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Hands-On Mathematics for Deep Learning

You're reading from  Hands-On Mathematics for Deep Learning

Product type Book
Published in Jun 2020
Publisher Packt
ISBN-13 9781838647292
Pages 364 pages
Edition 1st Edition
Languages
Author (1):
Jay Dawani Jay Dawani
Profile icon Jay Dawani

Table of Contents (19) Chapters

Preface 1. Section 1: Essential Mathematics for Deep Learning
2. Linear Algebra 3. Vector Calculus 4. Probability and Statistics 5. Optimization 6. Graph Theory 7. Section 2: Essential Neural Networks
8. Linear Neural Networks 9. Feedforward Neural Networks 10. Regularization 11. Convolutional Neural Networks 12. Recurrent Neural Networks 13. Section 3: Advanced Deep Learning Concepts Simplified
14. Attention Mechanisms 15. Generative Models 16. Transfer and Meta Learning 17. Geometric Deep Learning 18. Other Books You May Enjoy

Facial recognition in 3D

Let's go ahead and see how this translates to a real-world problem such as 3D facial recognition, which is used in phones, security, and so on. In 2D images, this would be largely dependent on the pose and illumination, and we don't have access to depth information. Because of this limitation, we use 3D faces instead so that we don't have to worry about lighting conditions, head orientation, and various facial expressions. For this task, the data we will be using is meshes.

In this case, our meshes make up an undirected, connected graph, G = (V, E, A), where |V| = n is the vertices, E is a set of edges, and contains the d-dimensional pseudo-coordinates, , where . The node feature matrix is denoted as , where each of the nodes contains d-dimensional features. We then define the lth channel of the feature map as fl, of which the ith node...

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