6661888
A wavelet approach to foveating images
Motivated by applications of foveated images in visualization, we introduce the foveation transform of an image. We study the basic properties of these transforms using the multiresolution framework of Mallat. We also consider practical methods of realizing such transforms. In particular, we introduce a new method for foveating images based on wavelets. Preliminary experimental results are shown.
42674644
Shortest Path amidst Disc Obstacles Is Computable
An open question in Exact Geometric Computation is whether there are transcendental computations that can be made "geometrically exact". Perhaps the simplest such problem in computational geometry is that of computing the shortest obstacle-avoiding path between two points p,q in the plane, where the obstacles are a collection of n discs. This problem can be solved in O(n2log n) time in the Real RAM model, but nothing was known about its computability in the standard (Turing) model of computation. We first give a direct proof of the Turing-computability of this problem, provided the radii of the discs are rationally related. We make the usual assumption that the numerical input data are real algebraic numbers. By appealing to effective bounds from transcendental number theory, we further show a single-exponential time upper bound when the input numbers are rational. Our result appears to be the first example of a non-algebraic combinatorial problem which is shown computable. It is also a rare example of transcendental number theory yielding positive computational results.
3079245
Statistics- and Spatiality-Based Feature Distance Measure for Error Resilient Image Authentication
Content-based image authentication typically assesses authenticity based on a distance measure between the image to be tested and its original. Commonly employed distance measures such as the Minkowski measures (including Hamming and Euclidean distances) may not be adequate for content-based image authentication since they do not exploit statistical and spatial properties in features. This paper proposes a feature distance measure for content-based image authentication based on statistical and spatial properties of the feature differences. The proposed statistics- and spatiality-based measure (SSM) is motivated by an observation that most malicious manipulations are localized whereas acceptable manipulations result in global distortions. A statistical measure, kurtosis, is used to assess the shape of the feature difference distribution; a spatial measure, the maximum connected component size, is used to assess the degree of object concentration of the feature differences. The experimental results have confirmed that our proposed measure is better than previous measures in distinguishing malicious manipulations from acceptable ones.
11249256
A unified framework for resolving ambiguity in copy detection
Copy detection is an important component of digital rights management and can be implemented using a retrieval-based approach. Under this approach, a query image, suspected to be a copy, is compared against all the images in the owner database. The comparison is done based on a distance metric in feature space. The performance of such a system depends on the mutual separation of the feature representation of the images in the database. In this paper we propose a framework that increases this mutual separation by literally shifting them away from each other. The idea of modifying the features derives its inspiration from the field of watermarking. It is also important to make sure that the semantics of the images do not change after modification. Thus the focus of this paper is on how to modify the images in the database, so that the mutual separation between the images in feature space is above a certain threshold and the distortion induced is minimized. This problem can be formulated as a non-convex optimization problem which is difficult to solve. We propose a restriction of the problem and solve it using second-order cone programming. We present a practical implementation of our framework, named RAM, which uses AFMT as the feature representation. We conduct experiments to test the performance of RAM.
472683
On the effectiveness of DDoS attacks on statistical filtering
Distributed denial of service (DDoS) attacks pose a serious threat to service availability of the victim network by severely degrading its performance. Recently, there has been significant interest in the use of statistical-based filtering to defend against and mitigate the effect of DDoS attacks. Under this approach, packet statistics are monitored to classify normal and abnormal behaviour. Under attack, packets that are classified as abnormal are dropped by the filter that guards the victim network. We study the effectiveness of DDoS attacks on such statistical-based filtering in a general context where the attackers are "smart". We first give an optimal policy for the filter when the statistical behaviours of both the attackers and the filter are static. We next consider cases where both the attacker and the filter can dynamically change their behaviour, possibly depending on the perceived behaviour of the other party. We observe that while an adaptive filter can effectively defend against a static attacker, the filter can perform much worse if the attacker is more dynamic than perceived.
