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A Review on Deep Learning Approaches for 3D Data Representations in Retrieval and Classifications

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Deep Learning Advances on Different 3D Data Representations: A Survey

3D data is a valuable asset in the field of computer vision as it provides rich information about the full geometry of sensed objects and scenes. With the recent availability of large 3D datasets and the increase in computational power, it is today possible to consider applying deep learning to learn specific tasks on 3D data such as segmentation, recognition and correspondence. Depending on the considered 3D data representation, different challenges may be foreseen in using existent deep learning architectures. In this paper, we provide a comprehensive overview of various 3D data representations highlighting the difference between Euclidean and non-Euclidean ones. We also discuss how deep learning methods are applied on each representation, analyzing the challenges to overcome.

Alexandre Saint

Abd El Rahman Shabayek

Kseniya Cherenkova

Djamila Aouada

Björn Ottersten

Related Research

Deep learning for scene classification: a survey, a survey on deep geometry learning: from a representation perspective, face recognition: from traditional to deep learning methods, hyperbolic deep learning in computer vision: a survey, deep neural networks and tabular data: a survey, recent advances on non-line-of-sight imaging: conventional physical models, deep learning, and new scenes, supporting future electrical utilities: using deep learning methods in ems and dms algorithms.

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Representing 3D point cloud data

A visual guide

Figure 1: A 3D point cloud of an abbey acquired in 2014 using photogrammetry or Lidar.  

Voxel-based models

Parametric model (cad).

Projections

Implicit representation.

• 3D point clouds are simple and efficient but lack connectivity
• 3D models such as 3D meshes, parametric models and voxel assemblies provide dedicated levels of additional information but approximate the base data
• Depth maps are well known and compact but essentially deal with 2.5D data
• Implicit representation encompasses all of the above and is beneficial for advanced processes that benefit from informative features that are difficult to represent visually
• Multi-view is complementary and leverages raster imagery but is prone to failure due to suboptimal viewpoint selection.
• Poux and R. Billen, Voxel-based 3D point cloud semantic segmentation: unsupervised geometric and relationship featuring vs deep learning methods, ISPRS International Journal of Geo-Information , vol. 8, no. 5, p. 213, May 2019.
• Poux, The Smart Point Cloud: Structuring 3D intelligent point data, Liège, 2019.
• Karara, R. Hajji, and F. Poux, 3D point cloud semantic augmentation: Instance segmentation of 360◦ panoramas by deep learning techniques, Remote Sensing , vol. 13, no. 18, p. 3647, Sep. 2021.

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MIT Libraries home DSpace@MIT

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• Doctoral Theses

Learning 3D Representations from Data

Terms of use

Date issued, collections.

1. Introduction

2. mathematical background.

• 3. Uniform and random samplings of SO(3)

4. Material textures and the square torus representation

5. discussion and conclusions.

research papers \(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Applications of the Clifford torus to material textures

a Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA * Correspondence e-mail: [email protected]

This paper introduces a new 2D representation of the orientation distribution function for an arbitrary material texture. The approach is based on the isometric square torus mapping of the Clifford torus, which allows for points on the unit quaternion hypersphere (each corresponding to a 3D orientation) to be represented in a periodic 2D square map. The combination of three such orthogonal mappings into a single RGB (red–green–blue) image provides a compact periodic representation of any set of orientations. Square torus representations of five different orientation sampling methods are compared and analyzed in terms of the Riesz s energies that quantify the uniformity of the samplings. The effect of crystallographic symmetry on the square torus map is analyzed in terms of the Rodrigues fundamental zones for the rotational symmetry groups. The paper concludes with example representations of important texture components in cubic and hexagonal materials. The new RGB representation provides a convenient and compact way of generating training data for the automated analysis of material textures by means of neural networks.

Keywords: orientation distribution functions ; texture ; symmetry ; quaternions ; Clifford torus .

2.1. Definitions

Scaling the circle to a radius of ρ and taking the Cartesian product of two such circles results in the Clifford torus,

The Clifford torus has the special property that it is flat, i.e. there exists an isometry from the torus to a 2D square with periodic boundaries; the edges of the square have length 2 π and cover the interval [− π ,  π ]. The isometric mapping, which can be shown to have a unit Jacobian, consists of taking the ratios

and inverting the relations to the coordinates ( X ,  Y ) = ( θ ,  φ ) in the square,

2.2. Projection of unit quaternions onto the Clifford torus

The projected coordinates in the square torus are then readily shown to be given by

We can think of the three coordinate pairs as three different isometric projections of an orientation onto three orthogonal square tori. We will label the square tori by their coordinate symbols; when no coordinate label is present, the ( X ,  Z Y ) projection will be assumed. In terms of the Rodrigues–Frank vector components, the cyclic permutations correspond to 120° rotations about the principal diagonal axis of the Rodrigues reference frame.

