Melodic similarity measurement is of key importance in music information retrieval. In this paper, we use geometric matching techniques to measure the similarity between two melodies. We represent music as sets of points or sets of horizontal line segments in the Euclidean plane and propose efficient algorithms for optimization problems inspired in two operations on melodies; linear scaling and audio compression. In the scaling problem, an incoming query melody is scaled forward until the similarity measure between the query and a reference melody is minimized. The compression problem asks for a subset of notes of a given melody such that the matching cost between the selected notes and the reference melody is minimized.
This paper presents a novel algorithm to plan energy-efficient trajectories for autonomous ornithopters. In general, trajectory optimization is quite a relevant problem for practical applications with \emph{Unmanned Aerial Vehicles} (UAVs). Even though the problem has been well studied for fixed and rotatory-wing vehicles, there are far fewer works exploring it for flapping-wing UAVs like ornithopters. These are of interest for many applications where long flight endurance, but also hovering capabilities are required. We propose an efficient approach to plan ornithopter trajectories that minimize energy consumption by combining gliding and flapping maneuvers. Our algorithm builds a tree of dynamically feasible trajectories and applies heuristic search for efficient online planning, using reference curves to guide the search and prune states. We present computational experiments to analyze and tune key parameters, as well as a comparison against a recent alternative probabilistic planning, showing best performance. Finally, we demonstrate how our algorithm can be used for planning perching maneuvers online.