12953441
A Simultaneous Search Problem
Abstract. We introduce a new search problem motivated by computational metrology. The problem is as follows: we would like to locate two unknown numbers x,y ∈ [0,1] with as little uncertainty as possible, using some given number k of probes. Each probe is specified by a real number r∈ [0,1] . After a probe at r , we are told whether x≤ r or x \geq r , and whether y≤ r or y\geq r . We derive the optimal strategy and prove that the asymptotic behavior of the total uncertainty after k probes is 13/7 2-(k+1)/2 for odd k and 13/10 2-k/2 for even k .
15908075
On Answering Queries in the Presence of Limited Access Patterns
In information-integration systems, source relations often have limitations on access patterns to their data; i.e., when one must provide values for certain attributes of a relation in order to retrieve its tuples. In this paper we consider the following fundamental problem: can we compute the complete answer to a query by accessing the relations with legal patterns? The complete answer to a query is the answer that we could compute if we could retrieve all the tuples from the relations. We give algorithms for solving the problem for various classes of queries, including conjunctive queries, unions of conjunctive queries, and conjunctive queries with arithmetic comparisons. We prove the problem is undecidable for datalog queries. If the complete answer to a query cannot be computed, we often need to compute its maximal answer. The second problem we study is, given two conjunctive queries on relations with limited access patterns, how to test whether the maximal answer to the first query is contained in the maximal answer to the second one? We show this problem is decidable using the results of monadic programs.
10654167
Enhanced perceptual distance functions and indexing for image replica recognition
The proliferation of digital images and the widespread distribution of digital data that has been made possible by the Internet has increased problems associated with copyright infringement on digital images. Watermarking schemes have been proposed to safeguard copyrighted images, but watermarks are vulnerable to image processing and geometric distortions and may not be very effective. Thus, the content-based detection of pirated images has become an important application. In this paper, we discuss two important aspects of such a replica detection system: distance functions for similarity measurement and scalability. We extend our previous work on perceptual distance functions, which proposed the Dynamic Partial Function (DPF), and present enhanced techniques that overcome the limitations of DPF. These techniques include the Thresholding, Sampling, and Weighting schemes. Experimental evaluations show superior performance compared to DPF and other distance functions. We then address the issue of using these perceptual distance functions to efficiently detect replicas in large image data sets. The problem of indexing is made challenging by the high-dimensionality and the nonmetric nature of the distance functions. We propose using Locality Sensitive Hashing (LSH) to index images while using the above perceptual distance functions and demonstrate good performance through empirical studies on a very large database of diverse images.
17899816
Invariant feature extraction and biased statistical inference for video surveillance
Using cameras for detecting hazardous or suspicious events has spurred new research for security concerns. To make such detection reliable, researchers trust overcome difficulties such as variation in camera capabilities, environmental factors. imbalances of positive and negative training data, and asymmetric costs of misclassifying events of different classes. Following up on the event-detection framework (Wu et al. (2003)) that we have proposed, we present in this paper the framework's two major components: invariant feature extraction and biased statistical inference. We report results of our experiments using the framework for detecting suspicious motion events in a parking lot.
17340449
On scalability of active learning for formulating query concepts
Query-by-example and query-by-keyword both suffer from the problem of "aliasing," meaning that example-images and keywords potentially have variable interpretations or multiple semantics. For discerning which semantic is appropriate for a given query, we have established that combining active learning with kernel methods is a very effective approach. In this work, we first examine active-learning strategies, and then focus on addressing the challenges of two scalability issues: scalability in dataset size and in concept complexity. We present remedies, explain limitations, and discuss future directions that research might take.
16585637
Learning with non-metric proximity matrices
Many emerging applications formulate non-metric proximity matrices (non-positive semidefinite), and hence cannot fit into the framework of kernel machines. A popular approach to this problem is to transform the spectrum of the similarity matrix so as to generate a positive semidefinite kernel matrix. In this paper, we explore four representative transformation methods: denoise, flip, diffusion, and shift. Theoretically, we discuss a generalization problem where the test data are not available during transformation, and thus propose an efficient algorithm to address the problem of updating the cross-similarity matrix between test and training data. Extensive experiments have been conducted to evaluate the performance of these methods on several real-world (dis)similarity matrices with semantic meanings.