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Jinhui Xu

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Presidency University, Kolkata

Jacques Verstraete

University of California, San Diego

Miroslav Chlebik

University of Sussex

STIKI INDONESIA

Tel Aviv University

UNITEC (Honduras)

Anastasios Sidiropoulos

Bundit Laekhanukit

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Papers by Jinhui Xu

On the connectivity preserving minimum cut problem

Journal of Computer and System Sciences, 2014

In this paper, we study a generalization of the classical minimum cut problem, called Connectivit... more In this paper, we study a generalization of the classical minimum cut problem, called Connectivity Preserving Minimum Cut (CPMC) problem, which seeks a minimum cut to separate a pair (or pairs) of source and destination nodes and meanwhile ensure the connectivity between the source and its partner node(s). The CPMC problem is a rather powerful formulation for a set of problems and finds applications in many other areas, such as network security, image processing, data mining, pattern recognition, and machine learning. For this important problem, we consider two variants, connectivity preserving minimum node cut (CPMNC) and connectivity preserving minimum edge cut (CPMEC). For CPMNC, we show that it cannot be approximated within αlogn for some constant α unless P =NP , and cannot be approximated within any poly(logn) unless NP has quasi-polynomial time algorithms. The hardness results hold even for graphs with unit weight and bipartite graphs. Particularly, we show that polynomial time solutions exist * Corresponding author, phone (

Novel Geometric Approach for Virtual Coiling

Theoretical computer science, Jan 22, 2018

Endovascular coiling is a primary treatment for intra-cranial aneurysm, which deploys a thin and ... more Endovascular coiling is a primary treatment for intra-cranial aneurysm, which deploys a thin and detachable metal wire inside the aneurysm so as to prevent its rupture. Emerging evidence from medical research and clinical practice has suggested that the coil configuration inside the aneurysm plays a vital role in properly treating aneurysm and predicting its outcome. In this paper, we propose a novel virtual coiling technique, called , for generating a coil configuration with ensured blocking ability. It can be used as an automatic tool for virtually simulating coiling before its implantation and thus optimizes such treatments. Our approach is based on integer linear programming and computational geometry techniques, and takes into consideration the packing density and coil distribution as the performance measurements. The resulting coiling is deployable (with the help of coil pre-shaping) and with minimized energy. Experimental results on both random and real aneurysm data suggest ...

Rapid virtual stenting for intracranial aneurysms

Medical Imaging 2016: Image-Guided Procedures, Robotic Interventions, and Modeling, 2016

The rupture of Intracranial Aneurysms is the most severe form of stroke with high rates of mortal... more The rupture of Intracranial Aneurysms is the most severe form of stroke with high rates of mortality and disability. One of its primary treatments is to use stent or Flow Diverter to divert the blood flow away from the IA in a minimal invasive manner. To optimize such treatments, it is desirable to provide an automatic tool for virtual stenting before its actual implantation. In this paper, we propose a novel method, called ball-sweeping, for rapid virtual stenting. Our method sweeps a maximum inscribed sphere through the aneurysmal region of the vessel and directly generates a stent surface touching the vessel wall without needing to iteratively grow a deformable stent surface. Our resulting stent mesh has guaranteed smoothness and variable pore density to achieve an enhanced occlusion performance. Comparing to existing methods, our technique is computationally much more efficient.

Special issue: Algorithmic aspects in information and management. Selected papers based on the presentations at the 4th international conference on algorithmic aspects in information and management (AAIM 2008), Fudan, China, June 23–25, 2008

Theoretical Computer Science, 2009

Solving the Chromatic Cone Clustering Problem via Minimum Spanning Sphere

Automata, Languages and Programming, 2011

In this paper, we study the following Chromatic Cone Clustering (CCC) problem: Given n point-sets... more In this paper, we study the following Chromatic Cone Clustering (CCC) problem: Given n point-sets with each containing k points in the first quadrant of the d-dimensional space R d , find k cones apexed at the origin such that each cone contains at least one distinct point (i.e., different from other cones) from every point-set and the total size of the k cones is minimized, where the size of a cone is the angle from any boundary ray to its center line. CCC is motivated by an important biological problem and finds applications in several other areas. For the CCC problem, we consider in this paper the cases that k is either 2 or some other constant number. Our approaches for solving the CCC problem relies on the solutions to the problem of computing a Minimum Spanning Sphere (MinSS) for point-sets. For the MinSS problem, we present two (1 +)-approximation algorithms based on core-sets and-net respectively. With these algorithms, we then show that the CCC problem admits (1 +)-approximation solutions for both cases. Our results use several interesting geometric techniques in high dimensional space, and are the first solutions to these problems.

