The Taub Faculty of Computer Science Events and Talks

New Algorithms for Ranking and Dimension Reduction The study of ranking crosses many disciplines. Social choice theoreticians have been interested for centuries in finding a good way to rank a set of candidates. Econometricians have been asking for decades how people choose from (and more generally rank) alternative sets. More recently, information retrieval theoreticians and practitioners have been interested in ranking search query results. In verification, practitione...
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Partial matching is probably one of the most challenging problems in shape analysis. The problem consists of matching similar parts of shapes that are dissimilar on the whole. Conceptually, two shapes can be considered partially matching if they have significant similar parts, with the simplest definition of significance being the size of the parts. Thus, partial matching can be defined as a multcriterion optimization problem trying to simultaneously maximize the similarit...
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An important goal in algorithms and communication protocols is getting the deterministic time complexity, respectively communication complexity, closer to the best known randomized complexity. In this work, we investigate the case where instead of one input, the algorithm \ protocol is given multiple \emph{independent} samples from an \emph{arbitrary unknown} distribution. We show that in this case a strong derandomization result can be obtained by a simple argument. O...
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DNA microarrays make it possible to record the complete molecular biological signals that guide the progression of cellular processes on genomic scales. I will describe the ability of mathematical models, that were created from these data using matrix and tensor computations, to predict previously unknown biological as well as physical principles, which govern the activities of DNA and RNA. 
First, I will describe the use of singular value decomposition to uncover "asymmetric He...
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Abstract: The Ramsey number $r_k(s,n)$ is the minimum $N$ such that every red-blue coloring of the $k$-tuples of an $N$-element set contains either a red set of size $s$ or a blue set of size $n$, where a set is called red (blue) if all $k$-tuples from this set are red (blue). The problem of estimating Ramsey numbers is one of the central problems in modern Combinatorics and it has received a considerable amount of attention in the last 80 years. In this talk we p...
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The growth in the number of digital photographs calls for new and improved image editing tools to help users view, navigate and manipulate them. Many of these tasks can be reduced to instances of organizing visual data to satisfy user constraints. In this talk I will present three such tools that help organize visual data at the pixel, patch and image level: Seam Carving, The Patch Transform, and Infinite Images. Seam Carving attempts to retarget an image to fit a specific displa...
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Many problems in image processing are addressed via the minimization of a cost functional. The most prominent optimization technique is the gradient descent, often used due to its simplicity and applicability where other techniques, e.g., those coming from discrete optimization, can not be used. Yet, gradient descent suffers from a slow convergence, and often to just local minima which highly depends on the condition number of the functional Hessian. Newton-type methods, on the ot...
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We will continue from "Policy syntax" this meeting (after a quick review of the previous one). We will also see how to write an SELinux module to keep a certain application under control. SELinux is an access permission system, which is running in many recent distributions (with or without the computer owner's awareness). Understanding how this system works seems to become a necessity for a smooth administration of an updated Linux machine. ...
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Subdivision schemes became popular in recent years in applications such as computer graphics and CAGD (computer aided geometric design). Their implementation is rather simple, yet there is a rich mathematical theory behind them. We will introduce two basic subdivision schemes, (corner cutting and the 4-point) and present implementation of them in computer graphics and in animation....
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Many interesting questions in coding theory revolve around conflicts (tradeoffs). Among them are a conflict between structure and randomness, and a conflict between density and symmetry. In some of the cases the conflicts are helpful in understanding solutions for questions (e.g. using the structure and randomness conflict we obtain improved analysis of Reed Muller codes), while in other cases these conflicts shed light on the inherent difficulty of the questions. In the...
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Small regulatory RNAs are a class of non-coding RNAs that are primarily involved in post-transcriptional gene silencing. The principle members of this growing class are microRNAs and small interfering RNAs (siRNAs) which guide a silencing complex to an mRNA target by base pairing at the 3 untranslated region (3UTR). In recent years, microRNAs have emerged as a major class of regulatory genes central to a wide range of cellular activities, and their importance i...
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We consider private data analysis in the setting in which a trusted and trustworthy curator, having obtained a large data set containing private information, releases to the public a "sanitization'' of the data set that simultaneously protects the privacy of the individual contributors of data and offers utility to the data analyst. We focus on the case where the process is non-interactive; once the sanitization has been released the original data and the curator play no...
