Dina Kravets

Bio: Dina Kravets is an academic researcher from New Jersey Institute of Technology. The author has contributed to research in topics: Hausdorff distance & Translation (geometry). The author has an hindex of 3, co-authored 3 publications receiving 191 citations.

Geometric pattern matching under Euclidean motion

Abstract: Given two planar sets A and B, we examine the problem of determining the smallest ϵ such that there is a Euclidean motion (rotation and translation) of A that brings each member of A within distance ϵ of some member of B. We establish upper bounds on the combinatorial complexity of this subproblem in model-based computer vision, when the sets A and B contain points, line segments, or (filled-in) polygons. We also show how to use our methods to substantially improve on existing algorithms for finding the minimum Hausdorff distance under Euclidean motion.

Geometric Pattern Matching Under Euclidean Motion.

Abstract: Given two planar sets A and B, we examine the problem of determining the smallest ϵ such that there is a Euclidean motion (rotation and translation) of A that brings each member of A within distance ϵ of some member of B. We establish upper bounds on the combinatorial complexity of this subproblem in model-based computer vision, when the sets A and B contain points, line segments, or (filled-in) polygons. We also show how to use our methods to substantially improve on existing algorithms for finding the minimum Hausdorff distance under Euclidean motion.

Parallel Searching in Generalized Monge Arrays

Abstract: This paper investigates the parallel time and processor complexities of several searching problems involving Monge, staircase-Monge, and Monge-composite arrays. We present array-searching algorithms for concurrent-read-exclusive-write (CREW) PRAMs, hypercubes, and several hypercubic networks. All these algorithms run in near-optimal time, and their processor-time products are all within an \(O (\lg n)\) factor of the worst-case sequential bounds. Several applications of these algorithms are also given. Two applications improve previous results substantially, and the others provide novel parallel algorithms for problems not previously considered.

Computing the fréchet distance between two polygonal curves

Abstract: As a measure for the resemblance of curves in arbitrary dimensions we consider the so-called Frechet-distance, which is compatible with parametrizations of the curves. For polygonal chains P and Q consisting of p and q edges an algorithm of runtime O(pq log(pq)) measuring the Frechet-distance between P and Q is developed. Then some important variants are considered, namely the Frechet-distance for closed curves, the nonmonotone Frechet-distance and a distance function derived from the Frechet-distance measuring whether P resembles some part of the curve Q.

State of the art in shape matching

Abstract: Large image databases are used in an extraordinary number of multimedia applications in fields such as entertainment, business, art, engineering, and science. Retrieving images by their content, as opposed to external features, has become an important operation. A fundamental ingredient for content-based image retrieval is the technique used for comparing images. There are two general methods for image comparison: intensity based (color and texture) and geometry based (shape). A recent user survey about cognition aspects of image retrieval shows that users are more interested in retrieval by shape than by color and texture [62]. However, retrieval by shape is still considered one of the most difficult aspects of content-based search. Indeed, systems such as IBM’s Query By Image Content, QBIC [57], perhaps one of the most advanced image retrieval systems to date, is relatively successful in retrieving by color and texture, but performs poorly when searching on shape. A similar behavior is exhibited in the new Alta Vista photo finder [10].

Triangulating a simple polygon in linear time

Abstract: We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm.

Shape matching: similarity measures and algorithms

Abstract: Shape matching is an important ingredient in shape retrieval, recognition and classification, alignment and registration, and approximation and simplification. This paper treats various aspects that are needed to solve shape matching problems: choosing the precise problem, selecting the properties of the similarity measure that are needed for the problem, choosing the specific similarity measure, and constructing the algorithm to compute the similarity. The focus is on methods that lie close to the field of computational geometry.

Efficient algorithms for geometric optimization

Abstract: We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, prune-and-search techniques for linear programming and related problems, and LP-type problems and their efficient solution. We then describe a wide range of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other query-type problems.