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Klara Kedem

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Ben Gurion University of the Negev

Morteza Valizadeh

Mohamed Cheriet

Tel Aviv University

Reza Farrahi Moghaddam

École de Technologie Supérieure

Tu Wien

Nikos Papamarkos

Democritus University of Thrace

Stefano Vezzosi

Quang-tuan Luong

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Papers by Klara Kedem

Evolution maps and applications

PeerJ Computer Science, 2016

Common tasks in document analysis, such as binarization, line extraction etc., are still consider... more Common tasks in document analysis, such as binarization, line extraction etc., are still considered difficult for highly degraded text documents. Having reliable fundamental information regarding the characters of the document, such as the distribution of character dimensions and stroke width, can significantly improve the performance of these tasks. We introduce a novel perspective of the image data which maps the evolution of connected components along the change in gray scale threshold. The maps reveal significant information about the sets of elements in the document, such as characters, noise, stains, and words. The information is further employed to improve state of the art binarization algorithm, and achieve automatically character size estimation, line extraction, stroke width estimation, and feature distribution analysis, all of which are hard tasks for highly degraded documents.

Voronoi diagrams of rigidly moving sets of points

ABSTRACT

Walking Around Fat Obstacles

Ipl, Apr 25, 1999

We prove that if an object O is convex and fat then, for any two points a and b on its boundary, ... more We prove that if an object O is convex and fat then, for any two points a and b on its boundary, there exists a path along the boundary, from a to b, whose length is bounded by the length of the line segment ab times some constant. This constant is a function of the fatness-constant and the dimension d. We prove bounds for and show how to e ciently nd paths on the boundary of O whose lengths are within these bounds. As an application of this result, we present a method for computing short paths among convex, fat obstacles in R d by applying de Berg's method for producing a linear-size subdivision of the space. Given a start site and a destination site in the free space, a standard obstacle-avoiding \straight-line" path that is at most some multiplicative constant factor longer than the length of the segment between the sites can be computed e ciently.

Determining Similarity of Conformational Polymorphs

Proceedings of the 10th Annual European Symposium on Algorithms, 2002

Conformational polymorphs are identical molecules that crystallize in different spatial formation... more Conformational polymorphs are identical molecules that crystallize in different spatial formations. Understanding the amount of difference between the polymorphs might aid drug design as there is a widespread assumption that there exists a direct connection between the conformations in the crystallized form of the molecule and the conformations in the solvent. We define a measure of similarity between conformational polymorphs

Geometric Pattern Matching

ABSTRACT We show that, using the L1 metric, the minimum Hausdorff distance under translation betw... more

Efficiently computing the hausdorff distance for point sets under translation

On dynamic Voronoi diagrams and the minimum Hausdorff distance for point sets under Euclidean motion in the plane

Proceedings of the Eighth Annual Symposium on Computational Geometry, Jul 1, 1992

Page 1. On Dynamic Voronoi Diagrams and the Minimum Hausdorff Distance for Point Sets Under Eucli... more

An Efficiently Computable Metric for Polygonal Shapes

Pami, 1986

Finding the Consensus Shape for a Protein Family (Extended Abstract)

Planning algorithm for a convex polygonal object in two-dimensional polygonal space

Discrete Computational Geometry, Jan 3, 1990

On Critical Orientations in the Kedem-Sharir Motion Planning Algorithm for a Convex Polygon in the Plane

Cccg, 1993

We introduce a new method of proving lower bounds on the depth of algebraic d-degree decision (re... more We introduce a new method of proving lower bounds on the depth of algebraic d-degree decision (resp. computation) trees and apply it to prove a lower bound (log N) (resp. (log N= log log N)) for testing membership to an n-dimensional convex polyhedron having N faces of all dimensions, provided that N > (nd) (n) (resp. N > n (n)). This bound apparently does not follow from the methods developed by M. Ben-Or, A. Bj orner, L. Lovasz, and A. Yao B. 83], BLY 93], Y 94] because topological invariants used in these methods become trivial for convex polyhedra.

Exact and Approximate Geometric Pattern Matching for Point Sets in the Plane under Similarity Transformations

Cccg, 2007

We consider the following geometric pattern matching problem: Given two sets of points in the pla... more We consider the following geometric pattern matching problem: Given two sets of points in the plane, P and Q, and some δ > 0, find a similarity transformation (translation, rotation and scale) such that h(T (P), Q) < δ, where h(., .) is the directional Hausdorff distance with L ∞ as the underlying metric. Similarity transformations have not been dealt with in the context of the directional Hausdorff distance and we fill the gap here. We present efficient, exact and approximate algorithms for this problem imposing a reasonable separation restriction on the set Q. For the exact case if the minimum L ∞ distance between every pair of points in Q is 8δ then the problem can be solved in O(n 2 m log n) time where m and n are the number of points in P and Q respectively. If the points in Q are just cδ apart from each other for any 0 < c < 1 we get a randomized approximate solution with expected runtime O(n 2 c −4 ε −8 log 4 mn), where ε > 0 controls the approximation and the answer is correct with high probability.