Special issue: Algorithmic aspects in information and management. Selected papers based on the presentations at the 4th international conference on algorithmic aspects in information and management (AAIM 2008), Fudan, China, June 23–25, 2008

Theoretical Computer Science

Geometric Spanner of Objects under L 1 Distance

Lecture Notes in Computer Science

Geometric spanner is a fundamental structure in computational geometry and plays an important rol... more Geometric spanner is a fundamental structure in computational geometry and plays an important role in many geometric networks design applications. In this paper, we consider the following generalized geometric spanner problem under L1 distance: Given a set of disjoint objects S, find a spanning network G with minimum size so that for any pair of points in different objects of S, there exists a path in G with length no more than t times their L1 distance, where t is the stretch factor. We specifically focus on three types of objects: rectilinear segments, axis aligned rectangles, and rectilinear polygons. By combining the ideas of t-weekly dominating set and imaginary Steiner points, we develop a 2-approximation algorithm for each type of objects. Our algorithms run in near quadratic time, and can be easily implemented for practical applications.

Gauging Association Patterns of Chromosome Territories via Chromatic Median

2013 IEEE Conference on Computer Vision and Pattern Recognition, 2013

Computing accurate and robust organizational patterns of chromosome territories inside the cell n... more Computing accurate and robust organizational patterns of chromosome territories inside the cell nucleus is critical for understanding several fundamental genomic processes, such as co-regulation of gene activation, gene silencing, X chromosome inactivation, and abnormal chromosome rearrangement in cancer cells. The usage of advanced fluorescence labeling and image processing techniques has enabled researchers to investigate interactions of chromosome territories at large spatial resolution. The resulting high volume of generated data demands for high-throughput and automated image analysis methods. In this paper, we introduce a novel algorithmic tool for investigating association patterns of chromosome territories in a population of cells. Our method takes as input a set of graphs, one for each cell, containing information about spatial interaction of chromosome territories, and yields a single graph that contains essential information for the whole population and stands as its structural representative. We formulate this combinatorial problem as a semi-definite programming and present novel techniques to efficiently solve it. We validate our approach on both artificial and real biological data; the experimental results suggest that our approach yields a nearoptimal solution, and can handle large-size datasets, which are significant improvements over existing techniques.

Chromatic Clustering in High Dimensional Space

In this paper, we study a new type of clustering problem, called {\em Chromatic Clustering}, in h... more In this paper, we study a new type of clustering problem, called {\em Chromatic Clustering}, in high dimensional space. Chromatic clustering seeks to partition a set of colored points into groups (or clusters) so that no group contains points with the same color and a certain objective function is optimized. In this paper, we consider two variants of the problem, chromatic $k$-means clustering (denoted as $k$-CMeans) and chromatic $k$-medians clustering (denoted as $k$-CMedians), and investigate their hardness and approximation solutions. For $k$-CMeans, we show that the additional coloring constraint destroys several key properties (such as the locality property) used in existing $k$-means techniques (for ordinary points), and significantly complicates the problem. There is no FPTAS for the chromatic clustering problem, even if $k=2$. To overcome the additional difficulty, we develop a standalone result, called {\em Simplex Lemma}, which enables us to efficiently approximate the me...

Limited view CT reconstruction via constrained metric labeling

2007 IEEE 11th International Conference on Computer Vision, 2007

This paper proposes an new optimization framework for tomographic reconstruction of 3D volumes wh... more This paper proposes an new optimization framework for tomographic reconstruction of 3D volumes when only a limited number of projection views are available. The problem has several important clinical applications spanning coronary angiographic imaging, breast tomosynthesis and dental imaging. We first show that the limited view reconstruction problem can be formulated as a "constrained" version of the metric labeling problem. This lays the groundwork for a linear programming framework that brings together metric labeling classification and classical algebraic tomographic reconstruction (ART) in a unified model. If the imaged volume is known to be comprised of a finite set of attenuation coefficients, given a regular limited view reconstruction as an input, we can view it as a "denoising" task-where voxels must be reassigned subject to maximally maintaining consistency with the input reconstruction and the objective of ART simultaneously. The approach can reliably reconstruct volumes with several multiple contrast objects as well as the simpler binary contrast case which can be solved near-optimally in practice. We present evaluations on cone bean computed tomography, it can also be readily extended to other tomographic modalities as a viable approach for limited-view tomographic reconstruction.