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Recent methods for learning the similarities between images have presented impressive results on the problem of pair-matching (same/not-same classification) of face images. In this talk we present pair-matching results comparing the performance of image descriptor based methods to the state of the art in same/not-same classification, obtained on the Labeled Faces in the Wild (LFW) image set. We propose various contributions, spanning several aspects of automatic ...
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A function $f$ is $\delta$-hard for some class of circuits if every circuit in the class errs on a $\delta$-fraction of the inputs. For various classes of constant depth small size circuits there are explicit functions that are $\delta$-hard for ``small'' values of $\delta$. For stronger circuit classes there are many ``hardness amplification theorems'' that show how to transform any $\delta$-hard function $f$ into a ``harder'' function $g$ that is $(1/2-\epsilon)$-har...
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In this reading group, we will study the parallel repetition theorem, its connection to unique games and tiling in high dimensional spaces. The parallel repetition theorem [Raz 1998] has been extremely useful to compute the exact inapproximability of several optimization problems. Two years ago, Holenstein gave a simplified proof of Raz's theorem. Since then, there has been a flurry of activity in this area: understanding the behavior for special type of 2-prover g...
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Consider the ``plain'' multiparty communication complexity model, where k players $P_1,\dots,P_k$ holding inputs $x_1,\dots,x_k\in\bit^n$ (respectively) communicate in order to compute the value $f(x_1,\dots,x_k)$. The main lower bound technique for such communication problems is that of {\em partition arguments}: partition the $k$-players into two disjoint sets of players and find a lower bound for the induced two-party communication complexity problem. In this paper, we s...
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The idea of using topology in order to solve combinatorial problems has been known for several decades, but only recently it started to become an organized theory. In my talk I will introduce several classical topological theorems such as Brouwer's fixed point theorem and Sperner's Lemma and give the basic methods for using them in combinatorial settings. I will also describe a new approach that may enable us to use the Borsuk Ulam theorem in similar settings and hopefully o...
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Ever since the work of Cook and Levin, satisfiability has been recognized as a central problem in computational complexity. It is widely believed to be intractable, and yet till recently even a linear-time logarithmic-space algorithm was not ruled out. The last few years have seen considerable progress in time-space lower bounds for satisfiability and closely related problems on various models of computation. This talk will describe the state-of-the-art on ...
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This talk provides an introduction to quasispecies theory, a framework for modeling evolutionary dynamics that was originally introduced to study problems related to the origin of life. Since the original formulation of the theory by Manfred Eigen in 1971, quasispecies theory has been used to study evolutionary processes in a variety of other contexts, but with a focus on molecular and viral evolution. In recent years, we have worked to steadily develop quasispecies theory into a ...
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We initiate the study of scenarios that combine both online decision making and interaction between non-cooperative agents. To this end we introduce the notion of online games that model such scenarios as non-cooperative games, and lay out the foundations for studying this model. Roughly speaking, an online game captures systems in which independent agents serve requests in a common environment. The requests arrive in an online fashion and each is designated to be served by a diff...
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Sensors, signal processing hardware, and algorithms are under increasing pressure to accommodate ever larger data sets; ever faster sampling and processing rates; ever lower power consumption; and radically new sensing modalities. Fortunately, there have been enormous increases in computational power. This progress has motivated Compressed Sensing (CS), an emerging field based on the revelation that a sparse signal can be reconstructed from a small number of linear measurem...
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The discussion of the structured condition number and Gauss' method for computing the roots of a polynomial shows that a sequence of greatest common divisor (GCD) computations of two polynomials must be performed. This is a classical problem in mathematics that is often solved by Euclid's algorithm. This algorithm is satisfactory for symbolic computations with exact polynomials, but the computation of the GCD of inexact polynomials is not trivial because it is ill-posed (not i...
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See program and invitation להלן הזמנה ותוכנית הכנס...
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In this talk, I would like to present a user interface for drawing mathematical figures which can be quite complex. The system is based on a sketch interface especially designed for drawing mathematical figures. I would also like to present a search interface that finds figures similar to the one drawn by the user. Given a sketch by the user, the system searches a database of pre-drawn figures, automatically finds similar figures, and shows them in a certain sorted order...