2.3. Relation between the square torus map and the Euler angle representation

This means that the ( Z ,  Y X ) square torus map is identical to a projection of Euler space along the Φ axis followed by a 45° rotation, bringing the φ 1 = φ 2 diagonal parallel to the Y X axis of the square torus map. The two other maps, ( X ,  Z Y ) and ( Y ,  X Z ), do not appear to have simple interpretations in terms of linear projections through Euler space; they are more complicated nonlinear projections.

2.4. Zone-plate function representation

with 〈 p ,  q 〉 the standard dot product between two quaternions projected onto the Clifford torus. q f is an arbitrary point on the torus, so that the zone-plate function uses the geodesic distance between q and q f along the surface of the torus. In this paper, we select the reference point

3. Uniform and random samplings of SO (3)

In this section, we explore a number of different orientation sampling approaches and their representation on the square torus using a zone-plate function. The following sampling approaches are used to generate orientation sets:

4.1. Fundamental zone representations

4.1.1. cyclic point-group symmetry, 4.1.2. dihedral, tetrahedral and octahedral point-group symmetry.

A few general trends can be observed in the zone plates for the four dihedral groups:

4.2. Basic texture-type representations

4.3. experimental texture representations.

corresponding to the Rodrigues vector

4.4. Fiber textures

4.4.1. f.c.c. fibers.

Consider the α fiber in an f.c.c. material. Its orientations are located around the line ( φ 1 ,  π /4,  π /2) in Euler space, with φ 1 ∈ [0,  π /2]. The corresponding unit quaternions are obtained by setting

4.4.2. B.c.c. fibers

Consider the α , γ and ε fibers in a b.c.c. material. In Euler space, all orientations lie along the following lines:

After conversion to the square torus coordinates, we find that the α fiber is represented by the curve

between the points ( X ,  Y ) = (0, − π /2) for Φ = 0 and (− π /4, − π /4) for Φ = π /2.

For the ε fiber we find

The γ fiber sits in between the two curves and is represented by

The intersection points of the γ fiber with the α and ε fibers have coordinates

for the α fiber and

4.5. Experimental fiber texture example

Different from more conventional 3D representations of material textures, the RGB square torus map representation opens a unique path to the use of neural networks to automate the analysis of material textures, in particular to determine the mixture of texture components that are present in the orientation distribution. The use of ST maps in this context is the topic of ongoing investigations.

Acknowledgements

The author would like to acknowledge stimulating discussions with A. D. Rollet, M. P. Echlin, T. M. Pollock, S. Wright, W. Lenthe, D. Rowenhorst, B. Hutchinson, C. Lafond, G. Austin and S. Niezgoda.

Funding information

The author acknowledges financial support from the National Science Foundation, Directorate for Mathematical and Physical Sciences (grant No. DMR-2203378), and the use of the computational resources of the Materials Characterization Facility at Carnegie Mellon University (grant No. MCF-677785). The author also acknowledges support from the John and Claire Bertucci Distinguished Professorship in Engineering.

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence , which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.

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Computer Science > Computer Vision and Pattern Recognition

Title: compgs: efficient 3d scene representation via compressed gaussian splatting.

Abstract: Gaussian splatting, renowned for its exceptional rendering quality and efficiency, has emerged as a prominent technique in 3D scene representation. However, the substantial data volume of Gaussian splatting impedes its practical utility in real-world applications. Herein, we propose an efficient 3D scene representation, named Compressed Gaussian Splatting (CompGS), which harnesses compact Gaussian primitives for faithful 3D scene modeling with a remarkably reduced data size. To ensure the compactness of Gaussian primitives, we devise a hybrid primitive structure that captures predictive relationships between each other. Then, we exploit a small set of anchor primitives for prediction, allowing the majority of primitives to be encapsulated into highly compact residual forms. Moreover, we develop a rate-constrained optimization scheme to eliminate redundancies within such hybrid primitives, steering our CompGS towards an optimal trade-off between bitrate consumption and representation efficacy. Experimental results show that the proposed CompGS significantly outperforms existing methods, achieving superior compactness in 3D scene representation without compromising model accuracy and rendering quality. Our code will be released on GitHub for further research.

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