Improvements on approximate pattern matching

Swat, 1992

An efficient motion planning algorithm for a convex polygonal object in 2-d polygonal space

We present an efficient algorithm for planning the motion of a convex polygonal body B in two-dim... more We present an efficient algorithm for planning the motion of a convex polygonal body B in two-dimensional space bounded by a collection of polygonal obstacles. Our algorithm extends and combines the techniques of Leven and Sharir and of Sifrony and Sharir used for the case in which B is a line segment (a "ladder"). It also makes use of the results of Kedem and Sharir on the planning of translational motion of B amidst polygonal obstacles, and of a recent result of Leven and Sharir on the number of free critical contacts of B with such polygonal obstacles. The algorithm runs in time O(knA6(kn) log kn), where k is the number of sides of B, n is the number of obstacle edges, and A,(q) is an almost linear function of q yielding the maximal number of connected portions of q continuous functions which compose the graph of their lower envelope, where it is assumed that each pair of these functions intersect in at most s points.

Simplifying the reading of historical manuscripts

2015 13th International Conference on Document Analysis and Recognition (ICDAR), 2015

Complex document layouts pose prominent challenges for document image understanding algorithms. T... more Complex document layouts pose prominent challenges for document image understanding algorithms. These layouts impose irregularities on the location of text paragraphs which consequently induces difficulties in reading the text. In this paper we present a robust framework for analyzing historical manuscripts with complex layouts. This framework aims to provide a convenient reading experience for historians through topnotch algorithms for text localization, classification and dewarping. We segment text into spatially coherent regions and text-lines using texture-based filters and refine this segmentation by exploiting Markov Random Fields (MRFs). A principled technique is presented for dewarping curvy text regions using a non-linear geometric transformation. The framework has been validated using a subset of a publicly available dataset of historical documents and it provided promising results.

An Eflicient Algorithm for Planrling Collision-free Translational Motion of a Convex Polygonal Object in 2-dimensional Space Amidst Polygonal Obstacles

Socg, 1985

We state and prove a theorem about the number of points of local nonconvexity in the union of m. ... more We state and prove a theorem about the number of points of local nonconvexity in the union of m. Minkowski sums of planar convex sets, and then apply it to planning a collision-free translational motion of a convex polygon B amidst several (convex) polygonal obstacles Al,…, Am, following a basic approach suggested by Lozano-Perez and Wesley. Assuming that the number

WebGT: An Interactive Web-Based System for Historical Document Ground Truth Generation

2013 12th International Conference on Document Analysis and Recognition, 2013

We present WebGT, the first web-based system to help users produce ground truth data for document... more We present WebGT, the first web-based system to help users produce ground truth data for document images. This user-friendly software system helps historians and computer scientists collectively annotate historical documents. It supports real time collaboration among remote sites independent of the local operating system and also provides several novel semiautomatic tools that have proven effective for annotating degraded documents.

Line Segmentation for Degraded Handwritten Historical Documents

2009 10th International Conference on Document Analysis and Recognition, 2009

We propose a novel approach for text line segmentation based on adaptive local projection profile... more We propose a novel approach for text line segmentation based on adaptive local projection profiles. Our algorithm is suitable for degraded documents with text lines written in large skew. The main novelty of our approach is applying the local algorithm in an incremental manner that adapts to the skew of each text line as it progresses. The proposed approach achieves very accurate results on a set of degraded documents with lines written in different skew angles and curvatures.

Methods for Quantitative Analysis of the Spatial Structure of Dendrites

this paper we present two methods for quantitative discrimination between the 3D structure of den... more this paper we present two methods for quantitative discrimination between the 3D structure of dendrites from different families of GIs, and for comparison between dendrites from the same family. These methods have been implemented at the Computer Science Laboratory at Ben-Gurion University and are now applied in the Zlotowski Center for Neurosciences at Ben-Gurion University. In what follows we present some of our experimental results. The program was written in C++ on a PC using the Visual C++ environment and the OpenGL API. The home page for the implementation is:

An efficient algorithm for planning collision-free translational motion of a convex polygonal object in 2-dimensional space amidst polygonal obstacles

Symposium on Computational Geometry, 1985

We state and prove a theorem about the number of points of local nonconvexity in the union of m. ... more We state and prove a theorem about the number of points of local nonconvexity in the union of m. Minkowski sums of planar convex sets, and then apply it to planning a collision-free translational motion of a convex polygon B amidst several (convex) polygonal obstacles Al,…, Am, following a basic approach suggested by Lozano-Perez and Wesley. Assuming that the number

