Improved Lower Bounds for Learning from Noisy Examples: An Information-Theoretic Approach

This paper presents a general information-theoretic approach for obtaining lower bounds on the number of examples required for Probably Approximately Correct (PAC) learning in the presence of noise. This approach deals directly with the fundamental information quantities, avoiding a Bayesian analysis. The technique is applied to several different models, illustrating its generality and power. The resulting bounds add logarithmic factors to (or improve the constants in) previously known lower bounds.     

Lower Bounds for the Weak Pigeonhole Principle and Random Formulas beyond Resolution

We work with an extension of Resolution, called Res(2), that allows clauses with conjunctions of two literals. In this system there are rules to introduce and eliminate such conjunctions. We prove that the weak pigeonhole principle PHP^cn_n and random unsatisfiable CNF formulas require exponential-size proofs in this system. This is the strongest system beyond Resolution for which such lower bounds are known. As a consequence to the result about the weak pigeonhole principle, Res(log) is exponentially more powerful than Res(2). Also we prove that Resolution cannot polynomially simulate Res(2) and that Res(2) does not have feasible monotone interpolation solving an open problem posed by Krají ek.     

A Continuous Probabilistic Framework for Image Matching

In this paper we describe a probabilistic image matching scheme in which the image representation is continuous and the similarity measure and distance computation are also defined in the continuous domain. Each image is first represented as a Gaussian mixture distribution and images are compared and matched via a probabilistic measure of similarity between distributions. A common probabilistic and continuous framework is applied to the representation as well as the matching process, ensuring an overall system that is theoretically appealing. Matching results are investigated and the application to an image retrieval system is demonstrated.     

Reduction of Permutation-Invariant Polynomials: A Noncommutative Case Study

Let R be a commutative ring with 1, let RX₁,…,X_n/I be the polynomial algebra in the n≥4 noncommuting variables X₁,…,X_n over R modulo the set of commutator relations I={(X₁+···+X_n)*X_i=X_i*(X₁+···+X_n)|1≤i≤n}. Furthermore, let G be an arbitrary group of permutations operating on the indeterminates X₁,…,X_n, and let RX₁,…,X_n/I^G be the R-algebra of G-invariant polynomials in RX₁,…,X_n/I. The first part of this paper is about an algorithm, which computes a representation for any fRX₁,…,X_n/I^G as a polynomial in multilinear G-invariant polynomials, i.e., the maximal variable degree of the generators of RX₁,…,X_n/I^G is at most 1. The algorithm works for any ring R and for any permutation group G. In addition, we present a bound for the number of necessary generators for the representation of all G-invariant polynomials in RX₁,…,X_n/I^G with a total degree of at most d. The second part contains a first but promising analysis of G-invariant polynomials of solvable polynomial rings.     

A Real-Time Approach to the Spotting, Representation, and Recognition of Hand Gestures for Human–Computer Interaction

Aiming at the use of hand gestures for human–computer interaction, this paper presents a real-time approach to the spotting, representation, and recognition of hand gestures from a video stream. The approach exploits multiple cues including skin color, hand motion, and shape. Skin color analysis and coarse image motion detection are joined to perform reliable hand gesture spotting. At a higher level, a compact spatiotemporal representation is proposed for modeling appearance changes in image sequences containing hand gestures. The representation is extracted by combining robust parameterized image motion regression and shape features of a segmented hand. For efficient recognition of gestures made at varying rates, a linear resampling technique for eliminating the temporal variation (time normalization) while maintaining the essential information of the original gesture representations is developed. The gesture is then classified according to a training set of gestures. In experiments with a library of 12 gestures, the recognition rate was over 90%. Through the development of a prototype gesture-controlled panoramic map browser, we demonstrate that a vocabulary of predefined hand gestures can be used to interact successfully with applications running on an off-the-shelf personal computer equipped with a home video camera.     

