Over the past decade, machine learning research has made great strides and significant impact in several fields. Its success is greatly attributed to the development of effective machine learning algorithms like deep neural networks (a.k.a. deep learning), availability of large-scale databases and access to specialized hardware like Graphic Processing Units. When designing and training machine learning systems, researchers often assume access to large quantities of data that capture different possible variations. Variations in the data is needed to incorporate desired invariance and robustness properties in the machine learning system, especially in the case of deep learning algorithms. However, it is very difficult to gather such data in a real-world setting. For example, in certain medical/healthcare applications, it is very challenging to have access to data from all possible scenarios or with the necessary amount of variations as required to train the system. Additionally, the over-parameterized and unconstrained nature of deep neural networks can cause them to be poorly trained and in many cases over-confident which, in turn, can hamper their reliability and generalizability. This dissertation is a compendium of my research efforts to address the above challenges. I propose building invariant feature representations by wedding concepts from topological data analysis and Riemannian geometry, that automatically incorporate the desired invariance properties for different computer vision applications. I discuss how deep learning can be used to address some of the common challenges faced when working with topological data analysis methods. I describe alternative learning strategies based on unsupervised learning and transfer learning to address issues like dataset shifts and limited training data. Finally, I discuss my preliminary work on applying simple orthogonal constraints on deep learning feature representations to help develop more reliable and better calibrated models.

Semantic image segmentation has been a key topic in applications involving image processing and computer vision. Owing to the success and continuous research in the field of deep learning, there have been plenty of deep learning-based segmentation architectures that have been designed for various tasks. In this thesis, deep-learning architectures for a specific application in material science; namely the segmentation process for the non-destructive study of the microstructure of Aluminum Alloy AA 7075 have been developed. This process requires the use of various imaging tools and methodologies to obtain the ground-truth information. The image dataset obtained using Transmission X-ray microscopy (TXM) consists of raw 2D image specimens captured from the projections at every beam scan. The segmented 2D ground-truth images are obtained by applying reconstruction and filtering algorithms before using a scientific visualization tool for segmentation. These images represent the corrosive behavior caused by the precipitates and inclusions particles on the Aluminum AA 7075 alloy. The study of the tools that work best for X-ray microscopy-based imaging is still in its early stages.

In this thesis, the underlying concepts behind Convolutional Neural Networks (CNNs) and state-of-the-art Semantic Segmentation architectures have been discussed in detail. The data generation and pre-processing process applied to the AA 7075 Data have also been described, along with the experimentation methodologies performed on the baseline and four other state-of-the-art Segmentation architectures that predict the segmented boundaries from the raw 2D images. A performance analysis based on various factors to decide the best techniques and tools to apply Semantic image segmentation for X-ray microscopy-based imaging was also conducted.

In recent years, the widespread use of deep neural networks (DNNs) has facilitated great improvements in performance for computer vision tasks like image classification and object recognition. In most realistic computer vision applications, an input image undergoes some form of image distortion such as blur and additive noise during image acquisition or transmission. Deep networks trained on pristine images perform poorly when tested on such distortions. DNN predictions have also been shown to be vulnerable to carefully crafted adversarial perturbations. Specifically, so-called universal adversarial perturbations are image-agnostic perturbations that can be added to any image and can fool a target network into making erroneous predictions. This work proposes selective DNN feature regeneration to improve the robustness of existing DNNs to image distortions and universal adversarial perturbations.

In the context of common naturally occurring image distortions, a metric is proposed to identify the most susceptible DNN convolutional filters and rank them in order of the highest gain in classification accuracy upon correction. The proposed approach called DeepCorrect applies small stacks of convolutional layers with residual connections at the output of these ranked filters and trains them to correct the most distortion-affected filter activations, whilst leaving the rest of the pre-trained filter outputs in the network unchanged. Performance results show that applying DeepCorrect models for common vision tasks significantly improves the robustness of DNNs against distorted images and outperforms other alternative approaches.

In the context of universal adversarial perturbations, departing from existing defense strategies that work mostly in the image domain, a novel and effective defense which only operates in the DNN feature domain is presented. This approach identifies pre-trained convolutional features that are most vulnerable to adversarial perturbations and deploys trainable feature regeneration units which transform these DNN filter activations into resilient features that are robust to universal perturbations. Regenerating only the top 50% adversarially susceptible activations in at most 6 DNN layers and leaving all remaining DNN activations unchanged can outperform existing defense strategies across different network architectures and across various universal attacks.

Antibiotic resistance is a very important issue that threatens mankind. As bacteria

are becoming resistant to multiple antibiotics, many common antibiotics will soon

become ineective. The ineciency of current methods for diagnostics is an important

cause of antibiotic resistance, since due to their relative slowness, treatment plans

are often based on physician's experience rather than on test results, having a high

chance of being inaccurate or not optimal. This leads to a need of faster, pointof-

care (POC) methods, which can provide results in a few hours. Motivated by

recent advances on computer vision methods, three projects have been developed

for bacteria identication and antibiotic susceptibility tests (AST), with the goal of

speeding up the diagnostics process. The rst two projects focus on obtaining features

from optical microscopy such as bacteria shape and motion patterns to distinguish

active and inactive cells. The results show their potential as novel methods for AST,

being able to obtain results within a window of 30 min to 3 hours, a much faster

time frame than the gold standard approach based on cell culture, which takes at

least half a day to be completed. The last project focus on the identication task,

combining large volume light scattering microscopy (LVM) and deep learning to

distinguish bacteria from urine particles. The developed setup is suitable for pointof-

care applications, as a large volume can be viewed at a time, avoiding the need

for cell culturing or enrichment. This is a signicant gain compared to cell culturing

methods. The accuracy performance of the deep learning system is higher than chance

and outperforms a traditional machine learning system by up to 20%.