Evolution maps and applications

PeerJ Computer Science, 2016

Common tasks in document analysis, such as binarization, line extraction etc., are still consider... more Common tasks in document analysis, such as binarization, line extraction etc., are still considered difficult for highly degraded text documents. Having reliable fundamental information regarding the characters of the document, such as the distribution of character dimensions and stroke width, can significantly improve the performance of these tasks. We introduce a novel perspective of the image data which maps the evolution of connected components along the change in gray scale threshold. The maps reveal significant information about the sets of elements in the document, such as characters, noise, stains, and words. The information is further employed to improve state of the art binarization algorithm, and achieve automatically character size estimation, line extraction, stroke width estimation, and feature distribution analysis, all of which are hard tasks for highly degraded documents.

Voronoi diagrams of rigidly moving sets of points

ABSTRACT

Walking Around Fat Obstacles

Ipl, Apr 25, 1999

We prove that if an object O is convex and fat then, for any two points a and b on its boundary, ... more We prove that if an object O is convex and fat then, for any two points a and b on its boundary, there exists a path along the boundary, from a to b, whose length is bounded by the length of the line segment ab times some constant. This constant is a function of the fatness-constant and the dimension d. We prove bounds for and show how to e ciently nd paths on the boundary of O whose lengths are within these bounds. As an application of this result, we present a method for computing short paths among convex, fat obstacles in R d by applying de Berg's method for producing a linear-size subdivision of the space. Given a start site and a destination site in the free space, a standard obstacle-avoiding \straight-line" path that is at most some multiplicative constant factor longer than the length of the segment between the sites can be computed e ciently.

Determining Similarity of Conformational Polymorphs

Proceedings of the 10th Annual European Symposium on Algorithms, 2002

Conformational polymorphs are identical molecules that crystallize in different spatial formation... more Conformational polymorphs are identical molecules that crystallize in different spatial formations. Understanding the amount of difference between the polymorphs might aid drug design as there is a widespread assumption that there exists a direct connection between the conformations in the crystallized form of the molecule and the conformations in the solvent. We define a measure of similarity between conformational polymorphs

Geometric Pattern Matching

ABSTRACT We show that, using the L1 metric, the minimum Hausdorff distance under translation betw... more

Efficiently computing the hausdorff distance for point sets under translation

On dynamic Voronoi diagrams and the minimum Hausdorff distance for point sets under Euclidean motion in the plane

Proceedings of the Eighth Annual Symposium on Computational Geometry, Jul 1, 1992

Page 1. On Dynamic Voronoi Diagrams and the Minimum Hausdorff Distance for Point Sets Under Eucli... more

An Efficiently Computable Metric for Polygonal Shapes

Pami, 1986

Finding the Consensus Shape for a Protein Family (Extended Abstract)

Planning algorithm for a convex polygonal object in two-dimensional polygonal space

Discrete Computational Geometry, Jan 3, 1990

On Critical Orientations in the Kedem-Sharir Motion Planning Algorithm for a Convex Polygon in the Plane

Cccg, 1993

We introduce a new method of proving lower bounds on the depth of algebraic d-degree decision (re... more We introduce a new method of proving lower bounds on the depth of algebraic d-degree decision (resp. computation) trees and apply it to prove a lower bound (log N) (resp. (log N= log log N)) for testing membership to an n-dimensional convex polyhedron having N faces of all dimensions, provided that N > (nd) (n) (resp. N > n (n)). This bound apparently does not follow from the methods developed by M. Ben-Or, A. Bj orner, L. Lovasz, and A. Yao B. 83], BLY 93], Y 94] because topological invariants used in these methods become trivial for convex polyhedra.

Exact and Approximate Geometric Pattern Matching for Point Sets in the Plane under Similarity Transformations

Cccg, 2007

We consider the following geometric pattern matching problem: Given two sets of points in the pla... more We consider the following geometric pattern matching problem: Given two sets of points in the plane, P and Q, and some δ > 0, find a similarity transformation (translation, rotation and scale) such that h(T (P), Q) < δ, where h(., .) is the directional Hausdorff distance with L ∞ as the underlying metric. Similarity transformations have not been dealt with in the context of the directional Hausdorff distance and we fill the gap here. We present efficient, exact and approximate algorithms for this problem imposing a reasonable separation restriction on the set Q. For the exact case if the minimum L ∞ distance between every pair of points in Q is 8δ then the problem can be solved in O(n 2 m log n) time where m and n are the number of points in P and Q respectively. If the points in Q are just cδ apart from each other for any 0 < c < 1 we get a randomized approximate solution with expected runtime O(n 2 c −4 ε −8 log 4 mn), where ε > 0 controls the approximation and the answer is correct with high probability.