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We study the limits of efficient computation in the context of constructing random-looking graph distributions that can be used to emulate huge random graphs over N=2^n vertices. We suggest and analyze a new criterion of faithful emulation, inspired by the famous 0/1-law of random graphs. This 0/1-law states that any graph property T holds with probability converging either to 0 or to 1, whenever T is expressible by a single formula on graphs. We consider preservi...
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The K-SVD algorithm is a powerful tool for image denoising but computationally quite intensive. In order to accelerate it we implement the most time consuming parts like sparse coding and assembling the final denoised image vectorized and in parallel on the Cell processor. The Cell processor is a heterogeneous multicore system consisting of a general purpose Power-PC processor unit (PPU) and several fast co-processors, the synergistic processor elements (SPEs). We present r...
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Identifying and quantifying the sharing of genetic material between individuals within a population is an important step in accurately using genealogical relationships for disease analysis as well as improving our understanding of demography. However, exhaustive pairwise analysis which has been successful in small cohorts cannot keep up with the current torrent of genotype data. We present GERMLINE, a robust algorithm for identifying pairwise segmental shar...
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Abstract: The discovery that deterministic statements can be proved by probabilistic reasoning, led already more than fifty years ago to several striking results in various mathematical disciplines. It soon became clear that the method, which is now called the probabilistic method, is a very powerful tool for proving results in Discrete Mathematics. After some light examples that illustrate the fact that probabilistic arguments may be counter-intuitive, I will sketch...
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The lecture topics are: 1) Real Time programming in a nutshell. 2) Programming languages comparison (Real Time related). 3) Java vs. C/C++ with relevant benchmarks. 4) Why Java, Why Java for Real Time? 5) What is the Real Time Java Standard? 6) Sun Real Time Java technology 7) Customers and case studies 6) Real Time Java competitive landscape For more information please contact David: David.Roitman at Sun.com ...
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We show that the NP-Complete language 3Sat has a PCP verifier that makes two queries to a proof of almost-linear size and achieves sub-constant probability of error o(1). The verifier performs only projection tests, meaning that the answer to the first query determines at most one accepting answer to the second query. Previously, by the parallel repetition theorem, there were PCP Theorems with two-query projection tests, but only (arbitrarily small) constant erro...
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will discuss a recent lower bound of Omega(n^(k/4)) on the size of depth-d circuits for the k-clique problem on n-node graphs. This improves previous lower bounds (e.g. Omega(n^(k/89d2)) [P. Beame '90]) by removing dependence on d from the exponent of n. This result has an interesting corollary in logic: it implies that the "bounded variable logics" FO1, FO2, ..., FO^k, ... (where FO^k consists of first-order sentences in which no subformula has no more than k free variab...
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We describe several new methodologies for developing and evaluating novel diagnostics for diabetes and cancer. In the first part of the talk we describe the Gene Network Enrichment Analysis (GNEA) methodology for identifying molecular markers for diabetes. This approach suggests that network based techniques might be more sensitive and accurate at identifying disease progression than single genes. At the same time we should pay significant attention to both the biological inter...
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This talk will describe new active learning processes for automated modeling of dynamical systems across a number of disciplines. One of the long-standing challenges in robotics is achieving robust and adaptive performance under uncertainty. One approach to adaptive behavior is based on self-modeling, where a system continuously evolves multiple simulators of itself in order to make useful predictions. The robot is rewarded for actions that cause disagreement among predictions of ...
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The recent ability to measure quickly and inexpensively dense sets of points on physical objects has deeply influenced the way engineers represent shapes in CAD systems, animation software or in the game industry. Many researchers advocated to completely bypass smooth surface representations, and to stick to a dense mesh model throughout the design process. Yet smooth analytic representations are still required in standard CAD systems and animation software, for reas...
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An error correcting code is said to be locally testable if there is a test that can check whether a given string is a codeword of the code, or rather far from the code, by reading only a constant number of symbols of the string. Locally Testable Codes (LTCs) were first explicitly studied by Goldreich and Sudan (J. ACM 53(4)) and since then several constructions of LTCs were suggested. While the best known construction of LTCs achieves very efficient parameter...
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The central problem in computational mechanism design is the tension between incentive compatibility and computational efficiency. We address this question in the context of a novel mechanism design problem which we call the combinatorial public project problem. We show that, even though this problem is easily solvable from a computational viewpoint, and from an economic perspective, no algorithm which is simultaneously truthful and runs in polynomial-time can obtain any...
