Chaman L. Sabharwal

Implementation of a divide-and-conquer method for intersection of parametric surfaces

Intersection of surfaces is a recurring problem in CAD/CAM and geometric modelling. Such intersections may yield any combination of curves and isolated points. Computation using analytic forms requires n(n - 1)/2 algorithms for n surface equations. Use of parametric forms of the surfaces allows development of a single algorithm dependent only on availability of parametric surface evaluators. The algorithm comprises four steps. First, the surfaces are subdivided using an iterative subdivision process. The subdivision criteria are the curvature and the boundary linearity of local subpieces. Oriented rectangular parallelepipeds cull subpiece pairs which are clearly disjoint. The second step is intersection of subpiece pairs. The subpieces (flat within the subdivision limits) are each approximated by two triangles. The intersection of these triangles in pairs yields a maximum of four linear segments. The third step is a sorting process, using subdivision trees to connect the segments. The final step is refinement of the intersection points. A Newton-Raphson like method improves the placement of the segment endpoints on the two surfaces. The selectivity of subdivision, and placement of refinement after location and sorting serve to reduce evaluations and hence running time for the algorithm. Design and implementation considerations and problems are discussed and some run-times are presented.

Perfect hash table algorithm for image databases using negative associated values

Abstract A 2D string data structure allows for efficient spatial reasoning on an image database for query and retrieval. A 2D string can be converted to a set of triples leading to an elegant O (1) solution for image retrieval with simple queries using a perfect hash table. For complex queries, the retrieval complexity is linear in this approach and depends on the number of possible pairings of picture objects in the query. The perfect hash table computation for this problem is mapped directly to a permutation problem. In an earlier paper [S. K. Bhatia and C. L. Sabharwal, Pattern Recognition 27 , 365–376 (1974)], we presented a set of heuristics that result in a fast computation of associated values, for picture objects, used in the calculation of hash addresses. In this paper, we present an additional heuristic leading to a 90% reduction in search space over our earlier algorithm. The new heuristic promises to generate a minimal perfect hash function for each experimental data set, which was not possible with the earlier algorithms. Mathematical analysis of complexity of the algorithms is presented and is supported by experimental results.

Image databases and near-perfect hash table

Abstract The 2D-string is one of the important data structures to represent spatial information in images and has been used to perform queries in image database systems. A 2D string can be readily converted to a set of triples which can be used to generate a perfect hash table for indexing the image database. The perfect hash table allows for O(1) retrieval in image database but the computation of the hash table itself, by the fastest heuristic algorithm, is of exponential time complexity. Every time the database is modified, the hash table needs to be recomputed. This limits the use of the hash table to applications where the image database is relatively fixed, such as the ones found on a CD-ROM. In this paper, we present an enhancement of the perfect hash table to allow for insertion and deletion in the hash table. The new hash table allows for a relatively small number of collisions and is called near-perfect hash table . It provides the flexibility of a live database while closely approximating the efficiency of retrieval with the perfect hash table as shown by the asymptotic analysis of the search procedure.

Dynamic ID3: a symbolic learning algorithm for many-valued attribute domains

Quinlan’s ID3 machine learning algorithm induces classification trees (rules) horn a set of tiaining exsntplea. The algorithm is extremely effective when training examples are composed of attributes whose values are taken from small discrete domains. The classification accuracy of ID3-po&tced trees on domains whose attributes are many-valued tends to be margirtaf due to the large number of possible values which may be associated with each attribute. Attempts to solve this problem by a priori grouping of attribute values into distinct subsets has met with limited success.

A multiple processor approach to data compression

Fast data compression is necessary for efficient use of computeT slorage and ~ . smiss ion line bandwidth. The importance of utilizing multiple processor computers to speedup the performance of this task grows as the availability of these machines increases. The approach taken in this paper is to distribute the task of data compression among multiple processors in a pipeline architecture. The implementation of this technique was found to beeffective at providing increased compression speeds as the number of processors increased. The ability to use different numbers of processors, in this algorithm, for compression than for decompression provides a basis for wider use and acceptance of this algorithm. The parallel algorithm was implemented on Intel iPSC/860 hypercuhe machine. A wide variety of dam sets found in literature were tested with this technique. Experimental results for speedup and compression ratio are presented. The results provide valuable insight into the effects of software architecture selection, complexity on the compression ratio and speect

