Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

Learning Probabilistic Features for Robotic Navigation Using Laser Sensors

SLAM is a popular task used by robots and autonomous vehicles to build a map of an unknown environment and, at the same time, to determine their location within the map. This paper describes a SLAM-based, probabilistic robotic system able to learn the essential features of different parts of its environment. Some previous SLAM implementations had computational complexities ranging from O(Nlog(N)) to O(N2), where N is the number of map features. Unlike these methods, our approach reduces the computational complexity to O(N) by using a model to fuse the information from the sensors after applying the Bayesian paradigm. Once the training process is completed, the robot identifies and locates those areas that potentially match the sections that have been previously learned. After the training, the robot navigates and extracts a three-dimensional map of the environment using a single laser sensor. Thus, it perceives different sections of its world. In addition, in order to make our system able to be used in a low-cost robot, low-complexity algorithms that can be easily implemented on embedded processors or microcontrollers are used.

Feature selection by multi-objective optimisation: Application to network anomaly detection by hierarchical self-organising maps

Feature selection is an important and active issue in clustering and classification problems. By choosing an adequate feature subset, a dataset dimensionality reduction is allowed, thus contributing to decreasing the classification computational complexity, and to improving the classifier performance by avoiding redundant or irrelevant features. Although feature selection can be formally defined as an optimisation problem with only one objective, that is, the classification accuracy obtained by using the selected feature subset, in recent years, some multi-objective approaches to this problem have been proposed. These either select features that not only improve the classification accuracy, but also the generalisation capability in case of supervised classifiers, or counterbalance the bias toward lower or higher numbers of features that present some methods used to validate the clustering/classification in case of unsupervised classifiers. The main contribution of this paper is a multi-objective approach for feature selection and its application to an unsupervised clustering procedure based on Growing Hierarchical Self-Organising Maps (GHSOMs) that includes a new method for unit labelling and efficient determination of the winning unit. In the network anomaly detection problem here considered, this multi-objective approach makes it possible not only to differentiate between normal and anomalous traffic but also among different anomalies. The efficiency of our proposals has been evaluated by using the well-known DARPA/NSL-KDD datasets that contain extracted features and labelled attacks from around 2 million connections. The selected feature sets computed in our experiments provide detection rates up to 99.8% with normal traffic and up to 99.6% with anomalous traffic, as well as accuracy values up to 99.12%.