Related papers: Isospectralization, or how to hear shape, style, a…
We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…
Several types of systems were put forward during the past decades to show that there exist {\it isospectral} systems which are {\it metrically} different. One important class consists of Laplace Beltrami operators for pairs of flat tori in…
Optical vibration sensing enables recovering the scene sound directly from the surface vibration of nearby objects, turning everyday objects into ``visual microphones''. However, most prior methods had focused on capturing the vibrations of…
We investigate the problem of pixelwise correspondence for deformable objects, namely cloth and rope, by comparing both classical and learning-based methods. We choose cloth and rope because they are traditionally some of the most difficult…
We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label…
This article adapts the framework of metamorphosis to solve inverse problems in imaging that includes joint reconstruction and image registration. The deformations in question have two components, one that is a geometric deformation moving…
Learning 3D shape representation with dense correspondence for deformable objects is a fundamental problem in computer vision. Existing approaches often need additional annotations of specific semantic domain, e.g., skeleton poses for human…
Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…
Calibration of radio interferometric observations becomes increasingly difficult towards lower frequencies. Below ~300 MHz, spatially variant refractions and propagation delays of radio waves traveling through the ionosphere cause phase…
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
We study a generalization of the isomonodromic deformation to the case of connections with irregular singularities. We call this generalization Isostokes Deformation. A new deformation parameter arises: one can deform the formal normal…
Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts…
Refraction is a common physical phenomenon and has long been researched in computer vision. Objects imaged through a refractive object appear distorted in the image as a function of the shape of the interface between the media. This hinders…
Rendering an accurate image of an isosurface in a volumetric field typically requires large numbers of data samples. Reducing the number of required samples lies at the core of research in volume rendering. With the advent of deep learning…
We present implicit displacement fields, a novel representation for detailed 3D geometry. Inspired by a classic surface deformation technique, displacement mapping, our method represents a complex surface as a smooth base surface plus a…
Establishing semantic correspondence across images when the objects in the images have undergone complex deformations remains a challenging task in the field of computer vision. In this paper, we propose a hierarchical method to tackle this…
Learning the graph Laplacian from observed data is one of the most investigated and fundamental tasks in Graph Signal Processing (GSP). Different variants of the Laplacian, such as the combinatorial, signless or signed Laplacians have been…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
We present a method which enables one to construct isospectral objects, such as quantum graphs and drums. One aspect of the method is based on representation theory arguments which are shown and proved. The complementary part concerns…
All the known counterexamples to Kac' famous question "can one hear the shape of a drum", i.e., does isospectrality of two Laplacians on domains imply that the domains are congruent, consist of pairs of domains composed of copies of…