A Probabilistic Model for Recovering Camera Translation

This paper describes the mathematical basis and application of a probabilistic model for recovering the direction of camera translation (heading) from optical flow. According to the theorem that heading cannot lie between two converging points in a stationary environment, one can compute the posterior probability distribution of heading across the image and choose the heading with maximum a posteriori (MAP). The model requires very simple computation, provides confidence level of the judgments, applies to both linear and curved trajectories, functions in the presence of camera rotations, and exhibited high accuracy up to 0.1°–0.2° in random dot simulations.     

Rollback-Dependency Trackability: A Minimal Characterization and Its Protocol

Considering a checkpoint and communication pattern, the rollback-dependency trackability (RDT) property stipulates that there is no hidden dependency between local checkpoints. In other words, if there is a dependency between two checkpoints due to a noncausal sequence of messages (Z-path), then there exists a causal sequence of messages (C-path) that doubles the noncausal one and that establishes the same dependency.This paper introduces the notion of RDT-compliance. A property defined on Z-paths is RDT-compliant if the causal doubling of Z-paths having this property is sufficient to ensure RDT. Based on this notion, the paper provides examples of such properties. Moreover, these properties are visible, i.e., they can be tested on the fly. One of these properties is shown to be minimal with respect to visible and RDT-compliant properties. In other words, this property defines a minimal visible set of Z-paths that have to be doubled for the RDT property to be satisfied.Then, a family of communication-induced checkpointing protocols that ensure on-the-fly RDT properties is considered. Assuming processes take local checkpoints independently (called basic checkpoints), protocols of this family direct them to take on-the-fly additional local checkpoints (called forced checkpoints) in order that the resulting checkpoint and communication pattern satisfies the RDT property. The second contribution of this paper is a new communication-induced checkpointing protocol . This protocol, based on a condition derived from the previous characterization, tracks a minimal set of Z-paths and breaks those not perceived as being doubled. Finally, a set of communication-induced checkpointing protocols are derived from . Each of these derivations considers a particular weakening of the general condition used by . It is interesting to note that some of these derivations produce communication-induced checkpointing protocols that have already been proposed in the literature.     

Novel Techniques for Robust Voxelization and Visualization of Implicit Surfaces

Voxelization is the transformation of geometric surfaces into voxels. Up to date this process has been done essentially using incremental algorithms. Incremental algorithms have the reputation of being efficient but they lack an important property: robustness. The voxelized representation should envelop its continuous model. However, without robust methods this cannot be guaranteed. This article describes novel techniques of robust voxelization and visualization of implicit surfaces. First of all our recursive subdivision voxelization algorithm is reviewed. This algorithm was initially inspired by Duff's image space subdivision method. Then, we explain the algorithm to voxelize implicit surfaces defined in spherical or cylindrical coordinates. Next, we show a new technique to produce infinite replications of implicit objects and their voxelization method. Afterward, we comment on the parallelization of our voxelization procedure. Finally we present our voxel visualization algorithm based on point display. Our voxelization algorithms can be used with any data structure, thanks to the fact that a voxel is only stored once the last subdivision level is reached. We emphasize the use of the octree, though, because it is a convenient way to store the discrete model hierarchically. In a hierarchy the discrete model refinement is simple and possible from any previous voxelized scene thanks to the fact that the voxelization algorithms are robust.     

A General Decomposition Theorem for the k-Server Problem

The first general decomposition theorem for the k-server problem is presented. Whereas all previous theorems are for the case of a finite metric with k+1 points, the theorem given here allows an arbitrary number of points in the underlying metric space. This theorem implies O(polylog(k))-competitive randomized algorithms for certain metric spaces consisting of a polylogarithmic number of widely separated subspaces and takes a first step toward a general O(polylog(k))-competitive algorithm. The only other cases for which polylogarithmic competitive randomized algorithms are known are the uniform metric space and the weighted cache metric space with two weights.     

