Deep learning: an introduction for applied mathematicians

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very brief introduction to the basic ideas that underlie deep learning from an applied mathematics perspective. Our target audience includes postgraduate and final year undergraduate students in mathematics who are keen to learn about the area. The article may also be useful for instructors in mathematics who wish to enliven their classes with references to the application of deep learning techniques. We focus on three fundamental questions: what is a deep neural network? how is a network trained? what is the stochastic gradient method? We illustrate the ideas with a short MATLAB code that sets up and trains a network. We also show the use of state-of-the art software on a large scale image classification problem. We finish with references to the current literature

Color-to-Grayscale: Does the Method Matter in Image Recognition?

In image recognition it is often assumed the method used to convert color images to grayscale has little impact on recognition performance. We compare thirteen different grayscale algorithms with four types of image descriptors and demonstrate that this assumption is wrong: not all color-to-grayscale algorithms work equally well, even when using descriptors that are robust to changes in illumination. These methods are tested using a modern descriptor-based image recognition framework, on face, object, and texture datasets, with relatively few training instances. We identify a simple method that generally works best for face and object recognition, and two that work well for recognizing textures

Shape Retrieval of Non-rigid 3D Human Models

3D models of humans are commonly used within computer graphics and vision, and so the ability to distinguish between body shapes is an important shape retrieval problem. We extend our recent paper which provided a benchmark for testing non-rigid 3D shape retrieval algorithms on 3D human models. This benchmark provided a far stricter challenge than previous shape benchmarks. We have added 145 new models for use as a separate training set, in order to standardise the training data used and provide a fairer comparison. We have also included experiments with the FAUST dataset of human scans. All participants of the previous benchmark study have taken part in the new tests reported here, many providing updated results using the new data. In addition, further participants have also taken part, and we provide extra analysis of the retrieval results. A total of 25 different shape retrieval methods are compared

I have seen enough: Transferring parts across categories

The recent successes of deep learning have been possible due to the availability of increasingly large quantities of annotated data. A natural question, therefore, is whether further progress can be indefinitely sustained by annotating more data, or whether there is a saturation point beyond which a problem is essentially solved, or the capacity of a model is saturated. In this paper we examine this question from the viewpoint of learning shareable semantic parts, a fundamental building block to generalize visual knowledge between object categories. We ask two research questions often neglected: whether semantic parts are also visually shareable between classes, and how many annotations are required to learn them. In order to answer such questions, we collect 15,000 images of 100 animal classes and annotate them with parts. We then thoroughly test active learning and domain adaptation techniques to generalize to unseen classes parts that are learned from a limited number of classes and example images. Our experiments show that, for a majority of the classes, part annotations transfer well, and that performance reaches 98% of the accuracy of the fully annotated scenario by providing only a few thousand examples