Analysis of farthest point sampling for approximating geodesics in a graph

Kamousi, Pegah; Lazard, Sylvain; Maheshwari, Anil; Wuhrer, Stefanie

doi:10.1016/j.comgeo.2016.05.005

Cited by 28 publications

(19 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In T-Less dataset, the 30 objects are mixed and grouped together to generate 20 sets of images, each set containing 504 images and each image gathering more than one symmetrical object. Since some original CAD object models are not easy to be used in computing surface curvatures, only the traditional technique of farthest point sampling (FPS) [35] is used to sample the 3D keypoints on object surface. We train those T-Less objects one by one and then do the testing with all objects presenting in those 20 sets of images by using the VSD metric.…”

Section: E Results On T-less Datasetmentioning

confidence: 99%

“…The criteria of our keypoint selection are not only to distribute them on the object surface as possible (e.g., like the farthest distance criterion in [35]), but also make them informative and representative for the object shape. In this technique, 3D curvature is an important information used to seek for object keypoints, which leads to a preference of keypoint localization on highly curved surfaces rather than flat, concave, or occluded ones (such as the object body and the flat bottom).…”

Section: A Curvature Point Samplingmentioning

confidence: 99%

See 1 more Smart Citation

Detecting Object Surface Keypoints From a Single RGB Image via Deep Learning Network for 6-DoF Pose Estimation

Aing

Lie

2021

IEEE Access

View full text Add to dashboard Cite

Estimating the 6-DoF (Degree of Freedom) object pose from a single RGB image is one of the challenging tasks in the field of computer vision. Before the pose which is defined as the translation and rotation parameters can be derived by the traditional PnP algorithm, 2D image projections of a set of 3D object keypoints must be accurately detected. In this paper, we present techniques for defining 3D object surface keypoints and predicting their corresponding 2D counterparts via deep-learning network architectures. The main technique to designate 3D object keypoints is to employ quadratic fitting scheme for calculating the principal surface curvatures as the weights and then select from all surface points the ones mostly distributive with larger curvatures to describe the object shape as possible. However, the 2D projected keypoints are not directly regressed from the network, but encoded as the unit vector fields pointing to them, so that the voting scheme to recover back those 2D keypoints can be performed. Moreover, an effective loss function with the regularization term is adopted in training ResNet for predicting image projections of object keypoints by focusing on small-scale errors. Experimental results show that our proposed technique outperforms stateof-the-art approaches in both "2D projection" and "3D transformation" metrics.INDEX TERMS 2D projected keypoints, 3D object keypoints, 6-DoF, deep learning network, PnP algorithm, object pose estimation, surface curvature.

show abstract

Section: E Results On T-less Datasetmentioning

confidence: 99%

Section: A Curvature Point Samplingmentioning

confidence: 99%

Detecting Object Surface Keypoints From a Single RGB Image via Deep Learning Network for 6-DoF Pose Estimation

Aing

Lie

2021

IEEE Access

View full text Add to dashboard Cite

show abstract

“…The FPS method was first introduced for generic graph clustering algorithm [30], and then applied to 2D images [31] and further extended to 3D point cloud [17]. The FPS method has been widely used for a variety of isometry-invariant surface processing tasks [32]. For example, [33] explores this sampling strategy to efficiently esti-mate geodesic distances.…”

Section: Farthest Point Sampling Methodsmentioning

confidence: 99%

Local k-NNs pattern in Omni-Direction graph convolution neural network for 3D point clouds

Zhang

Wang

et al. 2020

Neurocomputing

View full text Add to dashboard Cite

Effective representation of objects in irregular and unordered point clouds is one of the core challenges in 3D vision. Transforming point cloud into regular structures, such as 2D images and 3D voxels, are not ideal. It either obscures the inherent geometry information of 3D data or results in high computational complexity. Learning permutation invariance feature directly from raw 3D point clouds using deep neural network is a trend, such as PointNet and its variants, which are effective and computationally efficient. However, these methods are weak to reveal the spatial structure of 3D point clouds. Our method is delicately designed to capture both global and local spatial layout of point cloud by proposing a Local k-NNs Pattern in Omni-Direction Graph Convolution Neural Network architecture, called LKPO-GNN. Our method converts the unordered 3D point cloud into an ordered 1D sequence, to facilitate feeding the raw data into neural networks and simultaneously reducing the computational complexity. LKPO-GNN selects multi-directional k-NNs to form the local topological structure of a centroid, which describes local shapes in the point cloud. Afterwards, GNN is used to combine the local spatial structures and represent the unordered point clouds as a global graph. Experiments on ModelNet40, ShapeNetPart, ScanNet, and S3DIS datasets demonstrate that our proposed method outperforms most existing methods, which verifies the effectiveness and advantage of our work. Additionally, a deep analysis towards illustrating the rationality of our approach, in terms of the learned the topological structure feature

show abstract

“…The computation of shortest geodesic paths (Chen and Han, 1990;Mitchell et al, 1987;Novotni and Klein, 2002) is an important step in many algorithms that address problems in fields of computer science such as motion planning (Hwang and Ahuja, 1992), object representation and recognition (Hamza and Krim, 2003) and dimensionality reduction (Tenenbaum et al, 2000;Onclinx et al, 2010). More specifically, in the area of computer graphics, where triangle meshes are the standard object representation, which can be considered as polyhedra, geodesic paths provide solution to many diverse problems (Peyré et al, 2010;Bose et al, 2011;Ying et al, 2013;Kamousi et al, 2013;Li et al, 2012), including mesh parameterization (Zigelman et al, 2002), mesh watermarking (Wang et al, 2008), shape matching and classification (Hilaga et al, 2001;Bronstein et al, 2010) and shape retrieval (Rabin et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Faster Approximations of Shortest Geodesic Paths on Polyhedra Through Adaptive Priority Queue

Schwartz

Rezende²,

Pedrini

2015

Proceedings of the 10th International Conference on Computer Vision Theory and Applications

View full text Add to dashboard Cite

Computing shortest geodesic paths is a crucial problem in several application areas, including robotics, medical imaging, terrain navigation and computational geometry. This type of computation on triangular meshes helps to solve different tasks, such as mesh watermarking, shape classification and mesh parametrization. In this work, a priority queue based on a bucketing structure is applied to speed up graph-based methods that approximates shortest geodesic paths on polyhedra. Initially, the problem is stated, some of its properties are discussed and a review of relevant methods is presented. Finally, we describe the proposed method and show several results and comparisons that confirm its benefits.

show abstract

Analysis of farthest point sampling for approximating geodesics in a graph

Cited by 28 publications

References 19 publications

Detecting Object Surface Keypoints From a Single RGB Image via Deep Learning Network for 6-DoF Pose Estimation

Detecting Object Surface Keypoints From a Single RGB Image via Deep Learning Network for 6-DoF Pose Estimation

Local k-NNs pattern in Omni-Direction graph convolution neural network for 3D point clouds

Faster Approximations of Shortest Geodesic Paths on Polyhedra Through Adaptive Priority Queue

Contact Info

Product

Resources

About