Related papers: Extracting a functional representation from a dict…
The objective of this paper is to learn dense 3D shape correspondence for topology-varying generic objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead,…
A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilarities between classes. We introduce Self…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…
Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. a polynomial basis, and the parameters of the function are tuned given the data. This is a pragmatic and…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…
Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from implanted tetrodes in the human or animal brain. The LFP signals are curves observed at multiple tetrodes which are implanted…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
We introduce a new local meshfree method for the approximation of the Laplace-Beltrami operator on a smooth surface of co-dimension one embedded in $\R^3$. A key element of this method is that it does not need an explicit expression of the…
Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account…
A majority of shape correspondence frameworks are based on devising pointwise and pairwise constraints on the correspondence map. The functional maps framework allows for formulating these constraints in the spectral domain. In this paper,…
Perspective distortion (PD) leads to substantial alterations in the shape, size, orientation, angles, and spatial relationships of visual elements in images. Accurately determining camera intrinsic and extrinsic parameters is challenging,…
In this work, we introduce a novel local pairwise descriptor and then develop a simple, effective iterative method to solve the resulting quadratic assignment through sparsity control for shape correspondence between two approximate…
Infinite-dimensional orthonormal basis expansions play a central role in representing and computing with function spaces due to their favorable linear algebraic properties. However, common bases such as Fourier or wavelets are fixed and do…
The goal of this paper is to learn dense 3D shape correspondence for topology-varying objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead, our novel…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of the…
Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where…
Functional Dependencies (FDs) define attribute relationships based on syntactic equality, and, when usedin data cleaning, they erroneously label syntactically different but semantically equivalent values as errors. We explore…
Effectively parsing the facade is essential to 3D building reconstruction, which is an important computer vision problem with a large amount of applications in high precision map for navigation, computer aided design, and city generation…