Optimisation based approaches for machine learning

Machine learning has attracted a lot of attention in recent years and it has become an integral part of many commercial and research projects, with a wide range of applications. With current developments in technology, more data is generated and stored than ever before. Identifying patterns, trends and anomalies in these datasets and summarising them with simple quantitative models is a vital task. This thesis focuses on the development of machine learning algorithms based on mathematical programming for datasets that are relatively small in size. The first topic of this doctoral thesis is piecewise regression, where a dataset is partitioned into multiple regions and a regression model is fitted to each one. This work uses an existing algorithm from the literature and extends the mathematical formulation in order to include information criteria. The inclusion of such criteria targets to deal with overfitting, which is a common problem in supervised learning tasks, by finding a balance between predictive performance and model complexity. The improvement in overall performance is demonstrated by testing and comparing the proposed method with various algorithms from the literature on various regression datasets. Extending the topic of regression, a decision tree regressor is also proposed. Decision trees are powerful and easy to understand structures that can be used both for regression and classification. In this work, an optimisation model is used for the binary splitting of nodes. A statistical test is introduced to check whether the partitioning of nodes is statistically meaningful and as a result control the tree generation process. Additionally, a novel mathematical formulation is proposed to perform feature selection and ultimately identify the appropriate variable to be selected for the splitting of nodes. The performance of the proposed algorithm is once again compared with a number of literature algorithms and it is shown that the introduction of the variable selection model is useful for reducing the training time of the algorithm without major sacrifices in performance. Lastly, a novel decision tree classifier is proposed. This algorithm is based on a mathematical formulation that identifies the optimal splitting variable and break value, applies a linear transformation to the data and then assigns them to a class while minimising the number of misclassified samples. The introduction of the linear transformation step reduces the dimensionality of the examined dataset down to a single variable, aiding the classification accuracy of the algorithm for more complex datasets. Popular classifiers from the literature have been used to compare the accuracy of the proposed algorithm on both synthetic and publicly available classification datasets

Neural Implicit Surface Reconstruction using Imaging Sonar

We present a technique for dense 3D reconstruction of objects using an imaging sonar, also known as forward-looking sonar (FLS). Compared to previous methods that model the scene geometry as point clouds or volumetric grids, we represent the geometry as a neural implicit function. Additionally, given such a representation, we use a differentiable volumetric renderer that models the propagation of acoustic waves to synthesize imaging sonar measurements. We perform experiments on real and synthetic datasets and show that our algorithm reconstructs high-fidelity surface geometry from multi-view FLS images at much higher quality than was possible with previous techniques and without suffering from their associated memory overhead.Comment: 8 pages, 8 figures. This paper is under revie

Passive Micron-scale Time-of-Flight with Sunlight Interferometry

We introduce an interferometric technique for passive time-of-flight imaging and depth sensing at micrometer axial resolutions. Our technique uses a full-field Michelson interferometer, modified to use sunlight as the only light source. The large spectral bandwidth of sunlight makes it possible to acquire micrometer-resolution time-resolved scene responses, through a simple axial scanning operation. Additionally, the angular bandwidth of sunlight makes it possible to capture time-of-flight measurements insensitive to indirect illumination effects, such as interreflections and subsurface scattering. We build an experimental prototype that we operate outdoors, under direct sunlight, and in adverse environmental conditions such as mechanical vibrations and vehicle traffic. We use this prototype to demonstrate, for the first time, passive imaging capabilities such as micrometer-scale depth sensing robust to indirect illumination, direct-only imaging, and imaging through diffusers

On the appearance of translucent edges

Edges in images of translucent objects are very different from edges in images of opaque objects. The physical causes for these differences are hard to characterize analytically and are not well understood. This paper considers one class of translucency edges - those caused by a discontinuity in surface orientation - and describes the physical causes of their appearance. We simulate thousands of translucency edge profiles using many different scattering material parameters, and we explain the resulting variety of edge patterns by qualitatively analyzing light transport. We also discuss the existence of shape and material metamers, or combinations of distinct shape or material parameters that generate the same edge profile. This knowledge is relevant to visual inference tasks that involve translucent objects, such as shape or material estimation.National Science Foundation (U.S.) (IIS 1161564)National Science Foundation (U.S.) (IIS 1012454)National Science Foundation (U.S.) (IIS 1212928)National Science Foundation (U.S.) (IIS 1011919)National Institutes of Health (U.S.) (R01- EY019262-02)National Institutes of Health (U.S.) (R21-EY019741-02

Understanding the role of phase function in translucent appearance

Multiple scattering contributes critically to the characteristic translucent appearance of food, liquids, skin, and crystals; but little is known about how it is perceived by human observers. This article explores the perception of translucency by studying the image effects of variations in one factor of multiple scattering: the phase function. We consider an expanded space of phase functions created by linear combinations of Henyey-Greenstein and von Mises-Fisher lobes, and we study this physical parameter space using computational data analysis and psychophysics. Our study identifies a two-dimensional embedding of the physical scattering parameters in a perceptually meaningful appearance space. Through our analysis of this space, we find uniform parameterizations of its two axes by analytical expressions of moments of the phase function, and provide an intuitive characterization of the visual effects that can be achieved at different parts of it. We show that our expansion of the space of phase functions enlarges the range of achievable translucent appearance compared to traditional single-parameter phase function models. Our findings highlight the important role phase function can have in controlling translucent appearance, and provide tools for manipulating its effect in material design applications.National Institutes of Health (U.S.) (Award R01-EY019262-02)National Institutes of Health (U.S.) (Award R21-EY019741-02