Perceptual Organization Based Computational Model for Robust Segmentation of Moving Objects

The role of perceptual organization in motion analysis has heretofore been minimal. In this work we present a simple but powerful computational model and associated algorithms based on the use of perceptual organizational principles, such as temporal coherence (or common fate) and spatial proximity, for motion segmentation. The computational model does not use the traditional frame by frame motion analysis; rather it treats an image sequence as a single 3D spatio-temporal volume. It endeavors to find organizations in this volume of data over three levels—signal, primitive, and structural. The signal level is concerned with detecting individual image pixels that are probably part of a moving object. The primitive level groups these individual pixels into planar patches, which we call the temporal envelopes. Compositions of these temporal envelopes describe the spatio-temporal surfaces that result from object motion. At the structural level, we detect these compositions of temporal envelopes by utilizing the structure and organization among them. The algorithms employed to realize the computational model include 3D edge detection, Hough transformation, and graph based methods to group the temporal envelopes based on Gestalt principles. The significance of the Gestalt relationships between any two temporal envelopes is expressed in probabilistic terms. One of the attractive features of the adopted algorithm is that it does not require the detection of special 2D features or the tracking of these features across frames. We demonstrate that even with simple grouping strategies, we can easily handle drastic illumination changes, occlusion events, and multiple moving objects, without the use of training and specific object or illumination models. We present results on a large variety of motion sequences to demonstrate this robustness.     

Texture Classification and Segmentation by Cellular Neural Networks Using Genetic Learning

We present a new single-chip texture classifier based on the cellular neural network (CNN) architecture. Exploiting the dynamics of a locally interconnected 2D cell array of CNNs we have developed a theoretically new method for texture classification and segmentation. This technique differs from other convolution-based feature extraction methods since we utilize feedback convolution, and we use a genetic learning algorithm to determine the optimal kernel matrices of the network. The CNN operators we have found for texture recognition may combine different early vision effects. We show how the kernel matrices can be derived from the state equations of the network for convolution/deconvolution and nonlinear effects. The whole process includes histogram equalization of the textured images, filtering with the trained kernel matrices, and decision-making based on average gray-scale or texture energy of the filtered images. We present experimental results using digital CNN simulation with sensitivity analysis for noise, rotation, and scale. We also report a tested application performed on a programmable 22 × 20 CNN chip with optical inputs and an execution time of a few microseconds. We have found that this CNN chip with a simple 3 × 3 CNN kernel can reliably classify four textures. Using more templates for decision-making, we believe that more textures can be separated and adequate texture segmentation (< 1% error) can be achieved.     

Almost-Everywhere Superiority for Quantum Polynomial Time

Simon as extended by Brassard and Høyer shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine infinitely often. The present paper shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine almost everywhere.     

Decidability for Left-Linear Growing Term Rewriting Systems

A term rewriting system is called growing if each variable occurring on both the left-hand side and the right-hand side of a rewrite rule occurs at depth zero or one in the left-hand side. Jacquemard showed that the reachability and the sequentiality of linear (i.e., left-right-linear) growing term rewriting systems are decidable. In this paper we show that Jacquemard's result can be extended to left-linear growing rewriting systems that may have right-nonlinear rewrite rules. This implies that the reachability and the joinability of some class of right-linear term rewriting systems are decidable, which improves the results for right-ground term rewriting systems by Oyamaguchi. Our result extends the class of left-linear term rewriting systems having a decidable call-by-need normalizing strategy. Moreover, we prove that the termination property is decidable for almost orthogonal growing term rewriting systems.     

Communication Complexity Method for Measuring Nondeterminism in Finite Automata

While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem area is the study of different measures of nondeterminism in finite automata and the estimation of the sizes of minimal nondeterministic finite automata. In this paper the concept of communication complexity is applied in order to achieve progress in this problem area. The main results are as follows:1. Deterministic communication complexity provides lower bounds on the size of nfa's with bounded unambiguity. Applying this fact, the proofs of several results about nfa's with limited ambiguity can be simplified and presented in a uniform way.2. There is a family of languages KON_k² with an exponential size gap between nfa's with polynomial leaf number/ambiguity and nfa's with ambiguity k. This partially provides an answer to the open problem posed by B. Ravikumar and O. Ibarra (1989, SIAM J. Comput.18, 1263–1282) and H. Leung (1998, SIAM J. Comput.27, 1073–1082).     

