Bijective Feature-Aware Contour Matching

Abstract

Computing maps between data sequences is a fundamental problem with various applications in the fields of geometry and signal processing. As such, a multitude of approaches exist, that make trade-offs between flexibility, performance, and accuracy. Even recent approaches cannot be applied to periodic data, such as contours, without significant compromises due to their map representation or method of optimization. We propose a universal method to optimize maps between periodic and non periodic univariate sequences. By continuously optimizing a piecewise linear approximation of the smooth map on a common intermediate domain, we decouple the map and input resolution. Our optimization offers bijectivity guarantees and flexibility with regards to applications and data modality. To robustly converge towards a high quality solution we initially apply a lowpass filter to the input. This creates a scale space that suppresses local features in the early phase of the optimization (global phase) and gradually adds them back later (local phase). We demonstrate the versatility of our method on various scenarios with different types of sequences, including multi-contour morphing, signature prototypes, symmetry detection, and 3D motioncapture- data alignment.