In this paper, we propose a method for computing partial functional correspondence between non-rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace–Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford–Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings
The question whether one can recover the shape of a geometric object from its Laplacian spectrum ('hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While theoretically the answer to this question is negative (there exist examples of iso-spectral but non-isometric manifolds), little is known about the practical possibility of using the spectrum for shape reconstruction and optimization. In this paper, we introduce a numerical procedure called isospectralization, consisting of deforming one shape to make its Laplacian spectrum match that of another. We implement the isospectralization procedure using modern differentiable programming techniques and exemplify its applications in some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics such as shape reconstruction, pose and style transfer, and dense deformable correspondence.
Abstract-Artificial markers are successfully adopted to solve several vision tasks, ranging from tracking to calibration. While most designs share the same working principles, many specialized approaches exist to address specific application domains. Some are specially crafted to boost pose recovery accuracy. Others are made robust to occlusion or easy to detect with minimal computational resources. The sheer amount of approaches available in recent literature is indeed a statement to the fact that no silver bullet exists. Furthermore, this is also a hint to the level of scholarly interest that still characterizes this research topic. With this paper we try to add a novel option to the offer, by introducing a general purpose fiducial marker which exhibits many useful properties while being easy to implement and fast to detect. The key ideas underlying our approach are three. The first one is to exploit the projective invariance of conics to jointly find the marker and set a reading frame for it. Moreover, the tag identity is assessed by a redundant cyclic coded sequence implemented using the same circular features used for detection. Finally, the specific design and feature organization of the marker are well suited for several practical tasks, ranging from camera calibration to information payload delivery.
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