We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizi...

The medial axis is a classical representation of digital objects widely used in many applications. However, such a set of balls may not be optimal: subsets of the medial axis may exist without changing the reversivility of the input shape representation. In this article, we first prove that finding a minimum medial axis is an NP-hard problem for the Euclidean distance. Then, we compare two algo...

We present the CPMA, a new method for medial axis pruning with noise robustness and equivariance to isometric transformations. The CPMA leverages discrete cosine transform create smooth versions of shape $\Omega $ . use shapes compute score function $\mathcal {F}_{\Omega }$ that filters out spurious branches from original Our generalizes $n$ -dimensional given properties Discrete Cosine Transfo...

This paper is the second part of the author’s contribution on the topic of Safe Navigation for Indoor Mobile Robots. It presents a new solution to the exploration, self localization and map building problem taking advantage of the sensor-based navigation framework presented in the paper: Safe Navigation for Indoor Mobile Robots Part I: A Sensor-based Navigation Framework. The model of the indoo...

This paper is the second part of the author’s contribution on the topic of Safe Navigation for Indoor Mobile Robots. It presents a new solution to the exploration, self localization and map building problem taking advantage of the sensor-based navigation framework presented in the paper: Safe Navigation for Indoor Mobile Robots Part I: A Sensor-based Navigation Framework. The model of the indoo...

In this study, simulation tests for gravity gradient referenced navigation (GGRN) are conducted to verify the effects of various factors such as database (DB) and sensor errors, flight altitude, DB resolution, initial errors, and measurement update rates on the navigation performance. Based on the simulation results, requirements for GGRN are established for position determination with certain ...

This paper deals with the autonomous navigation of a mobile robot equipped with an insect-like visual sensor. The design of the sensor is based on models derived from the insect compound eyes that use optical ow information for navigation purposes. Restricting navigation to the ground-plane, we design a 1D panoramic sensor that performs parallel image processing and calculates local components ...

This paper presents a method that trains the WiFi fingerprint database using sensor-based navigation solutions. Since micro-electromechanical systems (MEMS) sensors provide only a short-term accuracy but suffer from the accuracy degradation with time, we restrict the time length of available indoor navigation trajectories, and conduct post-processing to improve the sensor-based navigation solut...