On DDoS Attack Related Minimum Cut Problems

In this paper, we study two important extensions of the classical minimum cut problem, called {\e... more In this paper, we study two important extensions of the classical minimum cut problem, called {\em Connectivity Preserving Minimum Cut (CPMC)} problem and {\em Threshold Minimum Cut (TMC)} problem, which have important applications in large-scale DDoS attacks. In CPMC problem, a minimum cut is sought to separate a of source from a destination node and meanwhile preserve the connectivity between the source and its partner node(s). The CPMC problem also has important applications in many other areas such as emergency responding, image processing, pattern recognition, and medical sciences. In TMC problem, a minimum cut is sought to isolate a target node from a threshold number of partner nodes. TMC problem is an important special case of network inhibition problem and has important applications in network security. We show that the general CPMC problem cannot be approximated within $logn$ unless $NP=P$ has quasi-polynomial algorithms. We also show that a special case of two group CPMC ...

Towards a theory for securing time synchronization in wireless sensor networks

Proceedings of the second ACM conference on Wireless network security - WiSec '09, 2009

Time synchronization in highly distributed wireless systems like sensor and ad hoc networks is ex... more Time synchronization in highly distributed wireless systems like sensor and ad hoc networks is extremely important in order to maintain a consistent notion of time throughout the network and to support the various timing-based applications. But, cheating behavior by the participating nodes in the network can severely jeopardize the accuracy of the associated time synchronization process. Despite recent advances in this direction, a key fundamental question still remains unanswered: Is it theoretically feasible to secure distributed time synchronization protocols, given complete (or global) time and time difference information in the network? In this paper, we attempt to answer this question with the help of sound mathematical modeling and analysis. We first formulate the problem of distributed time synchronization as a Constraint Satisfaction Problem (CSP) in a graphbased model of the network. Then, we prove that efficiently eliminating cheating behavior in distributed time synchronization protocols is combinatorially hard (NP-hard), i.e., it is highly unlikely that there exists an algorithm that solves, or even approximates, this problem in polynomial (in terms of total number of nodes) time. Due to this negative result for the general case, we focus on studying the problem for a special case of the graph-based model of the network, namely completely connected graphs. We derive an upper bound on the best possible solution quality for this problem, propose two polynomial-time approximation strategies, and present an empirical evaluation of their performance.

Computing Maximum Association Graph in Microscopic Nucleus Images

Lecture Notes in Computer Science, 2010

In this paper, we study the problem of finding organization patterns of chromosomes inside the ce... more In this paper, we study the problem of finding organization patterns of chromosomes inside the cell nucleus from microscopic nucleus images. Emerging evidence from cell biology research suggests that global chromosome organization has a vital role in fundamental cell processes related to gene expression and regulation. To understand how chromosome territories are neighboring (or associated) to each other, in this paper we present a novel technique for computing a common association pattern, represented as a Maximum Association Graph (MAG), from the nucleus images of a population of cells. Our approach is based on an interesting integer linear programming formulation of the problem and utilizes inherent observations of the problem to yield optimal solutions. A two-stage technique is also introduced for producing near optimal approximations for large data sets.

High-contrast artifact reduction in cone beam computed tomography by using geometric techniques

SPIE Proceedings, 2009

The use of cone beam computed tomography (CBCT) is growing in the clinical arena, due to its abil... more The use of cone beam computed tomography (CBCT) is growing in the clinical arena, due to its ability to provide 3-D information during interventions, its high diagnostic quality (sub-millimeter resolution), and its short scanning times (10 seconds). In many situations, the reconstructions suffer from artifacts from high contrast objects (due mainly to angular sampling by the projections or by beam hardening) which can reduce image quality. In this study, we propose a novel algorithm to reduce these artifacts. In our approach, these objects are identified and then removed in the sinogram space by using computational geometry techniques. In particular, the object is identified in a reconstruction from a few views. Then, the rays (projection lines) intersecting the high contrast objects are identified using the technique of topological walk in a dual space which effectively models the problem as a visibility problem and provides a solution in optimal time and space complexity. As a result, the corrections can be performed in real time, independent of the projection image size. Subsequently, a full reconstruction is performed by leaving out the high contrast objects in the reconstructions. Evaluations were performed using simulations and animal studies. The artifacts are significantly reduced when using our approach. This optimal time and space complexity and relative simple implementation makes our approach attractive for artifact reduction.

