An Algorithm for Inferring Quasi-Static Types

This report presents an algorithm, and its implementation, for doing type inference in the context of Quasi-Static Typing (QST) ["Quasy-static Typing." Satish Thatte Proc. ACM Symp. on Principles of Programming Languages, 1988]. The package infers types a la "QST" for the simply typed λ-calculus.

New Notions of Reduction and Non-Semantic Proofs of β-Strong Normalization in Typed λ-Calculi

Two new notions of reduction for terms of the λ-calculus are introduced and the question of whether a λ-term is beta-strongly normalizing is reduced to the question of whether a λ-term is merely normalizing under one of the new notions of reduction. This leads to a new way to prove beta-strong normalization for typed λ-calculi. Instead of the usual semantic proof style based on Girard's "candidats de réductibilité'', termination can be proved using a decreasing metric over a well-founded ordering in a style more common in the field of term rewriting. This new proof method is applied to the simply-typed λ-calculus and the system of intersection types.

Search by Shape Examples: Modeling Nonrigid Deformation

We describe our work on shape-based image database search using the technique of modal matching. Modal matching employs a deformable shape decomposition that allows users to select example objects and have the computer efficiently sort the set of objects based on the similarity of their shape. Shapes are compared in terms of the types of nonrigid deformations (differences) that relate them. The modal decomposition provides deformation "control knobs" for flexible matching and thus allows for selecting weighted subsets of shape parameters that are deemed significant for a particular category or context. We demonstrate the utility of this approach for shape comparison in 2-D image databases; however, the general formulation is applicable to signals of any dimensionality.

Physically-Based Combinations of Views: Representing Rigid and Nonrigid Motion

Nonrigid motion can be described as morphing or blending between extremal shapes, e.g., heart motion can be described as transitioning between the systole and diastole states. Using physically-based modeling techniques, shape similarity can be measured in terms of forces and strain. This provides a physically-based coordinate system in which motion is characterized in terms of physical similarity to a set of extremal shapes. Having such a low-dimensional characterization of nonrigid motion allows for the recognition and the comparison of different types of nonrigid motion.

On the Effectiveness of Genetic Search in Combinatorial Optimization

In this paper, we study the efficacy of genetic algorithms in the context of combinatorial optimization. In particular, we isolate the effects of cross-over, treated as the central component of genetic search. We show that for problems of nontrivial size and difficulty, the contribution of cross-over search is marginal, both synergistically when run in conjunction with mutation and selection, or when run with selection alone, the reference point being the search procedure consisting of just mutation and selection. The latter can be viewed as another manifestation of the Metropolis process. Considering the high computational cost of maintaining a population to facilitate cross-over search, its marginal benefit renders genetic search inferior to its singleton-population counterpart, the Metropolis process, and by extension, simulated annealing. This is further compounded by the fact that many problems arising in practice may inherently require a large number of state transitions for a near-optimal solution to be found, making genetic search infeasible given the high cost of computing a single iteration in the enlarged state-space.

On the Size Distribution of Autonomous Systems

This paper explores reasons for the high degree of variability in the sizes of ASes that have recently been observed, and the processes by which this variable distribution develops. AS size distribution is important for a number of reasons. First, when modeling network topologies, an AS size distribution assists in labeling routers with an associated AS. Second, AS size has been found to be positively correlated with the degree of the AS (number of peering links), so understanding the distribution of AS sizes has implications for AS connectivity properties. Our model accounts for AS births, growth, and mergers. We analyze two models: one incorporates only the growth of hosts and ASes, and a second extends that model to include mergers of ASes. We show analytically that, given reasonable assumptions about the nature of mergers, the resulting size distribution exhibits a power law tail with the exponent independent of the details of the merging process. We estimate parameters of the models from measurements obtained from Internet registries and from BGP tables. We then compare the models solutions to empirical AS size distribution taken from Mercator and Skitter datasets, and find that the simple growth-based model yields general agreement with empirical data. Our analysis of the model in which mergers occur in a manner independent of the size of the merging ASes suggests that more detailed analysis of merger processes is needed.