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Regarding the workings of the human mind, memory and pattern recognition seem to be intertwined. You generally do not have one without the other. Taking inspiration from life experience, a new form of computer memory has been devised. Certain conjectures about human memory are keys to the central idea. The design of a practical and useful "cognitive" memory system is contemplated, a memory system that may also serve as a model for many aspects of human memory. The new memory...
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With the recent advances in technology, we are faced with the need to process increasingly larger amounts of data increasingly faster. Originally, a problem was considered computable if there was an algorithm that could decide it in finite time given any input instance. Later came the notion of polynomial time computation, and then the possibility of making computations faster through use of parallel machines. However, the algorithms involved still face the obvious obstacle of...
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Quite a number of problems involving inference from data, whether visual data or otherwise, fall into the category of optimization. I will describe a general scheme for sequential and parallel (message passing) update rules based on the framework of Fenchel duality. The presentation will be done in the context of two applications (i) distributed (parallel) Support-Vector-Machines (SVM) for handling large scale problems (to be presented at CVPR'08), (ii) Graphical Model inference...
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Path planning for robots in unknown terrain has been studied in both theoretical robotics and theoretical computer science. However, empirical robotics researchers have often developed their own planning methods. These planning methods have been demonstrated on mobile robots that solve complex real-world tasks and perform well in practice. I will discuss some of these planning methods (namely, Planning with the Freespace Assumption, Greedy Mapping and Greedy Localization) and show...
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What does it take to build fast simulators for cloth and thin shells—in particular to do so with code that is simple to implement, debug, and maintain? Our group's belief is that simple geometric observations help to address all these goals. I will survey my students' recent work on the discrete differential geometry of thin, flexible surfaces, and focus on a couple simple geometric observations that lead to efficient and simple models for bending, stretching, and artisti...
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We introduce a variant of Quantum Multi Prover Interactive Proofs (QMIP), where the provers do not share entanglement, the communication between the verifier and the provers is quantum, but the provers are unlimited in the classical communication between them. At first, this model may seem very weak, as provers who exchange information seem to be equivalent in power to a simple prover. This in fact is not the case - we show that any language in NEXP can be recognized in thi...
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Digital processing of analog signals naturally requires a representation of continuous time signals as a discrete-time sequence. The most common representation of this type is based on the Shannon-Nyquist sampling theorem which provides an exact representation for band limited signals sampled at a sufficiently high rate but leads to aliasing error when the signal is under sampled. In this talk a number of other approaches are discussed to obtai...
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Eukaryotic splicing structures are known to involve a high degree of alternative forms derived from a premature transcript by alternative splicing (AS). With the advent of new sequencing technologies, evidence for new splice forms becomes more and more easily availablebit by bit revealing that the true splicing diversity of "AS events often comprises more than two alternatives and therefore cannot be sufficiently described by pairwise comparisons as conducted in analyzes hitherto....
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Classical results in high-dimensional geometry from the 1970's state that a random subspace of R^N of dimension N/2 has "distortion" O(1) w.h.p where the distortion is measured by sqrt{N} times the largest ratio of the L_2 to L_1 norms of a vector in the subspace. (So each vector in the subspace has its mass spread nearly evenly over a constant fraction of the coordinates.) This result is a particular example of the use of the probabilistic method, a technique which is ubiquitous ...
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Abstarct:In this talk we describe the ciphers and protocols used for the GSM cellular phone network, and discuss the (in)security of the system. We describe several techniques to attack the ciphers A5/2 and A5/1, and how they can be applied as a ciphertext-only attack. We also show that active attacks on the protocols can recover keys of ciphers that are not used during that transmission. As a result, it is possible to listen in to GSM phone conversations, steal calls during...
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3D Objects Description and Classification by Implicit Polynomials ...
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A Kakeya set in F^n, where F is a finite field, is a set containing a line in every direction. The finite field Kakeya conjecture states that the size of such sets is bounded from below by C_n*|F|^n, where C_n depends only on the dimension n. I will talk about the recent proof of this conjecture and its connection to problems in theoretical computer science....
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The black hole information loss paradox has plagued scientists since Hawking's discovery that black holes evaporate thermally in contradiction to the unitarity expected by quantum mechanics. I will explain just what the problem is, and show that one of the central presumptions of the debate is incorrect. It had been thought that (obviously) either all the information must remain in the black hole until it has completely evaportate OR it must leak out earlier. Howeve...
