Second-order Shape Optimization for Geometric Inverse Problems in Vision

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian, which is generally hard to compute and suffers from a series of degeneracies. Our analysis highlights the role of mean curvature motion in comparison with first-order schemes: instead of surface area, our approach penalizes deformation, either by its Dirichlet energy or total variation. Latter regularizer sparks the development of an alternating direction method of multipliers on triangular meshes. Therein, a conjugate-gradients solver enables us to bypass formation of the Gaussian normal equations appearing in the course of the overall optimization. We combine all of the aforementioned ideas in a versatile geometric variation-regularized Levenberg-Marquardt-type method applicable to a variety of shape functionals, depending on intrinsic properties of the surface such as normal field and curvature as well as its embedding into space. Promising experimental results are reported

NerVE: Neural Volumetric Edges for Parametric Curve Extraction from Point Cloud

Extracting parametric edge curves from point clouds is a fundamental problem in 3D vision and geometry processing. Existing approaches mainly rely on keypoint detection, a challenging procedure that tends to generate noisy output, making the subsequent edge extraction error-prone. To address this issue, we propose to directly detect structured edges to circumvent the limitations of the previous point-wise methods. We achieve this goal by presenting NerVE, a novel neural volumetric edge representation that can be easily learned through a volumetric learning framework. NerVE can be seamlessly converted to a versatile piece-wise linear (PWL) curve representation, enabling a unified strategy for learning all types of free-form curves. Furthermore, as NerVE encodes rich structural information, we show that edge extraction based on NerVE can be reduced to a simple graph search problem. After converting NerVE to the PWL representation, parametric curves can be obtained via off-the-shelf spline fitting algorithms. We evaluate our method on the challenging ABC dataset. We show that a simple network based on NerVE can already outperform the previous state-of-the-art methods by a great margin. Project page: https://dongdu3.github.io/projects/2023/NerVE/.Comment: Accepted by CVPR2023. Project page: https://dongdu3.github.io/projects/2023/NerVE

Iterative consolidation on unorganized point clouds and its application in design.

Chan, Kwan Chung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 63-69).Abstracts in English and Chinese.Abstract --- p.vAcknowledgements --- p.ixList of Figures --- p.xiiiList of Tables --- p.xvChapter 1 --- Introduction --- p.1Chapter 1.1 --- Main contributions --- p.4Chapter 1.2 --- Overview --- p.4Chapter 2 --- Related Work --- p.7Chapter 2.1 --- Point cloud processing --- p.7Chapter 2.2 --- Model repairing --- p.9Chapter 2.3 --- Deformation and reconstruction --- p.10Chapter 3 --- Iterative Consolidation on Un-orientated Point Clouds --- p.11Chapter 3.1 --- Algorithm overview --- p.12Chapter 3.2 --- Down-sampling and outliers removal --- p.14Chapter 3.2.1 --- Normal estimation --- p.14Chapter 3.2.2 --- Down-sampling --- p.15Chapter 3.2.3 --- Particle noise removal --- p.17Chapter 3.3 --- APSS based repulsion --- p.19Chapter 3.4 --- Refinement --- p.22Chapter 3.4.1 --- Adaptive up-sampling --- p.22Chapter 3.4.2 --- Selection of up-sampled points --- p.23Chapter 3.4.3 --- Sample noise removal --- p.23Chapter 3.5 --- Set constraints to sample points --- p.24Chapter 4 --- Shape Modeling by Point Set --- p.27Chapter 4.1 --- Principle of deformation --- p.27Chapter 4.2 --- Selection --- p.29Chapter 4.3 --- Stretching and compressing --- p.30Chapter 4.4 --- Bending and twisting --- p.30Chapter 4.5 --- Inserting points --- p.30Chapter 5 --- Results and Discussion --- p.37Chapter 5.1 --- Program environment --- p.37Chapter 5.2 --- Results of iterative consolidation on un-orientated points --- p.37Chapter 5.3 --- Effect of our de-noising based on up-sampled points --- p.44Chapter 6 --- Conclusions --- p.49Chapter 6.1 --- Advantages --- p.49Chapter 6.2 --- Factors affecting our algorithm --- p.50Chapter 6.3 --- Possible future works --- p.51Chapter 6.3.1 --- Improve on the quality of results --- p.51Chapter 6.3.2 --- Reduce user input --- p.52Chapter 6.3.3 --- Multi-thread computation --- p.52Chapter A --- Finding Neighbors --- p.53Chapter A.1 --- k-d Tree --- p.53Chapter A.2 --- Octree --- p.54Chapter A.3 --- Minimum spanning tree --- p.55Chapter B --- Principle Component Analysis --- p.57Chapter B.1 --- Principle component analysis --- p.57Chapter C --- UI of the program --- p.59Chapter C.1 --- User Interface --- p.59Chapter D --- Publications --- p.61Bibliography --- p.6

DIMENSIONALITY BASED SCALE SELECTION IN 3D LIDAR POINT CLOUDS

International audienceThis papers presents a multi-scale method that computes robust geometric features on lidar point clouds in order to retrieve the optimal neighborhood size for each point. Three dimensionality features are calculated on spherical neighborhoods at various radius sizes. Based on combinations of the eigenvalues of the local structure tensor, they describe the shape of the neighborhood, indicating whether the local geometry is more linear (1D), planar (2D) or volumetric (3D). Two radius-selection criteria have been tested and compared for finding automatically the optimal neighborhood radius for each point. Besides, such procedure allows a dimensionality labelling, giving significant hints for classification and segmentation purposes. The method is successfully applied to 3D point clouds from airborne, terrestrial, and mobile mapping systems since no a priori knowledge on the distribution of the 3D points is required. Extracted dimensionality features and labellings are then favorably compared to those computed from constant size neighborhoods