Axel Munk

The \textit{fuzzy vault} approach is one of the best studied and well accepted ideas for binding cryptographic security into biometric authentication. The vault has been implemented in connection with fingerprint data by Uludag and Jain. We show that this instance of the vault is vulnerable to brute force attack. An interceptor of the vault data can recover both secret and

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy.

We investigate the problem of estimating persistent homology of noisy one dimensional signals. We relate this to the problem of estimating the number of modes (i.e., local maxima) -- a well known question in statistical inference -- and we show how to do so without presmoothing the data. To this end, we extend the ideas of persistent homology by working with norms different from the (classical) supremum norm. As a particular case we investigate the so called Kolmogorov norm. We argue that this extension has certain statistical advantages. We offer confidence bands for the attendant Kolmogorov signatures, thereby allowing for the selection of relevant signatures with a statistically controllable error. As a result of independent interest, we show that so-called taut strings minimize the number of critical points for a very general class of functions. We illustrate our results by several numerical examples.

ABSTRACT The fuzzy vault scheme is a cryptographic primitive that can be used to protect human fingerprint templates where stored. Analyses for most implementations account for brute-force security only. There are, however, other risks that have to be consider, such as false-accept attacks, record multiplicity attacks, and information leakage from auxiliary data, such as alignment parameters. In fact, the existing work lacks analyses of these weaknesses and are even susceptible to a variety of them. In view of these vulnerabilities, we redesign a minutiae-based fuzzy vault implementation preventing an adversary from running attacks via record multiplicity. Furthermore, we propose a mechanism for robust absolute fingerprint prealignment. In combination, we obtain a fingerprint-based fuzzy vault that resists known record multiplicity attacks and that does not leak information about the protected fingerprints from auxiliary alignment data. By experiments, we evaluate the performance of our security-improved implementation that, even though it has slight usability merits as compared with other minutiae-based implementations, provides improved security. However, despite heavy efforts spent in improving security, our implementation is, like all other implementations based on a single finger, subjected to a fundamental security limitation related to the false acceptance rate, i.e., false-accept attack. Consequently, this paper supports the notion that a single finger is not sufficient to provide acceptable security. Instead, implementations for multiple finger or even multiple modalities should be deployed the security of which may be improved by the technical contributions of this paper.

ABSTRACT We derive rates of convergence and asymptotic normality of the least squares estimator for a large class of parametric inverse regression models Y = (Phi f)(X) e. Our theory provides a unified asymptotic tretament for estimation of f with discontinuities of certain order, including piecewise polynomials and piecewise kink functions. Our results cover several classical and new examples, including splines with free knots or the estimation of piecewise linear functions with indirect observations under a nonlinear Hammerstein integral operator. Furthermore, we show that l(o)-penalisation leads to a consistent model selection, using techniques from empirical process theory. The asymptotic normality is used to provide confidence bands for f. Simulation studies and a data example from rheology illustrate the results.

ABSTRACT Fast multiple change-point segmentation methods, which additionally provide faithful statistical statements on the number and size of the segments, have recently received great attention. For example, SMUCE, as introduced in (Frick, Munk, and Sieling, Multiscale change-point inference. J. R. Statist. Soc. B, 76:495-580, 2014), allows to control simultaneously over a large number of scales the error of overestimating the true number $K$ of change-points, $\mathbb{P}\{\hat K > K\} \le \alpha_S$, for a preassigned significance level $\alpha_S$, independent of the underlying change-point function. The control of this family-wise error rate (FWER), however, makes this method generally conservative. In this paper, we propose a multiscale segmentation method, which controls the false discovery rate (FDR) instead. It can be efficiently computed by a pruned dynamic program. We show a non-asymptotic upper bound for its FDR in a Gaussian setting, which allows to calibrate the new segmentation method properly. By switching from FWER to FDR, the detection power of the method significantly outperforms SMUCE. The favorable performance of the proposed method is examined by comparisons with some state of the art methods on both simulated and real datasets.

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our results cover other metrics like Skorokhod metric on the space of c\`{a}dl\`{a}g functions and uniform metrics on $C([0,1])$. We will show that these estimators are in an adaptive sense