Efficient Algorithms for Segmenting Globally Optimal and Smooth Multi-surfaces

Lecture Notes in Computer Science, 2011

Despite extensive studies in the past, the problem of segmenting globally optimal single and mult... more Despite extensive studies in the past, the problem of segmenting globally optimal single and multiple surfaces in 3D volumetric images remains challenging in medical imaging. The problem becomes even harder in highly noisy and edge-weak images. In this paper we present a novel and highly efficient graph-theoretical iterative method with bi-criteria of global optimality and smoothness for both single and multiple surfaces. Our approach is based on a volumetric graph representation of the 3D image that incorporates curvature information. To evaluate the convergence and performance of our method, we test it on a set of 14 3D OCT images. Our experiments suggest that the proposed method yields optimal (or almost optimal) solutions in 3 to 5 iterations. To the best of our knowledge, this is the first algorithm that utilizes curvature in objective function to ensure the smoothness of the generated surfaces while striving for achieving global optimality. Comparing to the best existing approaches, our method has a much improved running time, yields almost the same global optimality but with much better smoothness, which makes it especially suitable for segmenting highly noisy images.

Algorithms for congruent sphere packing and applications

Proceedings of the seventeenth annual symposium on Computational geometry - SCG '01, 2001

Towards a theory of a solution space for the biplane imaging geometry problem

Medical Physics, 2006

Biplane angiographic imaging is a primary method for visual and quantitative assessment of the va... more Biplane angiographic imaging is a primary method for visual and quantitative assessment of the vasculature. In order to reliably reconstruct the three-dimensional ͑3D͒ position, orientation, and shape of the vessel structure, a key problem is to determine the rotation matrix R and the translation vector t which relate the two coordinate systems. This so-called Imaging Geometry Determination problem is well studied in the medical imaging and computer vision communities and a number of interesting approaches have been reported. Each such technique determines a solution which yields 3D vasculature reconstructions with errors comparable to other techniques. From the literature, we see that different techniques with different optimization strategies yield reconstructions with equivalent errors. We have investigated this behavior, and it appears that the error in the input data leads to this equivalence effectively yielding what we call the solution space of feasible geometries, i.e., geometries which could be solutions given the error or uncertainty in the input image data. In this paper, we lay the theoretical framework for this concept of a solution space of feasible geometries using simple schematic constructions, deriving the underlying mathematical relationships, presenting implementation details, and discussing implications and applications of the proposed idea. Because the solution space of feasible geometries encompasses equivalent solutions given the input error, the solution space approach can be used to evaluate the precision of calculated geometries or 3D data based on known or estimated uncertainties in the input image data. We also use the solution space approach to calculate an imaging geometry, i.e., a solution.

Ensemble clustering using semidefinite programming with applications

Machine Learning, 2009

In this paper, we study the ensemble clustering problem, where the input is in the form of multip... more In this paper, we study the ensemble clustering problem, where the input is in the form of multiple clustering solutions. The goal of ensemble clustering algorithms is to aggregate the solutions into one solution that maximizes the agreement in the input ensemble. We obtain several new results for this problem. Specifically, we show that the notion of agreement under such circumstances can be better captured using a 2D string encoding rather than a voting strategy, which is common among existing approaches. Our optimization proceeds by first constructing a non-linear objective function which is then transformed into a 0-1 Semidefinite program (SDP) using novel convexification techniques. This model can be subsequently relaxed to a polynomial time solvable SDP. In addition to the theoretical contributions, our experimental results on standard machine learning and synthetic datasets show that this approach leads to improvements not only in terms of the proposed agreement measure but also the existing agreement measures based on voting strategies. In addition, we identify several new application scenarios for this problem. These include combining

Generalized median graphs and applications

Journal of Combinatorial Optimization, 2008

Abstract We study the so-called Generalized Median graph problem where the task is to construct a... more Abstract We study the so-called Generalized Median graph problem where the task is to construct a prototype (ie, a &amp;amp;amp;amp;amp;amp;#x27;model&amp;amp;amp;amp;amp;amp;#x27;) from an input set of graphs. While our pri-mary motivation comes from an important biological imaging application, the prob- ... This work was supported by NSF ...

Efficient Algorithms for Determining 3-D Bi-Plane Imaging Geometry

Journal of Combinatorial Optimization, 2005

Biplane projection imaging is one of the primary methods for imaging and visualizing the cardiova... more Biplane projection imaging is one of the primary methods for imaging and visualizing the cardiovascular system in medicine. A key problem in such a technique is to determine the imaging geometry (i.e., the relative rotation and translation) of two projections so that the 3-D structure can be accurately reconstructed. Based on interesting observations and efficient geometric techniques, we present in this paper new algorithmic solutions for this problem. Comparing with existing optimization-based approaches, our techniques yield better accuracy and have bounded execution time, thus is more suitable for on-line applications. Our techniques can easily detect outliers to further improve the accuracy.