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A $d$-dimensional polycube is a connected set of $d$-dimensional cubes on an orthogonal lattice, where connectivity is through $(d-1)$-dimensional faces. A polycube is said to be proper in $d$ dimensions if it spans all the $d$ dimensions, that is, the convex hull of the centers of all its cubes is $d$-dimensional. We prove a few new formulae for the numbers of (proper and total) polycubes, and show that (2d-3)e + O(1/d) is the asymptotic growth rate of the number o...
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Model checking is an automated technique for checking whether or not a given system model fulfills a desired property, described as a temporal logic formula. Yet, as real models tend to be very big, model checking encounters the state-explosion problem, which refers to its high space requirements. Two of the most successful approaches to fighting the state-explosion problem in model checking are abstraction and compositional model checking. Abstractions hide certain detai...
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Fluid simulations typically produce complex three-dimensional iso-surfaces whose geometry and topology change over time. The standard way of representing such dynamic geometry is by a set of iso-surfaces that are extracted individually at certain time steps. An alternative strategy is to represent the whole sequence as a four-dimensional tetrahedral mesh. The iso-surface at a specific time step can then be computed by intersecting the tetrahedral mesh with a three-dimens...
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$d$-dimensional polycubes are the generalization of planar polyominoes to higher dimensions. That is, a $d$-D polycube of size $n$ is a connected set of $n$ cells (hypercubes) of an orthogonal $d$-dimensional lattice, where connectivity is through $(d-1)$-dimensional faces of the cells. Computing $A_d(n)$, the number of distinct $d$-dimensional polycubes of size $n$, is a long-standing elusive problem in discrete geometry. In a previous work we described the generalization ...
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We survey applications of classical and of time-sequential sampling theory and some of its recent extensions, respectively, in two complementary areas. First to reduce the computation for tomographic reconstruction from $O(N^3)$ to $O(N^2\log N)$ for an $N \times N$ image, with similar acceleration for 3D images. And second, to reduce acquisition requirements for dynamic imaging below those predicted by classical theory. In both areas, the savings demonstrated in practic...
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We will describe the results from a series of papers, starting from papers of Forster, Ben-David and others to more recent works of Sherstov and Chattopadhyay. The topics of these papers are learning, communication and computational complexity. Examples of some contributions of these papers are 1. The first lower bound on unbounded error probabilistic communication complexity. 2. Definition and study of learning theoretic quantities such as margin complexity...
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In this work we study a wide range of online covering and packing problems with various objectives. We provide a unified approach, based on a clean primal-dual method, for the design and analysis of online algorithms for this large class of problems. In particular, our analysis uses weak duality rather than a tailor made (i.e., problem specific) potential function. We show how to apply the primal-dual approach to many interesting problems. Examples consist of the ski rental prob...
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I shall discuss the many ways one can do optimal image or signal denoising, and the difficulties in selecting between the various optimal solutions. ...
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A basic construct in many distributed systems is the detection of global properties over distributed data. Examples include a wireless sensor network, where we would like to receive an alert every time the average of the temperature readings taken by the sensors exceeds a given threshold, or a distributed search engine, where we would like to determine the set of search terms whose frequency of use exceeds a given threshold. Until recently, research has focus on detecting gl...
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Motion estimation plays an important role in modern video coders. In such coders, motion is estimated using a block matching algorithm that estimates the amount of motion on a block‐by‐block basis. A full search technique for finding the best matching blocks delivers good accuracy but is usually not practical because of its high computational complexity. In this talk, a novel fast block‐based motion estimation algorithm is presented. This algorithm uses an efficient projecti...
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Reingold, Vadhan and Wigderson [FOCS'00] introduced the graph zig-zag product. This product combines a large graph and a small graph into one graph, such that the resulting graph inherits its size from the large graph, its degree from the small graph and its spectral gap from both. Using this product they gave the first fully-explicit combinatorial construction of expander graphs. They showed how to construct $D$-regular graphs having spectral gap $1-O(D^{-\frac{1}{3}})$. In...
