3D Shape Analysis with Geometric Deep Learning- Research Plan

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INTRODUCTION

Geometric deep learning(GDL) is umbrella term for deep learning techniques in non-Euclidean domains such as graph and manifolds. In recent years GDL has been applied to many 3D shape analysis problems. The problems in 3D shape analysis can be classified mainly in two groups. First is local descriptor learning or shape correspondence learning and second is global descriptor learning or shape recognition learning. The Convolutional Neural Network architectures on non-Euclidean domains( mainly manifold structured data) are very helpful for 3d shape analysis.

RELATED WORKS

Geodesic CNN, proposed by J. Masci et al. in 2015, is an advanced Convolutional neural network non-Euclidean manifolds. Later in 2016 D.Boscaini et al. proposed AnistropicCNN architecture. This is used to study the dense correspondence between deformable shapes. Localized Spectral CNN(LSCNN) proposed by 2016 D.Boscaini et al. is based on frequency analysis and can be used for deformable shapes. FMNet, again a CNN framework proposed in 2017, is also used for dense correspondence between deformable 3D shapes.

PROBLEM STATEMENT

To construct a generalization of the Convolutional Neural Network architecture on manifold structured data for 3D shape analysis. To generalize a deep learning model on a manifold data requires to find manifold counterparts. It also needs generalization across different domains. During the generalization a model is trained on a set of non-Euclidean domains (3D shapes) and then this model is applied on previously unseen data. The 3D shape data is modeled as Riemannian manifolds and characterized as meshes. Finding intrinsic shape correspondence between deformable shapes is a classical tough problem that underlines a broad range of vision applications including texture mapping, scene understanding.

OBJECTIVES

To achieve better accuracy during training and validation on manifold data. To achieve less computational complexity and deeper architecture.

RESEARCH PLAN

EXPERIMENTAL DETAILS: The following two datasets will be used for training and validation purpose. The FAUST dataset (Fine Alignment Using Scan Texture): This contains 300 high resolution human body scans of 10 different subjects in 30 different poses.

The TOSCA dataset: high resolution 3D non-rigid shapes in a variety of poses for non-rigid shape similarity and correspondence experiment.

REFERENCES

[1] F. Monti, D. Boscaini, J. Masci, E. Rodol_a, J. Svoboda, M. M. Bronstein, "Geometric deep learning on graphs and manifolds using mixture model CNNs", Proc. CVPR 2017.

[2] M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, P. Vandergheynst, "Geometric deep learning: going beyond uclidean data", arXiv:1611.08097, 2016.

[3] J. Masci, D. Boscaini, M. M. Bronstein, P. Vandergheynst, "Geodesic convolutional neural networks on Riemannian manifolds", arXiv:1501.06297v2,2015.

[4] D. Boscaini, J. Masci, S. Melzi, M. M. Bronstein, U. Castellani, P.Vandergheynst, "Learning class-specifc escriptors for deformable shapes using localized spectral convolutional networks", Computer Graphics Forum 34(5):13-23, 2015.

[5] D. Boscaini, J. Masci, E. Rodol_a, M. M. Bronstein, "Learning shape correspondence with anisotropic convolutional neural networks", Proc. NIPS 2016.

[6] Wenming Cao, Zhiyue Yan, Zhiquan He, Zhihai He, "A comprehensive Survey on Geometric Deep Learning", IEEE Access (Volume:8), 19 February 2020.

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