325 research outputs found
Convolutions on digital surfaces: on the way iterated convolutions behave and preliminary results about curvature estimation
In [FoureyMalgouyres09] the authors present a generalized convolution operator for functions defined on digital surfaces. We provide here some extra material related to this notion. Some about the relative isotropy of the way a convolution kernel (or mask) grows when the convolution operator is iterated. We also provide preliminary results about a way to estimate curvatures on a digital surface, using the same convolution operator
Normals estimation for digital surfaces based on convolutions
International audienceIn this paper, we present a method that we call on-surface convolution which extends the classical notion of a 2D digital filter to the case of digital surfaces (following the cuberille model). We also define an averaging mask with local support which, when applied with the iterated convolution operator, behaves like an averaging with large support. The interesting property of the latter averaging is the way the resulting weights are distributed: given a digital surface obtained by discretization of a differentiable surface of R^3 , the masks isocurves are close to the Riemannian isodistance curves from the center of the mask. We eventually use the iterated averaging followed by convolutions with differentiation masks to estimate partial derivatives and then normal vectors over a surface. The number of iterations required to achieve a good estimate is determined experimentally on digitized spheres and tori. The precision of the normal estimation is also investigated according to the digitization step
3D Shape Reconstruction from Sketches via Multi-view Convolutional Networks
We propose a method for reconstructing 3D shapes from 2D sketches in the form
of line drawings. Our method takes as input a single sketch, or multiple
sketches, and outputs a dense point cloud representing a 3D reconstruction of
the input sketch(es). The point cloud is then converted into a polygon mesh. At
the heart of our method lies a deep, encoder-decoder network. The encoder
converts the sketch into a compact representation encoding shape information.
The decoder converts this representation into depth and normal maps capturing
the underlying surface from several output viewpoints. The multi-view maps are
then consolidated into a 3D point cloud by solving an optimization problem that
fuses depth and normals across all viewpoints. Based on our experiments,
compared to other methods, such as volumetric networks, our architecture offers
several advantages, including more faithful reconstruction, higher output
surface resolution, better preservation of topology and shape structure.Comment: 3DV 2017 (oral
Piecewise smooth reconstruction of normal vector field on digital data
International audienceWe propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio-Tortorelli functional, originally defined for denoising and contour extraction in image processing [AT90]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state-of- the-art normal field estimators like Voronoi Covariance Measure [MOG11] or Randomized Hough Transform [BM12]
Integral based Curvature Estimators in Digital Geometry
International audienceIn many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. When designing such estimators, we have to pay attention to both its theoretical properties and practical effectiveness. In this paper, we investigate a new class of estimators on digital shape boundaries based on Integral Invariants. More precisely, we provide proofs of multigrid convergence of curvature estimators which are easy to implement on digital data. Furthermore, we discuss about some algorithmic optimisations and detail a complete experimental evaluation
Integral based Curvature Estimators in Digital Geometry
International audienceIn many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. When designing such estimators, we have to pay attention to both its theoretical properties and practical effectiveness. In this paper, we investigate a new class of estimators on digital shape boundaries based on Integral Invariants. More precisely, we provide proofs of multigrid convergence of curvature estimators which are easy to implement on digital data. Furthermore, we discuss about some algorithmic optimisations and detail a complete experimental evaluation
Machine learning methods for 3D object classification and segmentation
Field of study: Computer science.Dr. Ye Duan, Thesis Supervisor.Includes vita."July 2018."Object understanding is a fundamental problem in computer vision and it has been extensively researched in recent years thanks to the availability of powerful GPUs and labelled data, especially in the context of images. However, 3D object understanding is still not on par with its 2D domain and deep learning for 3D has not been fully explored yet. In this dissertation, I work on two approaches, both of which advances the state-of-the-art results in 3D classification and segmentation. The first approach, called MVRNN, is based multi-view paradigm. In contrast to MVCNN which does not generate consistent result across different views, by treating the multi-view images as a temporal sequence, our MVRNN correlates the features and generates coherent segmentation across different views. MVRNN demonstrated state-of-the-art performance on the Princeton Segmentation Benchmark dataset. The second approach, called PointGrid, is a hybrid method which combines points and regular grid structure. 3D points can retain fine details but irregular, which is challenge for deep learning methods. Volumetric grid is simple and has regular structure, but does not scale well with data resolution. Our PointGrid, which is simple, allows the fine details to be consumed by normal convolutions under a coarser resolution grid. PointGrid achieved state-of-the-art performance on ModelNet40 and ShapeNet datasets in 3D classification and object part segmentation.Includes bibliographical references (pages 116-140)
Diffusion is All You Need for Learning on Surfaces
We introduce a new approach to deep learning on 3D surfaces such as meshes or
point clouds. Our key insight is that a simple learned diffusion layer can
spatially share data in a principled manner, replacing operations like
convolution and pooling which are complicated and expensive on surfaces. The
only other ingredients in our network are a spatial gradient operation, which
uses dot-products of derivatives to encode tangent-invariant filters, and a
multi-layer perceptron applied independently at each point. The resulting
architecture, which we call DiffusionNet, is remarkably simple, efficient, and
scalable. Continuously optimizing for spatial support avoids the need to pick
neighborhood sizes or filter widths a priori, or worry about their impact on
network size/training time. Furthermore, the principled, geometric nature of
these networks makes them agnostic to the underlying representation and
insensitive to discretization. In practice, this means significant robustness
to mesh sampling, and even the ability to train on a mesh and evaluate on a
point cloud. Our experiments demonstrate that these networks achieve
state-of-the-art results for a variety of tasks on both meshes and point
clouds, including surface classification, segmentation, and non-rigid
correspondence
PRS: Sharp Feature Priors for Resolution-Free Surface Remeshing
Surface reconstruction with preservation of geometric features is a
challenging computer vision task. Despite significant progress in implicit
shape reconstruction, state-of-the-art mesh extraction methods often produce
aliased, perceptually distorted surfaces and lack scalability to
high-resolution 3D shapes. We present a data-driven approach for automatic
feature detection and remeshing that requires only a coarse, aliased mesh as
input and scales to arbitrary resolution reconstructions. We define and learn a
collection of surface-based fields to (1) capture sharp geometric features in
the shape with an implicit vertexwise model and (2) approximate improvements in
normals alignment obtained by applying edge-flips with an edgewise model. To
support scaling to arbitrary complexity shapes, we learn our fields using local
triangulated patches, fusing estimates on complete surface meshes. Our feature
remeshing algorithm integrates the learned fields as sharp feature priors and
optimizes vertex placement and mesh connectivity for maximum expected surface
improvement. On a challenging collection of high-resolution shape
reconstructions in the ABC dataset, our algorithm improves over
state-of-the-art by 26% normals F-score and 42% perceptual
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