Related papers: Isospectralization, or how to hear shape, style, a…
Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of…
We answer Mark Kac's famous question, "can one hear the shape of a drum?" in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all…
In the following, we give an explicit construction of a Laplacian on the Minkowski curve, with energy forms that bear the geometric characteristic of the structure. The spectrum of the Laplacian is obtained by means of spectral decimation.
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…
Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
We introduce a variation on Kac's question, "Can one hear the shape of a drum?" Instead of trying to identify a compact manifold and its metric via its Laplace--Beltrami spectrum, we ask if it is possible to uniquely identify a point $x$ on…
It is well known that certain pairs of planar domains have the same spectra of the Laplacian operator. We prove that these domains are still isospectral for a wider class of physical problems, including the cases of heterogeneous drums and…
The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback…
The eigenfunctions of the Laplace-Beltrami operator have widespread applications in a number of disciplines of engineering, computer vision/graphics, machine learning, etc. These eigenfunctions or manifold harmonics, provide the means to…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
We describe a "spatio-spectral" deconvolution algorithm for wide-band imaging in radio interferometry. In contrast with the existing multi-frequency reconstruction algorithms, the proposed method does not rely on a model of the…
We present a new deep learning approach for matching deformable shapes by introducing {\it Shape Deformation Networks} which jointly encode 3D shapes and correspondences. This is achieved by factoring the surface representation into (i) a…
In this paper, we consider a certain convolutional Laplacian for metric measure spaces and investigate its potential for the statistical analysis of complex objects. The spectrum of that Laplacian serves as a signature of the space under…
We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
The advent of large aperture arrays, such as the ones currently under construction for the SKA project, allows for observing the Universe in the radio-spectrum at unprecedented resolution and sensitivity. To process the enormous amounts of…
We address the problem of 3D shape registration and we propose a novel technique based on spectral graph theory and probabilistic matching. The task of 3D shape analysis involves tracking, recognition, registration, etc. Analyzing 3D data…