LBO-Shape Densities: Efficient 3D Shape Retrieval Using Wavelet Density Estimation

Moyou, Mark; Ihou, Koffi Eddy; Peter, Adrian M.

doi:10.1109/icpr.2014.19

Cited by 6 publications

(6 citation statements)

References 15 publications

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“…Rich surface and hidden geometric/graph structure amply depict the discrepancy among shapes. The shape descriptors mentioned in [51] are practical in retrieval for polygon meshes and point clouds, e.g., global information [32], local features [11,43,39,12], Zernike moment [30], distribution [33,27], skeleton [37], topology [3,41]. Recently, deep learning methods for 3D shape retrieval based on shape structure have been proposed.…”

Section: D Shape Retrievalmentioning

confidence: 99%

A Robust Scheme for 3D Point Cloud Copy Detection

Yang,

Lu,

Chen

2021

Preprint

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Most existing 3D geometry copy detection research focused on 3D watermarking, which first embeds "watermarks" and then detects the added watermarks. However, this kind of methods is nonstraightforward and may be less robust to attacks such as cropping and noise. In this paper, we focus on a fundamental and practical research problem: judging whether a point cloud is plagiarized or copied to another point cloud in the presence of several manipulations (e.g., similarity transformation, smoothing). We propose a novel method to address this critical problem. Our key idea is first to align the two point clouds and then calculate their similarity distance. We design three different measures to compute the similarity. We also introduce two strategies to speed up our method. Comprehensive experiments and comparisons demonstrate the effectiveness and robustness of our method in estimating the similarity of two given 3D point clouds.

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Section: D Shape Retrievalmentioning

confidence: 99%

A Robust Scheme for 3D Point Cloud Copy Detection

Yang,

Lu,

Chen

2021

Preprint

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“…Scores:342 T score:342 Scores:23 T score: 23 Scores:14 T score:14 Scores:20 T score :20 Original Affine Shapes Grassmannian Representation LBO Eigenvector Representation with Sign-flips Figure 1: Visual overview of the GrassGraph algorithm. On the far left, we begin with the original shapes which differ by an affine transform.…”

Section: Introductionmentioning

confidence: 99%

A Grassmannian Graph Approach to Affine Invariant Feature Matching

Moyou¹,

Rangarajan

Corring

et al. 2020

IEEE Trans. on Image Process.

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In this work, we present a novel and practical approach to address one of the longstanding problems in computer vision: 2D and 3D affine invariant feature matching. Our Grassmannian Graph (GrassGraph) framework employs a two stage procedure that is capable of robustly recovering correspondences between two unorganized, affinely related feature (point) sets. The first stage maps the feature sets to an affine invariant Grassmannian representation, where the features are mapped into the same subspace. It turns out that coordinate representations extracted from the Grassmannian differ by an arbitrary orthonormal matrix. In the second stage, by approximating the Laplace-Beltrami operator (LBO) on these coordinates, this extra orthonormal factor is nullified, providing true affine-invariant coordinates which we then utilize to recover correspondences via simple nearest neighbor relations. The resulting GrassGraph algorithm is empirically shown to work well in non-ideal scenarios with noise, outliers, and occlusions. Our validation benchmarks use an unprecedented 440,000+ experimental trials performed on 2D and 3D datasets, with a variety of parameter settings and competing methods. State-of-the-art performance in the majority of these extensive evaluations confirm the utility of our method.

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“…With advantages such as elimination of topology-based preprocessing (e.g. curve or surface extraction) or curtailing explicit correspondence discovery [9], the representation of geometric shapes as probabilistic distributions has yielded state-of-the-art performance in a myriad of shape analysis tasks; spanning the gamut from registration [46,10,21,44] to metric learning and shape classication [38,37,59,33]. There are mathe- The benets of this probabilistic representation motivated us extend the shape modeling approach rst detailed in [44] and extended by [38].…”

Section: Introductionmentioning

confidence: 99%

“…The common theme between our 2D/3D shape classication methodologies is the use of the square-root wavelet density estimator [42] and its associated hypersphere geometry. The 2D approach outlined in [38] required the use of a 2D square-root wavelet density estimator, which was extended in [37] to three dimensions, making it the rst implementation of a 3D square- points. This present work aggrandizes the approach in [37] to subsume 2D shape matchingproviding a single unied framework for 2D and 3D shapesand thoroughly evaluates it on several 2D/3D shape benchmarks.…”

Section: Introductionmentioning

confidence: 99%

“…The 2D approach outlined in [38] required the use of a 2D square-root wavelet density estimator, which was extended in [37] to three dimensions, making it the rst implementation of a 3D square- points. This present work aggrandizes the approach in [37] to subsume 2D shape matchingproviding a single unied framework for 2D and 3D shapesand thoroughly evaluates it on several 2D/3D shape benchmarks. A key component of our approach, as previously demonstrated in these works, is the rich modeling power aorded by the non-parametric wavelet density estimator.…”

Section: Introductionmentioning

confidence: 99%

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LBO-Shape densities: A unified framework for 2D and 3D shape classification on the hypersphere of wavelet densities

Moyou

Ihou

Peter

2016

Computer Vision and Image Understanding

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Recent years have seen a sharp rise in shape classication applications, and following suit, several frameworks have been proposed for ecient indexing of shape models. Here we propose a state-of-the-art shape matching framework which concomitantly provides transformation invariance and computationally ecient querying. Shapes are represented as probability density functions estimated on the eigenspace of the shape's Laplace-Beltrami operator (LBO) and the ensuing manifold geometry is leveraged to classify query shapes. Specically, we estimate a nonparametric, squareroot wavelet density on the low-order eigenvectors of the LBO, capturing the rich geometric structure of 2D and 3D shapes with very minimal pre-processing requirements. By estimating 3D, square-root wavelet densities on each shape's eigenspace (LBO-shape densities), both 2D and 3D shapes become identiable with the unit hypersphere. Leveraging the hypersphere's simple geometry, our avant-garde model-to-mean indexing scheme computes the intrinsic Karcher mean for each shape category, and then uses the closed-form distance between a query shape and the means to assign labels. In 2D, the need for burdensome preprocessing like extracting closed curves along with topological and equal point set cardinality requirements are eliminated. Similarly, in 3D we gain isometry invariance and rid ourselves of the need for superuous feature extraction schemes. The extensive experimental results demonstrate that our approach is competitive with the state-of-the-art in 2D/3D shape matching algorithms.

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LBO-Shape Densities: Efficient 3D Shape Retrieval Using Wavelet Density Estimation

Cited by 6 publications

References 15 publications

A Robust Scheme for 3D Point Cloud Copy Detection

A Robust Scheme for 3D Point Cloud Copy Detection

A Grassmannian Graph Approach to Affine Invariant Feature Matching

LBO-Shape densities: A unified framework for 2D and 3D shape classification on the hypersphere of wavelet densities

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