14801189
Understanding object motion
Many types of common objects, such as tools and vehicles, usually move in simple ways when they are wielded or driven: the natural axes of the object tend to remain aligned with the local trihedron defined by the object's trajectory. Based on this observation we use a model called Frenet-Serret motion which corresponds to the motion of a moving trihedron along a space curve. Knowing how the Frenet-Serret frame is changing relative to the observer gives us essential information for understanding the object's motion. This is illustrated here for four examples, involving tools (a wrench and a saw) and vehicles (an accelerating van, a turning taxi).
20372308
Navigational Functionalities
203665251
Understanding Object Motion of Tools and Vehicles.
40896374
Qualitative description of camera motion from histograms of normal flow
If we histogram the normal flow vectors in images of a scene viewed by a moving observer, we can use the time-varying histogram to derive qualitative information about the observer's motion-for example, whether it is (primarily) translational or rotational, and whether the direction of translation or axis of rotation is (roughly) parallel or perpendicular to the camera axis. This is illustrated using flow histogram obtained from a variety of real image sequences.
29950481
Graphbots: Mobility in Discrete Spaces
Most previous theoretical work on motion planning has addressed the problem of path planning for geometrically simple robots in geometrically simple regions of Euclidean space (e.g., a planar region containing polygonal obstacles). In this paper we define a natural version of the motion planning problem in a graph theoretic setting. We establish conditions under which a “robot” or team of robots having a particular graph structure can move from any start location to any goal destination in a graph-structured space.
35830748
The function of documents
The purpose of a document is to facilitate the transfer of information from its author to its readers. It is the author's job to design the document so that the information it contains can be interpreted accurately and efficiently. To do this, the author can make use of a set of stylistic tools. In this paper, we introduce the concept of document functionality, which attempts to describe the roles of documents and their components in the process of transferring information. A functional description of a document provides insight into the type of the document, into its intended uses, and into strategies for automatic document interpretation and retrieval. To demonstrate these ideas, we define a taxonomy of functional document components and show how functional descriptions can be used to reverse-engineer the intentions of the author, to navigate in document space, and to provide important contextual information to aid in interpretation.
7200990
Geodesic Convexity in Discrete Spaces
Abstract A pebbled graph is called “(geodesically) convex” if at least one shortest path between any two unpebbled nodes has no pebbles on any of its nodes. There exist conditions on the node neighborhoods in a pebbled graph that imply convexity, but no such conditions can be necessary for convexity. The convex pebblings can be characterized for various special types of graphs, such as cycles, trees, and cliques. For a graph L whose nodes are the lattice points in the plane under the relation of row or column adjacency, we show that a pebbling of L is convex iff the set of unpebbled nodes is connected and orthoconvex.
46687960
Web Grammars
16184629
Digital straightness
A digital arc is called ‘straight’ if it is the digitization of a straight line segment. Since the concept of digital straightness was introduced in the mid-1970’s, dozens of papers on the subject have appeared; many characterizations of digital straight lines have been formulated, and many algorithms for determining whether a digital arc is straight have been defined. This paper reviews the literature on digital straightness and discusses its relationship to other concepts of geometry, the theory of words, and number theory.
206614039
Array Grammars
This tutorial briefly introduces array grammars, in which rewriting rules involve replacement of subarrays by subarrays. Strings can be regarded as one-dimensional arrays; but as we shall see, in higher dimensions special problems arise. In this tutorial we consider only the twodimensional case, but the extension to arbitrary dimensions is straightforward. A more detailed review of array grammars of various types, as well as the corresponding types of array acceptors, can be found in [1]. Array grammars (like string grammars) can be regarded as a class of graph grammars, but it seems more natural to regard them as rewriting systems of a special type.
11867822
Landmarks in Graphs
Navigation can be studied in a graph-structured framework in which the navigating agent (which we shall assume to be a point robot) moves from node to node of a “graph space”. The robot can locate itself by the presence of distinctively labeled “landmark” nodes in the graph space. For a robot navigating in Euclidean space, visual detection of a distinctive landmark provides information about the direction to the landmark, and allows the robot to determine its position by triangulation. On a graph, however, there is neither the concept of direction nor that of visibility. Instead, we shall assume that a robot navigating on a graph can sense the distances to a set of landmarks. 
 
Evidently, if the robot knows its distances to a sufficiently large set of landmarks, its position on the graph is uniquely determined. This suggests the following problem: given a graph, what are the fewest number of landmarks needed, and where should they be located, so that the distances to the landmarks uniquely determine the robot's position on the graph? This is actually a classical problem about metric spaces. A minimum set of landmarks which uniquely determine the robot's position is called a “metric basis”, and the minimum number of landmarks is called the “metric dimension” of the graph. In this paper we present some results about this problem. Our main new results are that the metric dimension of a graph with n nodes can be approximated in polynomial time within a factor of O(log n), and some properties of graphs with metric dimension two.