the risk zone. We present simulations on robotic platforms demonstrating both the natural paths produced by our cost function and the computational efficiency of our algorithm

Logic Programming Applications: What Are the Abstractions and Implementations?

This article presents an overview of applications of logic programming, classifying them based on the abstractions and implementations of logic languages that support the applications. The three key abstractions are join, recursion, and constraint. Their essential implementations are for-loops, fixed points, and backtracking, respectively. The corresponding kinds of applications are database queries, inductive analysis, and combinatorial search, respectively. We also discuss language extensions and programming paradigms, summarize example application problems by application areas, and touch on example systems that support variants of the abstractions with different implementations

Hiding in Plain Sight: Identifying Computational Thinking in the Ontario Elementary School Curriculum

Given a growing digital economy with complex problems, demands are being made for education to address computational thinking (CT) – an approach to problem solving that draws on the tenets of computer science. We conducted a comprehensive content analysis of the Ontario elementary school curriculum documents for 44 CT-related terms to examine the extent to which CT may already be considered within the curriculum. The quantitative analysis strategy provided frequencies of terms, and a qualitative analysis provided information about how and where terms were being used. As predicted, results showed that while CT terms appeared mostly in Mathematics, and concepts and perspectives were more frequently cited than practices, related terms appeared across almost all disciplines and grades. Findings suggest that CT is already a relevant consideration for educators in terms of concepts and perspectives; however, CT practices should be more widely incorporated to promote 21st century skills across disciplines. Future research would benefit from continued examination of the implementation and assessment of CT and its related concepts, practices, and perspectives