Mehmet Kivanc Mihcak

Robust perceptual image hashing via matrix invariants

In this paper we suggest viewing images (as well as attacks on them) as a sequence of linear operators and propose novel hashing algorithms employing transforms that are based on matrix invariants. To derive this sequence, we simply cover a two dimensional representation of an image by a sequence of (possibly overlapping) rectangles R/sub i/ whose sizes and locations are chosen randomly/sup 1/ from a suitable distribution. The restriction of the image (representation) to each R/sub i/ gives rise to a matrix A/sub i/. The fact that A/sub i/s will overlap and are random, makes the sequence (respectively) a redundant and non-standard representation of images, but is crucial for our purposes. Our algorithms first construct a secondary image, derived from input image by pseudo-randomly extracting features that approximately capture semi-global geometric characteristics. From the secondary image (which does not perceptually resemble the input), we further extract the final features which can be used as a hash value (and can be further suitably quantized). In this paper, we use spectral matrix invariants as embodied by singular value decomposition. Surprisingly, formation of the secondary image turns out be quite important since it not only introduces further robustness (i.e., resistance against standard signal processing transformations), but also enhances the security properties (i.e. resistance against intentional attacks). Indeed, our experiments reveal that our hashing algorithms extract most of the geometric information from the images and hence are robust to severe perturbations (e.g. up to %50 cropping by area with 20 degree rotations) on images while avoiding misclassification. Our methods are general enough to yield a watermark embedding scheme, which will be studied in another paper.

A framework for evaluating the data-hiding capacity of image sources

An information-theoretic model for image watermarking and data hiding is presented in this paper. Previous theoretical results are used to characterize the fundamental capacity limits of image watermarking and data-hiding systems. Capacity is determined by the statistical model used for the host image, by the distortion constraints on the data hider and the attacker, and by the information available to the data hider, to the attacker, and to the decoder. We consider autoregressive, block-DCT, and wavelet statistical models for images and compute data-hiding capacity for compressed and uncompressed host-image sources. Closed-form expressions are obtained under sparse-model approximations. Models for geometric attacks and distortion measures that are invariant to such attacks are considered.

New Iterative Geometric Methods for Robust Perceptual Image Hashing

We propose a novel and robust hashing paradigm that uses iterative geometric techniques and relies on observations that main geometric features within an image would approximately stay invariant under small perturbations. A key goal of this algorithm is to produce sufficiently randomized outputs which are unpredictable, thereby yielding properties akin to cryptographic MACs. This is a key component for robust multimedia identification and watermarking (for synchronization as well as content dependent key generation). Our algorithm withstands standard benchmark (e.g Stirmark) attacks provided they do not cause severe perceptually significant distortions. As verified by our detailed experiments, the approach is relatively media independent and works for audio as well.

A Perceptual Audio Hashing Algorithm: A Tool for Robust Audio Identification and Information Hiding

Assuming that watermarking is feasible (say, against a limited set of attacks of significant interest), current methods use a secret key to generate and embed a watermark. However, if the same key is used to watermark different items, then each instance may leak partial information and it is possible that one may extract the whole secret from a collection of watermarked items. Thus it will be ideal to derive content dependent keys, using a perceptual hashing algorithm (with its own secret key) that is resistant to small changes and otherwise having randomness and unpredictability properties analogous to cryptographic MACs.The techniques here are also useful for synchronizing in streams to find fixed locations against insertion and deletion attacks. Say, one may watermark a frame in a stream and can synchronize oneself to that frame using keyed perceptual hash and a known value for that frame. Our techniques can be used for identification of audio clips as well as database lookups in a way resistant to formatting and compression. We propose a novel audio hashing algorithm to be used for audio watermarking applications, that uses signal processing and traditional algorithmic analysis (against an adversary).

Theory and design of signal-adapted FIR paraunitary filter banks

We study the design of signal-adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi-infinite programming (SIP) problem. The remaining filters are related to the first through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex algorithm. We also show how regularity constraints may be incorporated into the design problem to obtain globally optimal (in the energy compaction sense) filter banks with specified regularity. We also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be DCT based. Such constraints may also be incorporated into our optimization algorithm; therefore, we are able to obtain globally optimal filter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters, as well as the effects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for FIR filter banks.