On the connectivity preserving minimum cut problem

Journal of Computer and System Sciences, 2014

In this paper, we study a generalization of the classical minimum cut problem, called Connectivit... more In this paper, we study a generalization of the classical minimum cut problem, called Connectivity Preserving Minimum Cut (CPMC) problem, which seeks a minimum cut to separate a pair (or pairs) of source and destination nodes and meanwhile ensure the connectivity between the source and its partner node(s). The CPMC problem is a rather powerful formulation for a set of problems and finds applications in many other areas, such as network security, image processing, data mining, pattern recognition, and machine learning. For this important problem, we consider two variants, connectivity preserving minimum node cut (CPMNC) and connectivity preserving minimum edge cut (CPMEC). For CPMNC, we show that it cannot be approximated within αlogn for some constant α unless P =NP , and cannot be approximated within any poly(logn) unless NP has quasi-polynomial time algorithms. The hardness results hold even for graphs with unit weight and bipartite graphs. Particularly, we show that polynomial time solutions exist * Corresponding author, phone (

Novel Geometric Approach for Virtual Coiling

Theoretical computer science, Jan 22, 2018

Endovascular coiling is a primary treatment for intra-cranial aneurysm, which deploys a thin and ... more Endovascular coiling is a primary treatment for intra-cranial aneurysm, which deploys a thin and detachable metal wire inside the aneurysm so as to prevent its rupture. Emerging evidence from medical research and clinical practice has suggested that the coil configuration inside the aneurysm plays a vital role in properly treating aneurysm and predicting its outcome. In this paper, we propose a novel virtual coiling technique, called , for generating a coil configuration with ensured blocking ability. It can be used as an automatic tool for virtually simulating coiling before its implantation and thus optimizes such treatments. Our approach is based on integer linear programming and computational geometry techniques, and takes into consideration the packing density and coil distribution as the performance measurements. The resulting coiling is deployable (with the help of coil pre-shaping) and with minimized energy. Experimental results on both random and real aneurysm data suggest ...

Rapid virtual stenting for intracranial aneurysms

Medical Imaging 2016: Image-Guided Procedures, Robotic Interventions, and Modeling, 2016

The rupture of Intracranial Aneurysms is the most severe form of stroke with high rates of mortal... more The rupture of Intracranial Aneurysms is the most severe form of stroke with high rates of mortality and disability. One of its primary treatments is to use stent or Flow Diverter to divert the blood flow away from the IA in a minimal invasive manner. To optimize such treatments, it is desirable to provide an automatic tool for virtual stenting before its actual implantation. In this paper, we propose a novel method, called ball-sweeping, for rapid virtual stenting. Our method sweeps a maximum inscribed sphere through the aneurysmal region of the vessel and directly generates a stent surface touching the vessel wall without needing to iteratively grow a deformable stent surface. Our resulting stent mesh has guaranteed smoothness and variable pore density to achieve an enhanced occlusion performance. Comparing to existing methods, our technique is computationally much more efficient.

Special issue: Algorithmic aspects in information and management. Selected papers based on the presentations at the 4th international conference on algorithmic aspects in information and management (AAIM 2008), Fudan, China, June 23–25, 2008

Theoretical Computer Science, 2009

Solving the Chromatic Cone Clustering Problem via Minimum Spanning Sphere

Automata, Languages and Programming, 2011

In this paper, we study the following Chromatic Cone Clustering (CCC) problem: Given n point-sets... more In this paper, we study the following Chromatic Cone Clustering (CCC) problem: Given n point-sets with each containing k points in the first quadrant of the d-dimensional space R d , find k cones apexed at the origin such that each cone contains at least one distinct point (i.e., different from other cones) from every point-set and the total size of the k cones is minimized, where the size of a cone is the angle from any boundary ray to its center line. CCC is motivated by an important biological problem and finds applications in several other areas. For the CCC problem, we consider in this paper the cases that k is either 2 or some other constant number. Our approaches for solving the CCC problem relies on the solutions to the problem of computing a Minimum Spanning Sphere (MinSS) for point-sets. For the MinSS problem, we present two (1 +)-approximation algorithms based on core-sets and-net respectively. With these algorithms, we then show that the CCC problem admits (1 +)-approximation solutions for both cases. Our results use several interesting geometric techniques in high dimensional space, and are the first solutions to these problems.