Geometric Generalizations of the Power of Two Choices

A well-known paradigm for load balancing in distributed systems is the``power of two choices,''whereby an item is stored at the less loaded of two (or more) random alternative servers. We investigate the power of two choices in natural settings for distributed computing where items and servers reside in a geometric space and each item is associated with the server that is its nearest neighbor. This is in fact the backdrop for distributed hash tables such as Chord, where the geometric space is determined by clockwise distance on a one-dimensional ring. Theoretically, we consider the following load balancing problem. Suppose that servers are initially hashed uniformly at random to points in the space. Sequentially, each item then considers d candidate insertion points also chosen uniformly at random from the space,and selects the insertion point whose associated server has the least load. For the one-dimensional ring, and for Euclidean distance on the two-dimensional torus, we demonstrate that when n data items are hashed to n servers,the maximum load at any server is log log n / log d + O(1) with high probability. While our results match the well-known bounds in the standard setting in which each server is selected equiprobably, our applications do not have this feature, since the sizes of the nearest-neighbor regions around servers are non-uniform. Therefore, the novelty in our methods lies in developing appropriate tail bounds on the distribution of nearest-neighbor region sizes and in adapting previous arguments to this more general setting. In addition, we provide simulation results demonstrating the load balance that results as the system size scales into the millions.

On the Convergence of Statistical Techniques for Inferring Network Traffic Demands

Accurate knowledge of traffic demands in a communication network enables or enhances a variety of traffic engineering and network management tasks of paramount importance for operational networks. Directly measuring a complete set of these demands is prohibitively expensive because of the huge amounts of data that must be collected and the performance impact that such measurements would impose on the regular behavior of the network. As a consequence, we must rely on statistical techniques to produce estimates of actual traffic demands from partial information. The performance of such techniques is however limited due to their reliance on limited information and the high amount of computations they incur, which limits their convergence behavior. In this paper we study strategies to improve the convergence of a powerful statistical technique based on an Expectation-Maximization iterative algorithm. First we analyze modeling approaches to generating starting points. We call these starting points informed priors since they are obtained using actual network information such as packet traces and SNMP link counts. Second we provide a very fast variant of the EM algorithm which extends its computation range, increasing its accuracy and decreasing its dependence on the quality of the starting point. Finally, we study the convergence characteristics of our EM algorithm and compare it against a recently proposed Weighted Least Squares approach.

Cryptographic Tamper Evidence

We propose a new notion of cryptographic tamper evidence. A tamper-evident signature scheme provides an additional procedure Div which detects tampering: given two signatures, Div can determine whether one of them was generated by the forger. Surprisingly, this is possible even after the adversary has inconspicuously learned (exposed) some-or even all-the secrets in the system. In this case, it might be impossible to tell which signature is generated by the legitimate signer and which by the forger. But at least the fact of the tampering will be made evident. We define several variants of tamper-evidence, differing in their power to detect tampering. In all of these, we assume an equally powerful adversary: she adaptively controls all the inputs to the legitimate signer (i.e., all messages to be signed and their timing), and observes all his outputs; she can also adaptively expose all the secrets at arbitrary times. We provide tamper-evident schemes for all the variants and prove their optimality. Achieving the strongest tamper evidence turns out to be provably expensive. However, we define a somewhat weaker, but still practical, variant: α-synchronous tamper-evidence (α-te) and provide α-te schemes with logarithmic cost. Our α-te schemes use a combinatorial construction of α-separating sets, which might be of independent interest. We stress that our mechanisms are purely cryptographic: the tamper-detection algorithm Div is stateless and takes no inputs except the two signatures (in particular, it keeps no logs), we use no infrastructure (or other ways to conceal additional secrets), and we use no hardware properties (except those implied by the standard cryptographic assumptions, such as random number generators). Our constructions are based on arbitrary ordinary signature schemes and do not require random oracles.

On the Emergence of Highly Variable Distributions in the Autonomous System Topology

Recent studies have noted that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [15, 22]. The most prominent explanatory model for this phenomenon is the Barabási-Albert (B-A) model [5, 2]. A central feature of the B-A model is preferential connectivity—meaning that the likelihood a new node in a growing graph will connect to an existing node is proportional to the existing node’s degree. In this paper we ask whether a more general explanation than the B-A model, and absent the assumption of preferential connectivity, is consistent with empirical data. We are motivated by two observations: first, AS degree and AS size are highly correlated [11]; and second, highly variable AS size can arise simply through exponential growth. We construct a model incorporating exponential growth in the size of the Internet, and in the number of ASes. We then show via analysis that such a model yields a size distribution exhibiting a power-law tail. In such a model, if an AS’s link formation is roughly proportional to its size, then AS degree will also show high variability. We instantiate such a model with empirically derived estimates of growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.