The parallel-Gaussian watermarking game

Rates of reliable transmission of hidden information are derived for watermarking problems involving parallel Gaussian sources, which are often used to model host images and audio signals. Constraints are imposed on the average squared-error distortion that can be introduced by the information hider and by the attacker. When distortions are measured with respect to the original host data, the optimal covert and attack channels are two banks of Gaussian test channels. The solution to the watermarking game involves an optimal allocation of distortions by the information hider and by the attacker to the different channels. A fast algorithm is given for computing the optimal solution based on duality theory. For each channel, we derive analytical expressions for two asymptotic regimes: weak and strong host signals. Finally, we extend these results to the class of stationary Gaussian host signals with bounded, continuous spectral density. The analysis also provides an upper bound on watermarking capacity for nonGaussian host signals.

An information-theoretic model for image watermarking and data hiding

An information-theoretic model for image watermarking and data hiding systems is presented. The fundamental capacity limits of these systems are determined by the statistical model used for the host image, by the distortion constraints on the data hider and the attacker, and by the information available to the data hider, to the attacker, and to the decoder. We consider wavelet statistical models for images and compute the data hiding capacity for compressed and uncompressed host image sources. Closed form expressions are obtained under sparse-model approximations.

Robust Image Hashing Via Non-Negative Matrix Factorizations

In this paper, we propose the use of non-negative matrix factorization (NMF) for robust image hashing. In particular, we view images as matrices and the goal of hashing as a randomized dimensionality reduction that retains the essence of the original image matrix while preventing against intentional attacks of guessing and forgery. Our work is motivated by the fact that standard-rank reduction techniques such as the QR, and singular value decomposition (SVD), produce low rank bases which do not respect the structure (i.e. non-negativity for images) of the original data. We observe that NMFs have two very desirable properties for secure image hashing applications: 1) The additivity property resulting from the non-negativity constraints results in bases that capture local characteristics of the image, thereby significantly reducing misclassification, and 2) the effect of geometric attacks on images in the spatial domain manifests (approximately) as independent identically distributed noise on NMF vectors, allowing design of detectors that are both computationally simple and at the same time optimal in the sense of minimizing error probabilities. ROC (receiver operating characteristics) analysis over a large image database reveals that the proposed algorithms significantly outperform existing approaches for robust image hashing

True Random Number Generation Via Sampling From Flat Band-Limited Gaussian Processes

We consider a true random number generator based on regularly sampling a thresholded wide sense stationary Gaussian noise source of which power spectral density is assumed to be flat between two known frequencies and zero everywhere else. We employ per-sample joint entropy of the resulting bit sequence as the main figure of merit and present novel analytical results on the optimum choice of the sampling period that ensures maximal randomness of the resulting bit sequence together with numerical results. In addition, we provide new results that follow from autocorrelation function of the noise source and introduce a new related metric, termed “spectral correlation” to quantify the pairwise dependence among the generated bits.

Rate-distortion-optimal subband coding without perfect-reconstruction constraints

We investigate the design of subband coders without the traditional perfect-reconstruction constraint on the filters. The coder uses scalar quantizers, and its filters and bit allocation are designed to optimize a rate-distortion criterion. Using convexity analysis, we show that optimality can be achieved using filterbanks that are the cascade of a (paraunitary) principal component filterbank for the input spectral process and a set of pre and postfilters surrounding each quantizer. Analytical expressions for the pre and postfilters are then derived. An algorithm for computing the globally optimal filters and bit allocation is given. We also develop closed-form solutions for the special case of two-channel coders under an exponential rate-distortion model. Finally, we investigate a constrained-length version of the filter design problem, which is applicable to practical coding scenarios. While the optimal filterbanks are nearly perfect-reconstruction at high rates, we demonstrate an apparently surprising advantage of optimal FIR filterbanks; they significantly outperform optimal perfect-reconstruction FIR filterbanks at all bit rates.