Language-based Performance Prediction for Distributed and Mobile Systems

We present a framework for performance prediction of distributed and mobile systems. We rely on process calculi and their structural operational semantics. The dynamic behaviour is described through transition systems whose transitions are labelled by encodings of their proofs that we then map into stochastic processes. We enhance related works by allowing general continuous distributions resorting to a notion of enabling between transitions. We also discuss how the number of resources available affects the overall model. Finally, we introduce a notion of bisimulation that takes stochastic information into account and prove it to be a congruence. When only exponential distributions are of interest our equivalence induces a lumpable partition on the underlying Markov process.     

Optimal Deterministic Protocols for Mobile Robots on a Grid

This paper studies a system of m robots operating in a set of n work locations connected by aisles in a × grid, where m≤n. From time to time the robots need to move along the aisles, in order to visit disjoint sets of locations. The movement of the robots must comply with the following constraints: (1) no two robots can collide at a grid node or traverse a grid edge at the same time; (2) a robot's sensory capability is limited to detecting the presence of another robot at a neighboring node. We present a deterministic protocol that, for any small constant ε>0, allows m≤(1-ε)n robots to visit their target locations in O( ) time, where each robot visits no more than d≤n targets and no target is visited by more than one robot. We also prove a lower bound showing that our protocol is optimal. Prior to this paper, no optimal protocols were known for d>1. For d=1, optimal protocols were known only for m≤ , while for general m≤n only a suboptimal randomized protocol was known.     

The Complexity of the Exponential Output Size Problem for Top-Down and Bottom-Up Tree Transducers,

The exponential output size problem is to determine whether the size of output trees of a tree transducer grows exponentially in the size of input trees. In this paper the complexity of this problem is studied. It is shown to be NL-complete for total top-down tree transducers, DEXPTIME-complete for general top-down tree transducers, and P-complete for bottom-up tree transducers.     

Cooperative Stereo–Motion: Matching and Reconstruction

One of the most interesting goals of computer vision is the 3D structure recovery of scenes. Traditionally, two cues are used: structure from motion and structure from stereo, two subfields with complementary sets of assumptions and techniques. This paper introduces a new general framework of cooperation between stereo and motion. This framework combines the advantages of both cues: (i) easy correspondence from motion and (ii) accurate 3D reconstruction from stereo. First, we show how the stereo matching can be recovered from motion correspondences using only geometric constraints. Second, we propose a method of 3D reconstruction of both binocular and monocular features using all stereo pairs in the case of a calibrated stereo rig. Third, we perform an analysis of the performance of the proposed framework as well as a comparison with an affine method. Experiments involving real and synthetic stereo pairs indicate that rich and reliable information can be derived from the proposed framework. They also indicate that robust 3D reconstruction can be obtained even with short image sequences.     

On the Power of Las Vegas for One-Way Communication Complexity, OBDDs, and Finite Automata

The study of the computational power of randomized computations is one of the central tasks of complexity theory. The main goal of this paper is the comparison of the power of Las Vegas computation and deterministic respectively nondeterministic computation. We investigate the power of Las Vegas computation for the complexity measures of one-way communication, ordered binary decision diagrams, and finite automata.(i) For the one-way communication complexity of two-party protocols we show that Las Vegas communication can save at most one half of the deterministic one-way communication complexity. We also present a language for which this gap is tight.(ii) The result (i) is applied to show an at most polynomial gap between determinism and Las Vegas for ordered binary decision diagrams.(iii) For the size (i.e., the number of states) of finite automata we show that the size of Las Vegas finite automata recognizing a language L is at least the square root of the size of the minimal deterministic finite automaton recognizing L. Using a specific language we verify the optimality of this lower bound.