2,602 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
Isonemal prefabrics with only parallel axes of symmetry
Isonemal weaving designs, introduced into mathematical literature by
Gr\"unbaum and Shephard, were classified into thirty-nine infinite sets and a
small number of exceptions by Richard Roth. This paper refines Roth's taxonomy
for the first ten of these families in order to solve three problems, which
designs exist in various sizes, which prefabrics can be doubled and remain
isonemal, and which can be halved and remain isonemal.Comment: 25 page
The Application of Preconditioned Alternating Direction Method of Multipliers in Depth from Focal Stack
Post capture refocusing effect in smartphone cameras is achievable by using
focal stacks. However, the accuracy of this effect is totally dependent on the
combination of the depth layers in the stack. The accuracy of the extended
depth of field effect in this application can be improved significantly by
computing an accurate depth map which has been an open issue for decades. To
tackle this issue, in this paper, a framework is proposed based on
Preconditioned Alternating Direction Method of Multipliers (PADMM) for depth
from the focal stack and synthetic defocus application. In addition to its
ability to provide high structural accuracy and occlusion handling, the
optimization function of the proposed method can, in fact, converge faster and
better than state of the art methods. The evaluation has been done on 21 sets
of focal stacks and the optimization function has been compared against 5 other
methods. Preliminary results indicate that the proposed method has a better
performance in terms of structural accuracy and optimization in comparison to
the current state of the art methods.Comment: 15 pages, 8 figure
Discovering Regularity in Point Clouds of Urban Scenes
Despite the apparent chaos of the urban environment, cities are actually replete with regularity. From the grid of streets laid out over the earth, to the lattice of windows thrown up into the sky, periodic regularity abounds in the urban scene. Just as salient, though less uniform, are the self-similar branching patterns of trees and vegetation that line streets and fill parks. We propose novel methods for discovering these regularities in 3D range scans acquired by a time-of-flight laser sensor. The applications of this regularity information are broad, and we present two original algorithms. The first exploits the efficiency of the Fourier transform for the real-time detection of periodicity in building facades. Periodic regularity is discovered online by doing a plane sweep across the scene and analyzing the frequency space of each column in the sweep. The simplicity and online nature of this algorithm allow it to be embedded in scanner hardware, making periodicity detection a built-in feature of future 3D cameras. We demonstrate the usefulness of periodicity in view registration, compression, segmentation, and facade reconstruction. The second algorithm leverages the hierarchical decomposition and locality in space of the wavelet transform to find stochastic parameters for procedural models that succinctly describe vegetation. These procedural models facilitate the generation of virtual worlds for architecture, gaming, and augmented reality. The self-similarity of vegetation can be inferred using multi-resolution analysis to discover the underlying branching patterns. We present a unified framework of these tools, enabling the modeling, transmission, and compression of high-resolution, accurate, and immersive 3D images
Planar Symmetry Detection and Quantification using the Extended Persistent Homology Transform
Symmetry is ubiquitous throughout nature and can often give great insights
into the formation, structure and stability of objects studied by
mathematicians, physicists, chemists and biologists. However, perfect symmetry
occurs rarely so quantitative techniques must be developed to identify
approximate symmetries. To facilitate the analysis of an independent variable
on the symmetry of some object, we would like this quantity to be a smoothly
varying real parameter rather than a boolean one. The extended persistent
homology transform is a recently developed tool which can be used to define a
distance between certain kinds of objects. Here, we describe how the extended
persistent homology transform can be used to visualise, detect and quantify
certain kinds of symmetry and discuss the effectiveness and limitations of this
method.Comment: 9 pages, 13 figure
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