Skin Color-Based Video Segmentation under Time-Varying Illumination

A novel approach for real-time skin segmentation in video sequences is described. The approach enables reliable skin segmentation despite wide variation in illumination during tracking. An explicit second order Markov model is used to predict evolution of the skin-color (HSV) histogram over time. Histograms are dynamically updated based on feedback from the current segmentation and predictions of the Markov model. The evolution of the skin-color distribution at each frame is parameterized by translation, scaling and rotation in color space. Consequent changes in geometric parameterization of the distribution are propagated by warping and resampling the histogram. The parameters of the discrete-time dynamic Markov model are estimated using Maximum Likelihood Estimation, and also evolve over time. The accuracy of the new dynamic skin color segmentation algorithm is compared to that obtained via a static color model. Segmentation accuracy is evaluated using labeled ground-truth video sequences taken from staged experiments and popular movies. An overall increase in segmentation accuracy of up to 24% is observed in 17 out of 21 test sequences. In all but one case the skin-color classification rates for our system were higher, with background classification rates comparable to those of the static segmentation.

The Specialized Mappings Architecture

A probabilistic, nonlinear supervised learning model is proposed: the Specialized Mappings Architecture (SMA). The SMA employs a set of several forward mapping functions that are estimated automatically from training data. Each specialized function maps certain domains of the input space (e.g., image features) onto the output space (e.g., articulated body parameters). The SMA can model ambiguous, one-to-many mappings that may yield multiple valid output hypotheses. Once learned, the mapping functions generate a set of output hypotheses for a given input via a statistical inference procedure. The SMA inference procedure incorporates an inverse mapping or feedback function in evaluating the likelihood of each of the hypothesis. Possible feedback functions include computer graphics rendering routines that can generate images for given hypotheses. The SMA employs a variant of the Expectation-Maximization algorithm for simultaneous learning of the specialized domains along with the mapping functions, and approximate strategies for inference. The framework is demonstrated in a computer vision system that can estimate the articulated pose parameters of a human’s body or hands, given silhouettes from a single image. The accuracy and stability of the SMA are also tested using synthetic images of human bodies and hands, where ground truth is known.

Discovering Clusters in Motion Time-Series Data

A new approach is proposed for clustering time-series data. The approach can be used to discover groupings of similar object motions that were observed in a video collection. A finite mixture of hidden Markov models (HMMs) is fitted to the motion data using the expectation-maximization (EM) framework. Previous approaches for HMM-based clustering employ a k-means formulation, where each sequence is assigned to only a single HMM. In contrast, the formulation presented in this paper allows each sequence to belong to more than a single HMM with some probability, and the hard decision about the sequence class membership can be deferred until a later time when such a decision is required. Experiments with simulated data demonstrate the benefit of using this EM-based approach when there is more "overlap" in the processes generating the data. Experiments with real data show the promising potential of HMM-based motion clustering in a number of applications.

Estimating 3D Hand Pose from a Cluttered Image

A method is proposed that can generate a ranked list of plausible three-dimensional hand configurations that best match an input image. Hand pose estimation is formulated as an image database indexing problem, where the closest matches for an input hand image are retrieved from a large database of synthetic hand images. In contrast to previous approaches, the system can function in the presence of clutter, thanks to two novel clutter-tolerant indexing methods. First, a computationally efficient approximation of the image-to-model chamfer distance is obtained by embedding binary edge images into a high-dimensional Euclide an space. Second, a general-purpose, probabilistic line matching method identifies those line segment correspondences between model and input images that are the least likely to have occurred by chance. The performance of this clutter-tolerant approach is demonstrated in quantitative experiments with hundreds of real hand images.

Database Indexing Methods for 3D Hand Pose Estimation

Estimation of 3D hand pose is useful in many gesture recognition applications, ranging from human-computer interaction to automated recognition of sign languages. In this paper, 3D hand pose estimation is treated as a database indexing problem. Given an input image of a hand, the most similar images in a large database of hand images are retrieved. The hand pose parameters of the retrieved images are used as estimates for the hand pose in the input image. Lipschitz embeddings of edge images into a Euclidean space are used to improve the efficiency of database retrieval. In order to achieve interactive retrieval times, similarity queries are initially performed in this Euclidean space. The paper describes ongoing work that focuses on how to best choose reference images, in order to improve retrieval accuracy.