相关论文: Registration-free localization of defects in 3-D p…
Recent work in on-line Statistical Process Control (SPC) of manufactured 3-dimensional (3-D) objects has been proposed based on the estimation of the spectrum of the Laplace-Beltrami (LB) operator, a differential operator that encodes the…
We present a new method for statistical process control (SPC) of a discrete part manufacturing system based on intrinsic geometrical properties of the parts, estimated from three-dimensional sensor data. An intrinsic method has the…
Del Castillo and Zhao (2020, 2021, 2022, 2024) have recently proposed a new methodology for the Statistical Process Control (SPC) of discrete parts whose 3-dimensional (3D) geometrical data are acquired with non-contact sensors. The…
Advanced manufacturing technologies allow for the production of intricate parts featuring high shape complexity and spatially-varying material composition. Data fusion of point clouds with chromatic attributes provides 4D point clouds, a…
Modern sensing technologies have enabled the collection of unstructured point cloud data (PCD) of varying sizes, which are used to monitor the geometric accuracy of 3D objects. PCD are widely applied in advanced manufacturing processes,…
We address the Statistical Process Control (SPC) of high-dimensional, dynamic industrial processes from two complementary perspectives: manifold fitting and manifold learning, both of which assume data lies on an underlying nonlinear, lower…
We consider the problem of localizing relevant subsets of non-rigid geometric shapes given only a partial 3D query as the input. Such problems arise in several challenging tasks in 3D vision and graphics, including partial shape similarity,…
This paper proposes to extend local image features in 3D to include invariance to discrete symmetry including inversion of spatial axes and image contrast. A binary feature sign $s \in \{-1,+1\}$ is defined as the sign of the Laplacian…
We consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to…
With the rapid expansion of applied 3D computational vision, shape descriptors have become increasingly important for a wide variety of applications and objects from molecules to planets. Appropriate shape descriptors are critical for…
We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace--Beltrami…
We present a progressive 3D registration framework that is a highly-efficient variant of classical non-rigid Iterative Closest Points (N-ICP). Since it uses the Laplace-Beltrami operator for deformation regularisation, we view the overall…
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…
We consider problems of dimensionality reduction and learning data representations for continuous spaces with two or more independent degrees of freedom. Such problems occur, for example, when observing shapes with several components that…
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…
Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape.…
A robust and informative local shape descriptor plays an important role in mesh registration. In this regard, spectral descriptors that are based on the spectrum of the Laplace-Beltrami operator have been a popular subject of research for…
The eigenfunctions of the Laplace Beltrami operator (Manifold Harmonics) define a function basis that can be used in spectral analysis on manifolds. In [21] the authors recast the problem as an orthogonality constrained optimization problem…
We develop theory and methodology for the problem of nonparametric registration of functional data that have been subjected to random deformation (warping) of their time scale. The separation of this phase variation ("horizontal" variation)…
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…