Efficient Image Retrieval through Vantage Objects

We describe a new indexing structure for general image retrieval that relies solely on a distance function giving the similarity between two images. For each image object in the database, its distance to a set of m predetermined vantage objects is calculated; the m-vector of these distances specifies a point in the m-dimensional vantage space. The database objects that are similar (in terms of the distance function) to a given query object can be determined by means of an efficient nearest-neighbor search on these points. We demonstrate the viability of our approach through experimental results obtained with a database of about 48,000 hieroglyphic polylines

Range Searching in Low-Density Environments

this paper we argue that this property, which is in fact more general than the fatness condition, may be more suitable for the analysis of "real life" motion planning problems. The floorplan for a building, for instance, will often contain long and thin walls and is therefore not modelled well as a set of fat objects. Still, it may often form a low-density environment (a formal definition of this notion is given below). The results of van der Stappen do not immediately generalize to this more general setting. The reason for this is that most of his algorithms are based on a data structure due to Overmars and van der Stappen for range searching with small ranges [5]. This data structure stores a set of fat objects. A query consists of an arbitrarily shaped range whose size is comparable to the size of the smallest object, and returns the set of objects intersecting the range. This data structure is interesting because it implements range searching queries by performing many point location queries in the set of objects, which are themselves implemented using a structure due to Overmars [4]. The number of point location queries depends on the shape of the objects---van der Stappen could only prove bounds for convex and for polygonal fat objects---, their size, the size of the query range, and on the "fatness coefficient" of the objects (see below for details). Even in simple cases, this number can be quite large. In the example of Figure 1, for instance, 156;800 point location queries are necessary with their approach to determine the objects intersecting the query region R. In this paper we show that the data structures for point location and for range searching with small ranges can indeed be generalized to low-density R Fig. 1. A set of 20-fat objects and a sample que..

Motion Planning for Multiple Robots

We study the motion-planning problem for pairs and triples of robots operating in a shared workspace containing n obstacles. A standard way to solve such problems is to view the collection of robots as one composite robot, whose number of degrees of freedom is d, the sum of the numbers of degrees of freedom of the individual robots. We show that it is su cient to consider a constant number of robot systems whose number of degrees of freedom is at most d, 1 for pairs of robots, and d, 2 for triples. (The result for a pair assumes that the sum of the number of degrees of freedom of the robots constituting the pair reduces by at least one if the robots are required to stay incontact; for triples a similar assumption is made. Moreover, for triples we need to assume that a solution with positive clearance exists.) We use this to obtain an O(n d) time algorithm to solve the motion-planning problem for a pair of robots; this is one order of magnitude faster than what the standard method would give. For a triple of robots the running time becomes O(n d,1), which istwo orders of magnitude faster than the standard method. We also apply our method to the case of a collection of bounded-reach robots moving in a low-density environment. Here the running time of our algorithm becomes O(n log n) both for pairs and triples

Realistic Input Models for Geometric Algorithms

Many algorithms developed in computational geometry are needlessly complicated and slow because they have to be prepared for very complicated, hypothetical inputs. To avoid this, realistic models are needed that describe the properties that realistic inputs have, so that algorithms can de designed that take advantage of these properties. This can lead to algorithms that are provably efficient in realistic situations. We obtain some fundamental results in this research direction. In particular, we have the following results. ffl We show the relations between various models that have been proposed in the literature. ffl For several of these models, we give algorithms to compute the model parameter(s) for a given scene; these algorithms can be used to verify whether a model is appropriate for typical scenes in some application area. ffl As a case study, we give some experimental results on the appropriateness of some of the models for one particular type of scenes often encountered in ..

Motion Planning for Multiple Robots

We study the motion-planning problem for pairs and triples of robots operating in a shared workspace containing n obstacles. A standard way to solve such problems is to view the collection of robots as one composite robot, whose number of degrees of freedom is d, the sum of the numbers of degrees of freedom of the individual robots. We show that it is sufficient to consider a constant number of robot systems whose number of degrees of freedom is at most d \Gamma 1 for pairs of robots, and d \Gamma 2 for triples. (The result for a pair assumes that the sum of the number of degrees of freedom of the robots constituting the pair reduces by at least one if the robots are required to stay in contact; for triples a similar assumption is made. Moreover, for triples we need to assume that a solution with positive clearance exists.) We use this to obtain an O(n d ) time algorithm to solve the motion-planning problem for a pair of robots; this is one order of magnitude faster than what the st..

Models and motion planning

AbstractWe study the complexity of the motion planning problem for a bounded-reach robot in the situation where the n obstacles in its workspace satisfy two of the realistic models proposed in the literature, namely unclutteredness and small simple-cover complexity. We show that the maximum complexity of the free space of a robot with f degrees of freedom in the plane is Θ(nf/2+n) for uncluttered environments as well as environments with small simple-cover complexity. The maximum complexity of the free space of a robot moving in a three-dimensional uncluttered environment is Θ(n2f/3+n). All these bounds fit nicely between the Θ(n) bound for the maximum free-space complexity for low-density environments and the Θ(nf) bound for unrestricted environments. Surprisingly—because contrary to the situation in the plane—the maximum free-space complexity is Θ(nf) for a three-dimensional environment with small simple-cover complexity

Realistic Input Models for Geometric Algorithms

Many algorithms developed in computational geometry are needlessly complicated and slow because they have to be prepared for very complicated, hypothetical inputs. To avoid this, realistic models are needed that describe the properties that realistic inputs have, so that algorithms can de designed that take advantage of these properties. This can lead to algorithms that are provably e cient in realistic situations. We obtain some fundamental results in this research direction. In particular, we have the following results. We show the relations between various models that have been proposed in the literature. For several of these models, we give algorithms to compute the model parameter(s) for a given scene; these algorithms can be used to verify whether a model is appropriate for typical scenes in some application area. As a case study, we give some experimental results on the appropriateness of some of the models for one particular type of scenes often encountered in geographic information systems, namely certain triangulated irregular networks

Models and Motion Planning

We study the complexity of the motion planning problem for a bounded-reach robot in the situation where the n obstacles in its workspace satisfy two of the realistic models proposed in the literature, namely unclutteredness and small simple-cover complexity. We show that the maximum complexity of the free space of a robot with f degrees of freedom in the plane is #(n f/2 + n) for uncluttered environments as well as environments with small simple-cover complexity. The maximum complexity of the free space of a robot moving in a three-dimensional uncluttered environment is #(n 2f/3 +n). All these bounds fit nicely between the #(n) bound for the maximum free-space complexity for low-density environments and the #(n f ) bound for unrestricted environments. Surprisingly---because contrary to the situation in the plane---the maximum free-space complexity is #(n f ) for a three-dimensional environment with small simple-cover complexity