Catch them ... if you can

An important part of forensic science is dedicated to the evaluation of physical traces left at the crime scene like fingerprints, bullets, toolmarks etc. These traces are compared with traces from a suspect. The evaluation of physical traces can be interpreted as the comparison of two noisy signals. We introduce an evaluation of the matching of two noisy signals at diverse scales and localisations in space. In a multi-resolution way a "probability" of matching is computed. Furthermore, a description is given to evaluate the complexity of a shoemark. A likelihood ratio approach is used for comparing two shoemark traces

Fast pseudo-CT synthesis from MRI T1-weighted images using a patch-based approach

MRI-based bone segmentation is a challenging task because bone tissue and air both present low signal intensity on MR images, making it difficult to accurately delimit the bone boundaries. However, estimating bone from MRI images may allow decreasing patient ionization by removing the need of patient-specific CT acquisition in several applications. In this work, we propose a fast GPU-based pseudo-CT generation from a patient-specific MRI T1-weighted image using a group-wise patch-based approach and a limited MRI and CT atlas dictionary. For every voxel in the input MR image, we compute the similarity of the patch containing that voxel with the patches of all MR images in the database, which lie in a certain anatomical neighborhood. The pseudo-CT is obtained as a local weighted linear combination of the CT values of the corresponding patches. The algorithm was implemented in a GPU. The use of patch-based techniques allows a fast and accurate estimation of the pseudo-CT from MR T1-weighted images, with a similar accuracy as the patient-specific CT. The experimental normalized cross correlation reaches 0.9324±0.0048 for an atlas with 10 datasets. The high NCC values indicate how our method can accurately approximate the patient-specific CT. The GPU implementation led to a substantial decrease in computational time making the approach suitable for real applications

Reconstruction of one-dimensional chaotic maps from sequences of probability density functions

In many practical situations, it is impossible to measure the individual trajectories generated by an unknown chaotic system, but we can observe the evolution of probability density functions generated by such a system. The paper proposes for the first time a matrix-based approach to solve the generalized inverse Frobenius–Perron problem, that is, to reconstruct an unknown one-dimensional chaotic transformation, based on a temporal sequence of probability density functions generated by the transformation. Numerical examples are used to demonstrate the applicability of the proposed approach and evaluate its robustness with respect to constantly applied stochastic perturbations

Adaptive estimation of mean and volatility functions in (auto-)regressive models

In this paper, we study the problem of nonparametric estimation of the mean and variance functions b and [sigma]2 in a model: Xi+1=b(Xi)+[sigma](Xi)[var epsilon]i+1. For this purpose, we consider a collection of finite dimensional linear spaces. We estimate b using a mean squares estimator built on a data driven selected linear space among the collection. Then an analogous procedure estimates [sigma]2, using a possibly different collection of models. Both data driven choices are performed via the minimization of penalized mean squares contrasts. The penalty functions are random in order not to depend on unknown variance-type quantities. In all cases, we state nonasymptotic risk bounds in empirical norm for our estimators and we show that they are both adaptive in the minimax sense over a large class of Besov balls. Lastly, we give the results of intensive simulation experiments which show the good performances of our estimator.Nonparametric regression Least-squares estimator Adaptive estimation Autoregression Variance estimation Mixing processes