Special issue: Algorithmic aspects in information and management. Selected papers based on the presentations at the 4th international conference on algorithmic aspects in information and management (AAIM 2008), Fudan, China, June 23–25, 2008

Theoretical Computer Science

Geometric Spanner of Objects under L 1 Distance

Lecture Notes in Computer Science

Geometric spanner is a fundamental structure in computational geometry and plays an important rol... more Geometric spanner is a fundamental structure in computational geometry and plays an important role in many geometric networks design applications. In this paper, we consider the following generalized geometric spanner problem under L1 distance: Given a set of disjoint objects S, find a spanning network G with minimum size so that for any pair of points in different objects of S, there exists a path in G with length no more than t times their L1 distance, where t is the stretch factor. We specifically focus on three types of objects: rectilinear segments, axis aligned rectangles, and rectilinear polygons. By combining the ideas of t-weekly dominating set and imaginary Steiner points, we develop a 2-approximation algorithm for each type of objects. Our algorithms run in near quadratic time, and can be easily implemented for practical applications.

Gauging Association Patterns of Chromosome Territories via Chromatic Median

2013 IEEE Conference on Computer Vision and Pattern Recognition, 2013

Computing accurate and robust organizational patterns of chromosome territories inside the cell n... more Computing accurate and robust organizational patterns of chromosome territories inside the cell nucleus is critical for understanding several fundamental genomic processes, such as co-regulation of gene activation, gene silencing, X chromosome inactivation, and abnormal chromosome rearrangement in cancer cells. The usage of advanced fluorescence labeling and image processing techniques has enabled researchers to investigate interactions of chromosome territories at large spatial resolution. The resulting high volume of generated data demands for high-throughput and automated image analysis methods. In this paper, we introduce a novel algorithmic tool for investigating association patterns of chromosome territories in a population of cells. Our method takes as input a set of graphs, one for each cell, containing information about spatial interaction of chromosome territories, and yields a single graph that contains essential information for the whole population and stands as its structural representative. We formulate this combinatorial problem as a semi-definite programming and present novel techniques to efficiently solve it. We validate our approach on both artificial and real biological data; the experimental results suggest that our approach yields a nearoptimal solution, and can handle large-size datasets, which are significant improvements over existing techniques.

Chromatic Clustering in High Dimensional Space

In this paper, we study a new type of clustering problem, called {\em Chromatic Clustering}, in h... more In this paper, we study a new type of clustering problem, called {\em Chromatic Clustering}, in high dimensional space. Chromatic clustering seeks to partition a set of colored points into groups (or clusters) so that no group contains points with the same color and a certain objective function is optimized. In this paper, we consider two variants of the problem, chromatic $k$-means clustering (denoted as $k$-CMeans) and chromatic $k$-medians clustering (denoted as $k$-CMedians), and investigate their hardness and approximation solutions. For $k$-CMeans, we show that the additional coloring constraint destroys several key properties (such as the locality property) used in existing $k$-means techniques (for ordinary points), and significantly complicates the problem. There is no FPTAS for the chromatic clustering problem, even if $k=2$. To overcome the additional difficulty, we develop a standalone result, called {\em Simplex Lemma}, which enables us to efficiently approximate the me...

Limited view CT reconstruction via constrained metric labeling

2007 IEEE 11th International Conference on Computer Vision, 2007

This paper proposes an new optimization framework for tomographic reconstruction of 3D volumes wh... more This paper proposes an new optimization framework for tomographic reconstruction of 3D volumes when only a limited number of projection views are available. The problem has several important clinical applications spanning coronary angiographic imaging, breast tomosynthesis and dental imaging. We first show that the limited view reconstruction problem can be formulated as a "constrained" version of the metric labeling problem. This lays the groundwork for a linear programming framework that brings together metric labeling classification and classical algebraic tomographic reconstruction (ART) in a unified model. If the imaged volume is known to be comprised of a finite set of attenuation coefficients, given a regular limited view reconstruction as an input, we can view it as a "denoising" task-where voxels must be reassigned subject to maximally maintaining consistency with the input reconstruction and the objective of ART simultaneously. The approach can reliably reconstruct volumes with several multiple contrast objects as well as the simpler binary contrast case which can be solved near-optimally in practice. We present evaluations on cone bean computed tomography, it can also be readily extended to other tomographic modalities as a viable approach for limited-view tomographic reconstruction.