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CGGC Seminar: Deforming objects in a "shape preserving" manner is a challenging problem with various applications in geometric modeling and computer graphics. In this talk I will examine two geometric-driven approaches to the problem. First, reformulating the problem using the notion of Cartan's moving frames reveals an intriguing relationship between harmonic maps into the group of rotations and shape preserving deformations. The moving frames are known in di...
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The basic foundations of the Internet are surprisingly vulnerable to simple attacks that could be mounted by rogue hackers or result from simple misconfiguration. One area that remains particularly exposed to attacks is routing: packets usually traverse many intermediate routers on their way from a source to their destination. Since these routers may belong to other (possibly malicious) organizations, how do we guarantee that our packets arrive as intended at their desti...
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The lecture deals with invariance in image processing, with emphasis on invariance of shapes and curves. There are two main topics. First, we consider scale invariance, review existing scale invariant measures and discuss the different ways in which an algorithm can be scale invariant. We then point out some dangers inherent in fully scale invariant algorithms. Second, we present an equi-affine invariant shape matching mathod, which is also invariant to resampling, robust to...
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The edit distance between two strings is defined as the number of insertions/deletions/substitutions needed to transform one string into the other. This distance plays a key role in several fields like computational biology and text processing. Edit distance appears to be notoriously difficult to deal with algorithmically (both theoretically and in practice). However, no nontrivial computational lower bounds for it are known, and the only negative evidence known i...
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The mathematical theorem having the longest proof is the classification of the finite simple groups. In this talk we will try to understand the statement of the theorem and its importance. The lecture will be in Hebrew. ההרצאה תינתן בעברית....
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Multi-camera environments allow exploiting spatial redundancy that might be used by analysis algorithms to produce more robust results. These algorithms may be applied for a variety of tasks ranging from human 3D scene volume reconstruction, human motion capture, gesture analysis or focus of attention tracking. Combining this multi-camera information with audio information would allow defining multimodal data analysis systems. This talk will present two research lines within...
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We show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits. More formally, if there exists an explicit polynomial f(x_1,...,x_m) that cannot be computed by a depth d arithmetic circuit of small size then there exists an efficient deterministic algorithm to test whether a given depth d-8 circuit is identically zero or not (assuming the individual degrees of the tested circuit are ...
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Our world is filled with nonrigid objects that can deform and bend. Nonrigid shapes appear at all scales - from our body, its organs and tissues, to tiny bacteria and microscopic protein molecules. When trying to analyze nonrigid shapes the richness of the possible deformations poses a challenge due to the large number of degrees of freedom. Thus, generally speaking, explicit analysis of nonrigid objects has so far been avoided. Today, there is a co...
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Random field models characterize the correlation among neighboring pixels in an image. Specifically, a wide-sense Markov model is obtained by assuming a separable correlation function for a 2D auto-regressive (AR) model. This model is applicable to image restoration, image compression, and texture classification and segmentation. In this work we explore the effect of sampling on statistical features of an image such as histogram and the autocorrelation function. We show that the M...
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"The Challenge", Definitions, GUI, basic and smart geometry in 2D and 3D, basic model, "styled" model, shape manipulations, hybrid design, develop challenge. ...
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Given a function f:[n]-->{0,1}, its k-wise direct product encoding is the function F:[n]^k --> {0,1}^k defined by F(x_1,..x_k) = (f(x_1),...,f(x_k)) This simple "encoding" is useful in PCP-like settings, when we want to simulate reading k arbitrary values of f by accessing only a constant number of inputs of the encoding F. The main challenge is to test that a given F is indeed a "correct" encoding of some f by reading only few (ultimately 2) random values in F. This is ca...
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Multiple sequence alignments possess important information, not only about functionally and structurally important conserved regions, but also about coupling between residues. Recently we have developed a unique method to detect such coupling based on substitution matrices of residue pairs. I will describe the method and show how it performs at structural analysis tasks as contact prediction and discrimination of decoy sets. I will then show recent results that demonstrate how cor...
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Consider the following simple type of approximation algorithms: limit the set of possible outcomes, and completely optimize over the restricted subrange. In this talk we will study the power of this type of algorithms in two settings: multi-unit auctions, and combinatorial auctions with subadditive bidders. From a game-theoretic point of view, our results provide a characterization of the power of the main positive result of mechanism design the VCG mechanism. Another ...
