# Geometric Unifified Method in 3D Object Classifification

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## Description

Geometric Unifified Method in 3D Object Classifification, Is A Well-Researched Topic, It Is To Be Used As A Guide Or Framework For Your Research

## Abstract

3D object classification is one of the most popular topics in the field of
computer vision and computational geometry. Currently, the most popular state-of-the-art algorithm is the so-called Convolutional Neural Network (CNN) models with various representations that capture different features of the given 3D data, including voxels, local features, multi-view 2D features, and so on. With CNN as a holistic approach, researches focus on improving the accuracy and efficiency by designing the neural network architecture.

This thesis aims to examine the existing work on 3D object classification
and explore the underlying theory by integrating geometric approaches. By using geometric algorithms to pre-process and select data points, we dive into an existing architecture of directly feeding points into a deep CNN, and explore how geometry measures how important different points are in a CNN model. Moreover, we attempt to extract useful geometric features directly from the object data to introduce the feature matrix representation, which can be classified with distance-based approaches. We present all results of experiments and analyzed for future improvement.

Abstract iii
Acknowledgments xiii
1 Introduction to 3D Object Classification 1
2 Introduction to Convolutional Neural Network 5
3 PreviousWorks 11
3.1 Volumetric Convolutional Neural Network . . . . . . . . . . 11
3.2 Surface Polygon Mesh . . . . . . . . . . . . . . . . . . . . . . 15
3.3 Multi-View Convolutional Neural Network . . . . . . . . . . 20
3.4 PointNet: Direct Point Cloud Representation . . . . . . . . . . 23
3.5 Geometric Feature Extraction . . . . . . . . . . . . . . . . . . 29
4 Geometry and CNN: Comparison and Combination 35
5 Alpha Shape: The Shape Formed By Points 39
5.1 A GameWith Ice Cream Spoon . . . . . . . . . . . . . . . . . 39
5.2 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3 Edelsbrunner’s Algorithm . . . . . . . . . . . . . . . . . . . . 42
5.4 Alpha-shape on Real Examples . . . . . . . . . . . . . . . . . 45
6 Curvature: The Amount of Deviation 49
6.1 Basic Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.2 Interpolation and Curvature in Real Data . . . . . . . . . . . 51
6.3 Curvature for Surfaces . . . . . . . . . . . . . . . . . . . . . . 52
6.4 Curvature for Riemannian Manifold . . . . . . . . . . . . . . 55

vi Contents
7 Feature Matrix and Shape Partial Derivative 57
7.1 Feature Matrix: Idea and Definition . . . . . . . . . . . . . . 57
7.2 Distance Function Design . . . . . . . . . . . . . . . . . . . . 59
7.3 Shape Partial Derivative: Another Measure . . . . . . . . . . 61
8 Data, Experiment and Results 63
8.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
8.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
8.3 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . 66
8.4 FutureWorks . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Bibliography 69