Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search

Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as respectively used by informed graph-based searches and anytime sampling-based planners. Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient but leaves their performance dependent on the chosen approximation. If its resolution is too low then they may not find a (suitable) solution but if it is too high then they may take a prohibitively long time to do so. Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously and but may be prohibitively inefficient at containing a solution. This paper unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16 Figure

Variational methods and its applications to computer vision

Many computer vision applications such as image segmentation can be formulated in a ''variational'' way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Open Acces

The k-labeled spanning forest problem : complexity, approximability, formulations and algorithms

In this work, we study the k-labeled spanning forest problem (KLSF). The input of the KLSF is an undirected graph with labeled edges and a positive integer k. The goal is to find a spanning forest of the graph with at most k different labels associated with the edges, that minimizes the number of components. KLSF finds practical applications in different scenarios related to networks design and telecommunications. Its solutions may help to reduce the negative impact of electromagnetic fields exposure on the population health or to increase profits of internet management companies, among others. The in terest in the KLSF problem is not only practical but also theoretical since the problem generalizes the best-known NP-hard minimum labeling spanning tree problem (MLST). This work reinforces the NP-hardness of the KLSF and ensures that, even for the simple instances where the components of the original graph are only triangles and edges, the problem is NP-hard. Also as a theoretical result, an inapproximability proof is presented for it, ensuring that unless P = NP there is no polynomial time algorithm with approxi mation factor polynomial in the number of the labels. To complete the theoretical results a trivial 3-approximation result is presented for the particular case where the input graph components are edges or triangles. From the application side, to approach KLSF, we propose a fix-and-optimize matheuristic that was tested over several instances, achieving high-quality solutions in reasonable computational time. When compared to the best known algorithms in the literature, our matheuristic outperformed the other proposals in most cases, finding better solutions in less computational time for the most challenging instances

Interactive image segmentation

Segmentation of objects from still images has many practical applications. In the past decade, combinatorial graph cut algorithms have been successfully applied to get fairly accurate object segmentation, along with considerable reduction in the amount of user interaction required. In particular, the Grabcut algorithm has been found to provide satisfactory results for a wide variety of images. This work is an extension to the Grabcut algorithm. The Grabcut algorithm uses Gaussian mixture models to fit the color data. The number of Gaussian components used in mixture model is however fixed. We apply an unsupervised algorithm for estimating the number of Gaussian components to be used for the models. The results obtained show that segmentation accuracy is increased by estimating the Gaussian components required, prior to applying the Grabcut algorithm