On DDoS Attack Related Minimum Cut Problems

In this paper, we study two important extensions of the classical minimum cut problem, called {\e... more In this paper, we study two important extensions of the classical minimum cut problem, called {\em Connectivity Preserving Minimum Cut (CPMC)} problem and {\em Threshold Minimum Cut (TMC)} problem, which have important applications in large-scale DDoS attacks. In CPMC problem, a minimum cut is sought to separate a of source from a destination node and meanwhile preserve the connectivity between the source and its partner node(s). The CPMC problem also has important applications in many other areas such as emergency responding, image processing, pattern recognition, and medical sciences. In TMC problem, a minimum cut is sought to isolate a target node from a threshold number of partner nodes. TMC problem is an important special case of network inhibition problem and has important applications in network security. We show that the general CPMC problem cannot be approximated within $logn$ unless $NP=P$ has quasi-polynomial algorithms. We also show that a special case of two group CPMC ...

Towards a theory for securing time synchronization in wireless sensor networks

Proceedings of the second ACM conference on Wireless network security - WiSec '09, 2009

Time synchronization in highly distributed wireless systems like sensor and ad hoc networks is ex... more Time synchronization in highly distributed wireless systems like sensor and ad hoc networks is extremely important in order to maintain a consistent notion of time throughout the network and to support the various timing-based applications. But, cheating behavior by the participating nodes in the network can severely jeopardize the accuracy of the associated time synchronization process. Despite recent advances in this direction, a key fundamental question still remains unanswered: Is it theoretically feasible to secure distributed time synchronization protocols, given complete (or global) time and time difference information in the network? In this paper, we attempt to answer this question with the help of sound mathematical modeling and analysis. We first formulate the problem of distributed time synchronization as a Constraint Satisfaction Problem (CSP) in a graphbased model of the network. Then, we prove that efficiently eliminating cheating behavior in distributed time synchronization protocols is combinatorially hard (NP-hard), i.e., it is highly unlikely that there exists an algorithm that solves, or even approximates, this problem in polynomial (in terms of total number of nodes) time. Due to this negative result for the general case, we focus on studying the problem for a special case of the graph-based model of the network, namely completely connected graphs. We derive an upper bound on the best possible solution quality for this problem, propose two polynomial-time approximation strategies, and present an empirical evaluation of their performance.

Computing Maximum Association Graph in Microscopic Nucleus Images

Lecture Notes in Computer Science, 2010

In this paper, we study the problem of finding organization patterns of chromosomes inside the ce... more In this paper, we study the problem of finding organization patterns of chromosomes inside the cell nucleus from microscopic nucleus images. Emerging evidence from cell biology research suggests that global chromosome organization has a vital role in fundamental cell processes related to gene expression and regulation. To understand how chromosome territories are neighboring (or associated) to each other, in this paper we present a novel technique for computing a common association pattern, represented as a Maximum Association Graph (MAG), from the nucleus images of a population of cells. Our approach is based on an interesting integer linear programming formulation of the problem and utilizes inherent observations of the problem to yield optimal solutions. A two-stage technique is also introduced for producing near optimal approximations for large data sets.

High-contrast artifact reduction in cone beam computed tomography by using geometric techniques

SPIE Proceedings, 2009

The use of cone beam computed tomography (CBCT) is growing in the clinical arena, due to its abil... more The use of cone beam computed tomography (CBCT) is growing in the clinical arena, due to its ability to provide 3-D information during interventions, its high diagnostic quality (sub-millimeter resolution), and its short scanning times (10 seconds). In many situations, the reconstructions suffer from artifacts from high contrast objects (due mainly to angular sampling by the projections or by beam hardening) which can reduce image quality. In this study, we propose a novel algorithm to reduce these artifacts. In our approach, these objects are identified and then removed in the sinogram space by using computational geometry techniques. In particular, the object is identified in a reconstruction from a few views. Then, the rays (projection lines) intersecting the high contrast objects are identified using the technique of topological walk in a dual space which effectively models the problem as a visibility problem and provides a solution in optimal time and space complexity. As a result, the corrections can be performed in real time, independent of the projection image size. Subsequently, a full reconstruction is performed by leaving out the high contrast objects in the reconstructions. Evaluations were performed using simulations and animal studies. The artifacts are significantly reduced when using our approach. This optimal time and space complexity and relative simple implementation makes our approach attractive for artifact reduction.

