1024289
Strong arcs in fuzzy graphs
An arc of a fuzzy graph is called strong if its weight is at least as great as the strength of connectedness of its end nodes when it is deleted. An arc is strong iff its weight is equal to the strength of connectedness of its end nodes. A bridge is strong, but a strong arc need not be a bridge. An arc of maximum weight is strong, but a strong arc need not have maximum weight. In a connected graph, there is a strong path (a path consisting of strong arcs) between any two nodes. A fuzzy graph is a fuzzy tree iff there is a unique strong path between any two of its nodes. In a fuzzy tree, an arc is strong iff it is a bridge, and a strong path between two nodes is a path of maximum strength between them.
11015048
Centers of sets of pixels
Abstract The center of a connected graph G is the set of nodes of G for which the maximum distance to any other node of G is as small as possible. If G is a simply connected set of lattice points (“pixels”) with graph structure defined by 4-neighbor adjacency, we show that the center of G is either a 2×2 square block, a diagonal staircase, or a (dotted) diagonal line with no gaps.
1884675
Fuzzy end nodes in fuzzy graphs
We define a fuzzy end node in a fuzzy graph, and show that no node can be both a cut node and a fuzzy end node. In a fuzzy tree, every node is either a cut node or a fuzzy end node, but the converse is not true. We also show that any nontrivial fuzzy tree has at least two fuzzy end nodes, and we characterize fuzzy cycles that have no cut nodes or no fuzzy end nodes.
20372308
Navigational Functionalities
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).
17212106
Estimating relative vehicle motions in traffic scenes
Abstract Autonomous operation of a vehicle on a road calls for understanding of various events involving the motions of the vehicles in its vicinity. In this paper we show how a moving vehicle which is carrying a camera can estimate the relative motions of nearby vehicles. We show how to “smooth” the motion of the observing vehicle, i.e. to correct the image sequence so that transient motions (primarily rotations) resulting from bumps, etc. are removed and the sequence corresponds more closely to the sequence that would have been collected if the motion had been smooth. We also show how to detect the motions of nearby vehicles relative to the observing vehicle. We present results for several road image sequences which demonstrate the effectiveness of our approach.
121993192
Recognition by Functional Parts
Abstract We present an approach to function-based object recognition that reasons about the functionality of an object's intuitive parts. We extend the popular "recognition by parts" shape recognition framework to support "recognition by functional parts," by combining a set of functional primitives and their relations with a set of abstract volumetric shape primitives and their relations. Previous approaches have relied on more global object features, often ignoring the problem of object segmentation and thereby restricting themselves to range images of unoccluded scenes. We show how these shape primitives and relations can be easily recovered from superquadric ellipsoids which, in turn, can be recovered from either range or intensity images of occluded scenes, Furthermore, the proposed framework supports both unexpected (bottom-up) object recognition and expected (top-down) object recognition, We demonstrate the approach on a simple domain by recognizing a restricted class of hand-tools from 2-D images.
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.