Improvements on approximate pattern matching

Swat, 1992

An efficient motion planning algorithm for a convex polygonal object in 2-d polygonal space

We present an efficient algorithm for planning the motion of a convex polygonal body B in two-dim... more We present an efficient algorithm for planning the motion of a convex polygonal body B in two-dimensional space bounded by a collection of polygonal obstacles. Our algorithm extends and combines the techniques of Leven and Sharir and of Sifrony and Sharir used for the case in which B is a line segment (a "ladder"). It also makes use of the results of Kedem and Sharir on the planning of translational motion of B amidst polygonal obstacles, and of a recent result of Leven and Sharir on the number of free critical contacts of B with such polygonal obstacles. The algorithm runs in time O(knA6(kn) log kn), where k is the number of sides of B, n is the number of obstacle edges, and A,(q) is an almost linear function of q yielding the maximal number of connected portions of q continuous functions which compose the graph of their lower envelope, where it is assumed that each pair of these functions intersect in at most s points.

Simplifying the reading of historical manuscripts

2015 13th International Conference on Document Analysis and Recognition (ICDAR), 2015

Complex document layouts pose prominent challenges for document image understanding algorithms. T... more Complex document layouts pose prominent challenges for document image understanding algorithms. These layouts impose irregularities on the location of text paragraphs which consequently induces difficulties in reading the text. In this paper we present a robust framework for analyzing historical manuscripts with complex layouts. This framework aims to provide a convenient reading experience for historians through topnotch algorithms for text localization, classification and dewarping. We segment text into spatially coherent regions and text-lines using texture-based filters and refine this segmentation by exploiting Markov Random Fields (MRFs). A principled technique is presented for dewarping curvy text regions using a non-linear geometric transformation. The framework has been validated using a subset of a publicly available dataset of historical documents and it provided promising results.

An Eflicient Algorithm for Planrling Collision-free Translational Motion of a Convex Polygonal Object in 2-dimensional Space Amidst Polygonal Obstacles

Socg, 1985

We state and prove a theorem about the number of points of local nonconvexity in the union of m. ... more We state and prove a theorem about the number of points of local nonconvexity in the union of m. Minkowski sums of planar convex sets, and then apply it to planning a collision-free translational motion of a convex polygon B amidst several (convex) polygonal obstacles Al,…, Am, following a basic approach suggested by Lozano-Perez and Wesley. Assuming that the number

WebGT: An Interactive Web-Based System for Historical Document Ground Truth Generation

2013 12th International Conference on Document Analysis and Recognition, 2013

We present WebGT, the first web-based system to help users produce ground truth data for document... more We present WebGT, the first web-based system to help users produce ground truth data for document images. This user-friendly software system helps historians and computer scientists collectively annotate historical documents. It supports real time collaboration among remote sites independent of the local operating system and also provides several novel semiautomatic tools that have proven effective for annotating degraded documents.

Line Segmentation for Degraded Handwritten Historical Documents

2009 10th International Conference on Document Analysis and Recognition, 2009

We propose a novel approach for text line segmentation based on adaptive local projection profile... more We propose a novel approach for text line segmentation based on adaptive local projection profiles. Our algorithm is suitable for degraded documents with text lines written in large skew. The main novelty of our approach is applying the local algorithm in an incremental manner that adapts to the skew of each text line as it progresses. The proposed approach achieves very accurate results on a set of degraded documents with lines written in different skew angles and curvatures.

Methods for Quantitative Analysis of the Spatial Structure of Dendrites

this paper we present two methods for quantitative discrimination between the 3D structure of den... more this paper we present two methods for quantitative discrimination between the 3D structure of dendrites from different families of GIs, and for comparison between dendrites from the same family. These methods have been implemented at the Computer Science Laboratory at Ben-Gurion University and are now applied in the Zlotowski Center for Neurosciences at Ben-Gurion University. In what follows we present some of our experimental results. The program was written in C++ on a PC using the Visual C++ environment and the OpenGL API. The home page for the implementation is:

An efficient algorithm for planning collision-free translational motion of a convex polygonal object in 2-dimensional space amidst polygonal obstacles

Symposium on Computational Geometry, 1985

We state and prove a theorem about the number of points of local nonconvexity in the union of m. ... more We state and prove a theorem about the number of points of local nonconvexity in the union of m. Minkowski sums of planar convex sets, and then apply it to planning a collision-free translational motion of a convex polygon B amidst several (convex) polygonal obstacles Al,…, Am, following a basic approach suggested by Lozano-Perez and Wesley. Assuming that the number