Efficient Algorithms for Segmenting Globally Optimal and Smooth Multi-surfaces

Lecture Notes in Computer Science, 2011

Despite extensive studies in the past, the problem of segmenting globally optimal single and mult... more Despite extensive studies in the past, the problem of segmenting globally optimal single and multiple surfaces in 3D volumetric images remains challenging in medical imaging. The problem becomes even harder in highly noisy and edge-weak images. In this paper we present a novel and highly efficient graph-theoretical iterative method with bi-criteria of global optimality and smoothness for both single and multiple surfaces. Our approach is based on a volumetric graph representation of the 3D image that incorporates curvature information. To evaluate the convergence and performance of our method, we test it on a set of 14 3D OCT images. Our experiments suggest that the proposed method yields optimal (or almost optimal) solutions in 3 to 5 iterations. To the best of our knowledge, this is the first algorithm that utilizes curvature in objective function to ensure the smoothness of the generated surfaces while striving for achieving global optimality. Comparing to the best existing approaches, our method has a much improved running time, yields almost the same global optimality but with much better smoothness, which makes it especially suitable for segmenting highly noisy images.

Algorithms for congruent sphere packing and applications

Proceedings of the seventeenth annual symposium on Computational geometry - SCG '01, 2001

Towards a theory of a solution space for the biplane imaging geometry problem

Medical Physics, 2006

Biplane angiographic imaging is a primary method for visual and quantitative assessment of the va... more Biplane angiographic imaging is a primary method for visual and quantitative assessment of the vasculature. In order to reliably reconstruct the three-dimensional ͑3D͒ position, orientation, and shape of the vessel structure, a key problem is to determine the rotation matrix R and the translation vector t which relate the two coordinate systems. This so-called Imaging Geometry Determination problem is well studied in the medical imaging and computer vision communities and a number of interesting approaches have been reported. Each such technique determines a solution which yields 3D vasculature reconstructions with errors comparable to other techniques. From the literature, we see that different techniques with different optimization strategies yield reconstructions with equivalent errors. We have investigated this behavior, and it appears that the error in the input data leads to this equivalence effectively yielding what we call the solution space of feasible geometries, i.e., geometries which could be solutions given the error or uncertainty in the input image data. In this paper, we lay the theoretical framework for this concept of a solution space of feasible geometries using simple schematic constructions, deriving the underlying mathematical relationships, presenting implementation details, and discussing implications and applications of the proposed idea. Because the solution space of feasible geometries encompasses equivalent solutions given the input error, the solution space approach can be used to evaluate the precision of calculated geometries or 3D data based on known or estimated uncertainties in the input image data. We also use the solution space approach to calculate an imaging geometry, i.e., a solution.

Ensemble clustering using semidefinite programming with applications

Machine Learning, 2009

In this paper, we study the ensemble clustering problem, where the input is in the form of multip... more In this paper, we study the ensemble clustering problem, where the input is in the form of multiple clustering solutions. The goal of ensemble clustering algorithms is to aggregate the solutions into one solution that maximizes the agreement in the input ensemble. We obtain several new results for this problem. Specifically, we show that the notion of agreement under such circumstances can be better captured using a 2D string encoding rather than a voting strategy, which is common among existing approaches. Our optimization proceeds by first constructing a non-linear objective function which is then transformed into a 0-1 Semidefinite program (SDP) using novel convexification techniques. This model can be subsequently relaxed to a polynomial time solvable SDP. In addition to the theoretical contributions, our experimental results on standard machine learning and synthetic datasets show that this approach leads to improvements not only in terms of the proposed agreement measure but also the existing agreement measures based on voting strategies. In addition, we identify several new application scenarios for this problem. These include combining

Generalized median graphs and applications

Journal of Combinatorial Optimization, 2008

Abstract We study the so-called Generalized Median graph problem where the task is to construct a... more Abstract We study the so-called Generalized Median graph problem where the task is to construct a prototype (ie, a &amp;amp;amp;amp;amp;amp;#x27;model&amp;amp;amp;amp;amp;amp;#x27;) from an input set of graphs. While our pri-mary motivation comes from an important biological imaging application, the prob- ... This work was supported by NSF ...

Efficient Algorithms for Determining 3-D Bi-Plane Imaging Geometry

Journal of Combinatorial Optimization, 2005

Biplane projection imaging is one of the primary methods for imaging and visualizing the cardiova... more Biplane projection imaging is one of the primary methods for imaging and visualizing the cardiovascular system in medicine. A key problem in such a technique is to determine the imaging geometry (i.e., the relative rotation and translation) of two projections so that the 3-D structure can be accurately reconstructed. Based on interesting observations and efficient geometric techniques, we present in this paper new algorithmic solutions for this problem. Comparing with existing optimization-based approaches, our techniques yield better accuracy and have bounded execution time, thus is more suitable for on-line applications. Our techniques can easily detect outliers to further improve the accuracy.