1,151 research outputs found
PRS-Net: planar reflective symmetry detection net for 3D models
In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces
PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models
In geometry processing, symmetry is a universal type of high-level structural
information of 3D models and benefits many geometry processing tasks including
shape segmentation, alignment, matching, and completion. Thus it is an
important problem to analyze various symmetry forms of 3D shapes. Planar
reflective symmetry is the most fundamental one. Traditional methods based on
spatial sampling can be time-consuming and may not be able to identify all the
symmetry planes. In this paper, we present a novel learning framework to
automatically discover global planar reflective symmetry of a 3D shape. Our
framework trains an unsupervised 3D convolutional neural network to extract
global model features and then outputs possible global symmetry parameters,
where input shapes are represented using voxels. We introduce a dedicated
symmetry distance loss along with a regularization loss to avoid generating
duplicated symmetry planes. Our network can also identify generalized cylinders
by predicting their rotation axes. We further provide a method to remove
invalid and duplicated planes and axes. We demonstrate that our method is able
to produce reliable and accurate results. Our neural network based method is
hundreds of times faster than the state-of-the-art methods, which are based on
sampling. Our method is also robust even with noisy or incomplete input
surfaces.Comment: Corrected typo
A normalized mirrored correlation measure for data symmetry detection
Symmetry detection algorithms are enjoying a renovated interest in the scientific community, fueled by recent advancements in computer vision and computer graphics applications. This paper is inspired by recent efforts in building a symmetric object detection system in natural images. In particular, it is first shown how correlation can be a core operator that allows finding local reflection symmetry points in 1-D sequences that are optimal in an energetic sense. Then, the importance of 2-D correlation in natural images to correctly align the symmetric object axis is demonstrated. Using the correlation as described is crucial in boosting the performance of the system, as proven by the results on a standard dataset
Symmetry sensitivities of Derivative-of-Gaussian filters
We consider the measurement of image structure using linear filters, in particular derivative-of-Gaussian (DtG) filters, which are an important model of V1 simple cells and widely used in computer vision, and whether such measurements can determine local image symmetry. We show that even a single linear filter can be sensitive to a symmetry, in the sense that specific responses of the filter can rule it out. We state and prove a necessary and sufficient, readily computable, criterion for filter symmetry-sensitivity. We use it to show that the six filters in a second order DtG family have patterns of joint sensitivity which are distinct for 12 different classes of symmetry. This rich symmetry-sensitivity adds to the properties that make DtG filters well-suited for probing local image structure, and provides a set of landmark responses suitable to be the foundation of a nonarbitrary system of feature categories
Leading Digit Laws on Linear Lie Groups
We determine the leading digit laws for the matrix components of a linear Lie
group . These laws generalize the observations that the normalized Haar
measure of the Lie group is and that the scale invariance
of implies the distribution of the digits follow Benford's law, which is
the probability of observing a significand base of at most is
; thus the first digit is with probability ).
Viewing this scale invariance as left invariance of Haar measure, we determine
the power laws in significands from one matrix component of various such .
We also determine the leading digit distribution of a fixed number of
components of a unit sphere, and find periodic behavior when the dimension of
the sphere tends to infinity in a certain progression.Comment: Version 1.0, 17 pages, 1 figur
Nonlinear Dimensionality Reduction for the Thermodynamics of Small Clusters of Particles
This work employs tools and methods from computer science to study clusters comprising a small number N of interacting particles, which are of interest in science, engineering, and nanotechnology. Specifically, the thermodynamics of such clusters is studied using techniques from spectral graph theory (SGT) and machine learning (ML). SGT is used to define the structure of the clusters and ML is used on ensembles of cluster configurations to detect state variables that can be used to model the thermodynamic properties of the system. While the most fundamental description of a cluster is in 3N dimensions, i.e., the Cartesian coordinates of the particles, the ML results demonstrate that sub-spaces of much lower dimension can describe the observed structural motifs. Furthermore, these sub-spaces correlate with meaningful physical variables such as radius of gyration r g and discrete connectivity c, which can be used as state variables in thermodynamic property descriptions. The overarching theme of this thesis is to develop the practice of utilizing data-driven computational techniques to solve problems in natural sciences. Code for this project can be found at https://github.com/AdityaDendukuri/DimReductionThermodynamics
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