This paper aimed to devise an efficient algorithm applicable to ground penetrating radar (GPR) and to enable an automatic landmine detection. Proposed is a machine learning approach in which we put the main emphasis on fast performance of the scanning procedure analyzing the C-scans, i.e., 3-D images defined over the coordinate system, i.e., along track by across track by time, where the time axis can be associated with depth. The approach is based on our proposition of 3-D Haar-like features. Learning of the detector is carried out by boosted decision trees.Practical experiments on metal and plastic antitank mines in a garden soil are carried out. A prototype mobile platform is designed to scan the subsurface of the ground, equipped with a GPR based on a standard vector network analyzer and our original antenna system. We report the results, particularly the following: detection sensitivity, false alarm rates, receiver operating characteristic curves, and times of learning and detection.

We construct a set of special complex-valued integral images and an algorithm that allows to calculate Zernike moments fast, namely in constant time. The technique is suitable for dense detection procedures, where the image is scanned by a sliding window at multiple scales, and where rotational invariance is required at the level of each window. We assume no preliminary image segmentation. Owing to the proposed integral images and binomial expansions, the extraction of each feature does not depend on the number of pixels in the window and thereby is an calculation. We analyze algorithmic properties of the proposition, such as: number of needed integral images, complex-conjugacy of integral images, number of operations involved in feature extraction, speed-up possibilities based on lookup tables. We also point out connections between Zernike and orthogonal Fourier--Mellin moments in the context of computations backed with integral images. Finally, we demonstrate three examples of detection tasks of varying difficulty. Detectors are trained on the proposed features by the RealBoost algorithm. When learning, the classifiers get acquainted only with examples of target objects in their upright position or rotated within a limited range. At the testing stage, generalization onto the full 360° angle takes place automatically.

No abstract

Under study is an application of Ground Penetrating Radar (GPR) to landmine detection problem. We focus on the detection of antitank mines carried out in the 3D GPR images, so-called C-scans, by means of a machine learning approach. In that approach, we particularly pursue a technique for fast extraction of image features based on an initial calculation of multiple integral images. This allows later to calculate each feature in constant time, regardless of the scanning window position and size. The features we study are statistical moments formulated in their 3D variant. We present a comparison of detection results for different sizes and parameterizations of feature sets. All results are obtained from a prototype GPR system of our original construction in terms of both hardware and software.

Gompertz-related distributions have dominated mortality studies for 187 years. However, nonrelated distributions also fit well to mortality data. These compete with the Gompertz and Gompertz-Makeham data when applied to data with varying extents of truncation, with no consensus as to preference. In contrast, Gaussian-related distributions are rarely applied, despite the fact that Lexis in 1879 suggested that the normal distribution itself fits well to the right of the mode. Study aims were therefore to compare skew-t fits to Human Mortality Database data, with Gompertz-nested distributions, by implementing maximum likelihood estimation functions (mle2, R package bbmle; coding given). Results showed skew-t fits obtained lower Bayesian information criterion values than Gompertz-nested distributions, applied to low-mortality country data, including 1711 and 1810 cohorts. As Gaussian-related distributions have now been found to have almost universal application to error theory, one conclusion could be that a Gaussian-related distribution might replace Gompertz-related distributions as the basis for mortality studies.