A fast implementation of a perfect hash function for picture objects

Abstract In image database systems, symbolic pictures are represented by two-dimensional (2D) strings that are converted into triples. Each triple is mapped to a unique hash address for timely retrieval of pictures, reducing the pattern-matching problem corresponding to a query to that of computation of a hash function. The values associated with the picture objects are used to compute hash addresses for triples developed from the query. Heuristics are proposed to speed up the computation of the associated values for the picture objects. Experimental results show that the new algorithm achieves almost a 90% gain, in search space, over existing algorithms to compute the associated values.

A scalable constraint-based Q-hash indexing for moving objects

In this paper, we develop a Q-hash index structure to efficiently store the position of moving objects. An environment of moving objects contains continuously changing locations which are hard to index using traditional index structures such as R-trees, QuadTrees and their variants. In order to answer the queries accurately, one of the problems faced in storing these positions is the number of updates that have to be made to the database whenever locations change. The high maintenance overhead on updates leads to performance degradation of these index structures; additionally, it makes the database very bulky which results in very poor performance in terms of query execution time. One of the main objectives of the structure we propose is to minimize the number of updates to the database to an optimal number so that the accuracy and response time of the query result are not compromised and at the same time the number of wireless communications can be reduced. The indexing is done using a hashing technique where the hashing function makes use of a region based QuadTree structure. To improve the efficiency of the query processing our index structure helps us define constraints over speed, direction and location of the moving object at the device level which controls the number of updates. In addition, in order to answer different query types efficiently at all levels we propose a three-tier (moving object, regional server, central repository) architecture. Our extensive performance evaluation and comparison of the proposed technique concludes that our scheme outperforms existing Q+R-tree and QuadTree in terms of range query execution time by a high order of magnitude.

Spatial relations between 3D objects

With the proliferation of 3D image data comes the need for advances in automated spatial reasoning. One specific challenge is the need for a practical mapping between spatial reasoning and human cognition, where human cognition is expressed through natural-language terminology. With respect to human understanding, researchers have found that errors about spatial relations typically tend to be metric rather than topological; that is, errors tend to be made with respect to quantitative differences in spatial features. However, topology alone has been found to be insufficient for conveying spatial knowledge in natural-language communication. Based on previous work that has been done to define metrics for two lines and a line and a 2D region in order to facilitate a mapping to natural-language terminology, herein we define metrics appropriate for 3D regions. These metrics extend the notions of previously defined terms such as splitting, closeness, and approximate alongness. The association between this collection of metrics, 3D connectivity relations, and several English-language spatial terms was tested in a human subject study. As spatial queries tend to be in natural language, this study provides preliminary insight into how 3D topological relations and metrics correlate in distinguishing natural-language terms. Defined 3D dependencies and intra-relationships between topological relations and metrics.Association between metrics, 3D connectivity relations, and natural-language terms tested.Found three metric equivalence classes that could define natural-language terms for 3D objects.Found that using topological relation with metrics made no difference in terms of accuracy.

Efficient reasoning with RCC-3D

Qualitative spatial reasoning is an important function of the human brain. Artificial systems that can perform such reasoning have many applications such as Geographic Information Systems (GIS), robotics, biomedicine, and engineering. Automation of such analytical processes alleviates manual labor, and may increase the accuracy of the spatial assessments because the reasoning can be done objectively using 3D digital representations of the objects. Herein we introduce an algorithm to determine the spatial relation that exists between a pair of 3D objects when no a priori spatial knowledge is given. A second algorithm is presented to efficiently find the spatial relation that holds between each pair of objects in a set of 3D objects.

An efficient implementation of parametric line and polygon clipping algorithm

An improved parametric line clipping algorithm is presented. The line clipping algorithm is extended to polygon clipping. The implementations of both the algorithms are novel and outperform many previous algorithms in the literature. This is supported by theoretical consideration and experimental results on randomly selected lines and polygons. The algorithms are implemented in Java. The Java applet allows the user to visualize the experimental results by comparing the existing algorithms and the new algorithms.