MelodyShape at MIREX 2014 Symbolic Melodic Similarity

ABSTRACT This short paper describes our three submissions to the 2014 edition of the MIREX Symbolic Melodic Similarity task. All three submissions rely on a geometric model that represents melodies as spline curves in the pitch-time plane. The similarity between two melodies is then computed with a sequence alignment algorithm between sequences of spline spans: the more similar the shape of the curves, the more similar the melodies they represent. As in the previous MIREX 2010MIREX , 2011MIREX , 2012 and 2013 editions, our systems ranked first for all effectiveness measures. The main difference with last year is that we submitted a re-implementation of all algorithms, contained in the new open source library MelodyShape

Piecewise rigid curve deformation via a Finsler steepest descent

This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study non-convex optimization problems where the geometry of the space might play a crucial role to avoid poor local minima. We show some applications to the curve matching problem. In particular, we characterize piecewise rigid deformations on the space of curves and we study several models to perform piecewise rigid evolution of curves

Contour Generator Points for Threshold Selection and a Novel Photo-Consistency Measure for Space Carving

Space carving has emerged as a powerful method for multiview scene reconstruction. Although a wide variety of methods have been proposed, the quality of the reconstruction remains highly-dependent on the photometric consistency measure, and the threshold used to carve away voxels. In this paper, we present a novel photo-consistency measure that is motivated by a multiset variant of the chamfer distance. The new measure is robust to high amounts of within-view color variance and also takes into account the projection angles of back-projected pixels. Another critical issue in space carving is the selection of the photo-consistency threshold used to determine what surface voxels are kept or carved away. In this paper, a reliable threshold selection technique is proposed that examines the photo-consistency values at contour generator points. Contour generators are points that lie on both the surface of the object and the visual hull. To determine the threshold, a percentile ranking of the photo-consistency values of these generator points is used. This improved technique is applicable to a wide variety of photo-consistency measures, including the new measure presented in this paper. Also presented in this paper is a method to choose between photo-consistency measures, and voxel array resolutions prior to carving using receiver operating characteristic (ROC) curves

A relaxed approach for curve matching with elastic metrics

In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the family of $H^2$-metrics with constant coefficients and scale-invariant $H^2$-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.Comment: 27 page

Robust similarity registration technique for volumetric shapes represented by characteristic functions

This paper proposes a novel similarity registration technique for volumetric shapes implicitly represented by their characteristic functions (CFs). Here, the calculation of rotation parameters is considered as a spherical crosscorrelation problem and the solution is therefore found using the standard phase correlation technique facilitated by principal components analysis (PCA).Thus, fast Fourier transform (FFT) is employed to vastly improve efficiency and robustness. Geometric moments are then used for shape scale estimation which is independent from rotation and translation parameters. It is numericallydemonstrated that our registration method is able to handle shapes with various topologies and robust to noise and initial poses. Further validation of our method is performed by registering a lung database