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A Delaunay triangulation restricted to a surface is obtained by filtering a 3D Delaunay triangulation. Filtering herein consists of selecting a subset of the 3D Delaunay facets whose dual edges intersect the surface. In this talk I will explain how the restricted Delaunay triangulation paradigm can be used to simultaneously mesh a surface together with its interior. I will then describe two mesh generation algorithms along these lines and show a demo made with components fro...
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The complex diffusion process, recently introduced in image processing and computer vision by combining the linear diffusion equation and the 'free-particle' Schrödinger equation, is further generalized by incorporating the Schrödinger potential. We incorporate the potential into the complex diffusion equation, introducing some kind of 'dynamic boundary conditions' that serve as a filtering or even enhancing mechanism for textures. The Schrödinger potential is self-adopting to ...
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1. Basic concepts in algebraic geometry (affine and projective varieties, morphisms, dimension, degree) 2. Computational tools: Groebner basis, resultants 3. Basic applications including solving polynomial systems 4. Some more involved constructions like Grassmannians and Chow forms. ...
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The Computational Geometry Algorithms Library, CGAL, is the largest software collection of algorithms and data structures in Computational Geometry available today. It started a little over a decade ago as a European research project with a small number of partners and has grown over the years to be a huge open source project. The arrangement package of CGAL, developed at Tel Aviv University, constructs, maintains, traverses, and answers queries on two-dimensional arrangem...
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We show that disjointness requires randomized communication Omega(n^{1/2k} / (k-1)2^{k-1}2^{2^{k-1}}) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound was Omega (\log n / k-1). By results of Beame, Pitassi, and Segerlind, this implies 2^{n^{Omega(1)}} lower bounds on the size of tree-like Lovasz-Schrijver proof systems needed to refute certain unsatisfiable CNFs, and super-polynomial lower bounds on the size of any tree-lik...
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We show that disjointness requires randomized communication Omega(n^{1/2k}/{(k-1)2^{k-1}2^{2^{k-1}}) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound was Omega((log n)/k-1). By results of Beame, Pitassi, and Segerlind, this implies 2^{n^{Omega(1)} lower bounds on the size of tree-like Lovasz-Schrijver proof systems needed to refute certain unsatisfiable CNFs, and super-polynomial lower bounds on the size of any tree-like p...
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Algorithms for video-based human motion capture typically assume the body shape is known a priori and is represented coarsely (e.g. using cylinders to model body parts). These body models stand in sharp contrast to the richly detailed 3D body models used by by animators. In this talk we describe a method for recovering detailed body shape models directly from images. Specifically, we represent the body using a recently proposed triangulated mesh model called SCAPE which employs a ...
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In this paper we study multilinear formulas, monotone arithmetic circuits, maximal partition discrepancy, best partition communication complexity and mixed two source extractors. We will first define maximal partition discrepancy, and construct a function f that has exponentially small maximal partition discrepancy. We will then review several application of this construction: 1. The best partition communication complexity of f is \Theta(n). ...
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This research concerns the image deblurring and noise removal problem in a variational framework. Energy functionals in this study consist of a fidelity term and a regularizer that is based on Mumford-Shah segmentation, such that the recovered image and its discontinuities set are simultaneously extracted in the course of the deblurring process. We first consider the image deblurring problem in the presence of Gaussian/impulsive noise and present a convergence result for t...
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Recent studies stressed the importance of objects comparison for category learning. Recently we compared adults' capacity to learn new categorization principle in a condition in which few exemplars were identified as belong to the same category, versus a condition in which exemplars were identified as belong to different categories. We found that almost all participants learned the categorization rule quite efficiently in the Same-Class Exemplars condition. In contrast, when not p...
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This talk describes 3D virtual colonoscopy (VC), a combination of computed tomography (CT) scanning and volume visualization technology, and is poised to become the procedure of choice in lieu of the conventional optical colonoscopy for mass screening for colon cancer. The talk further discusses a novel pipeline of computer-aided detection (CAD) of colonic polyps – the precursor of colorectal cancer – complementing VC. In VC, the patient abdomen is imaged by a helical CT scan...
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Non-rigid shape similarity is an important problem in computer vision and pattern recognition. Broadly speaking, non-rigid shape similarity criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the objects and the latter to the geometry of the shapes in the Euclidean space. Both criteria have their advantages and disadvantages; extrinsic similarity is sensitive to non-rigid deformations of the shapes, while intrinsic similarity is sensit...
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