This thesis introduces new techniques for clustering distributional data according to their geometric similarities. This work builds upon the optimal transportation (OT) problem that seeks global minimum cost for matching distributional data and leverages the connection between OT and power diagrams to solve different clustering problems. The OT formulation is based on the variational principle to differentiate hard cluster assignments, which was missing in the literature. This thesis shows multiple techniques to regularize and generalize OT to cope with various tasks including clustering, aligning, and interpolating distributional data. It also discusses the connections of the new formulation to other OT and clustering formulations to better understand their gaps and the means to close them. Finally, this thesis demonstrates the advantages of the proposed OT techniques in solving machine learning problems and their downstream applications in computer graphics, computer vision, and image processing.

At present, the vast majority of human subjects with neurological disease are still diagnosed through in-person assessments and qualitative analysis of patient data. In this paper, we propose to use Topological Data Analysis (TDA) together with machine learning tools to automate the process of Parkinson’s disease classification and severity assessment. An automated, stable, and accurate method to evaluate Parkinson’s would be significant in streamlining diagnoses of patients and providing families more time for corrective measures. We propose a methodology which incorporates TDA into analyzing Parkinson’s disease postural shifts data through the representation of persistence images. Studying the topology of a system has proven to be invariant to small changes in data and has been shown to perform well in discrimination tasks. The contributions of the paper are twofold. We propose a method to 1) classify healthy patients from those afflicted by disease and 2) diagnose the severity of disease. We explore the use of the proposed method in an application involving a Parkinson’s disease dataset comprised of healthy-elderly, healthy-young and Parkinson’s disease patients.

The autonomous vehicle technology has come a long way, but currently, there are no companies that are able to offer fully autonomous ride in any conditions, on any road without any human supervision. These systems should be extensively trained and validated to guarantee safe human transportation. Any small errors in the system functionality may lead to fatal accidents and may endanger human lives. Deep learning methods are widely used for environment perception and prediction of hazardous situations. These techniques require huge amount of training data with both normal and abnormal samples to enable the vehicle to avoid a dangerous situation.



The goal of this thesis is to generate simulations from real-world tricky collision scenarios for training and testing autonomous vehicles. Dashcam crash videos from the internet can now be utilized to extract valuable collision data and recreate the crash scenarios in a simulator. The problem of extracting 3D vehicle trajectories from videos recorded by an unknown monocular camera source is solved using a modular approach. The framework is divided into two stages: (a) extracting meaningful adversarial trajectories from short crash videos, and (b) developing methods to automatically process and simulate the vehicle trajectories on a vehicle simulator.

This thesis addresses the problem of recommending a viewpoint for aesthetic photography. Viewpoint recommendation is suggesting the best camera pose to capture a visually pleasing photograph of the subject of interest by using any end-user device such as drone, mobile robot or smartphone. Solving this problem enables to capture visually pleasing photographs autonomously in areal photography, wildlife photography, landscape photography or in personal photography.

The viewpoint recommendation problem can be divided into two stages: (a) generating a set of dense novel views based on the basis views captured about the subject. The dense novel views are useful to better understand the scene and to know how the subject looks from different viewpoints and (b) each novel is scored based on how aesthetically good it is. The viewpoint with the greatest aesthetic score is recommended for capturing a visually pleasing photograph.

Over the last decade, deep neural networks also known as deep learning, combined with large databases and specialized hardware for computation, have made major strides in important areas such as computer vision, computational imaging and natural language processing. However, such frameworks currently suffer from some drawbacks. For example, it is generally not clear how the architectures are to be designed for different applications, or how the neural networks behave under different input perturbations and it is not easy to make the internal representations and parameters more interpretable. In this dissertation, I propose building constraints into feature maps, parameters and and design of algorithms involving neural networks for applications in low-level vision problems such as compressive imaging and multi-spectral image fusion, and high-level inference problems including activity and face recognition. Depending on the application, such constraints can be used to design architectures which are invariant/robust to certain nuisance factors, more efficient and, in some cases, more interpretable. Through extensive experiments on real-world datasets, I demonstrate these advantages of the proposed methods over conventional frameworks.

The depth richness of a scene translates into a spatially variable defocus blur in the acquired image. Blurring can mislead computational image understanding; therefore, blur detection can be used for selective image enhancement of blurred regions and the application of image understanding algorithms to sharp regions. This work focuses on blur detection and its application to image enhancement.

This work proposes a spatially-varying defocus blur detection based on the quotient of spectral bands; additionally, to avoid the use of computationally intensive algorithms for the segmentation of foreground and background regions, a global threshold defined using weak textured regions on the input image is proposed. Quantitative results expressed in the precision-recall space as well as qualitative results overperform current state-of-the-art algorithms while keeping the computational requirements at competitive levels.

Imperfections in the curvature of lenses can lead to image radial distortion (IRD). Computer vision applications can be drastically affected by IRD. This work proposes a novel robust radial distortion correction algorithm based on alternate optimization using two cost functions tailored for the estimation of the center of distortion and radial distortion coefficients. Qualitative and quantitative results show the competitiveness of the proposed algorithm.

Blur is one of the causes of visual discomfort in stereopsis. Sharpening applying traditional algorithms can produce an interdifference which causes eyestrain and visual fatigue for the viewer. A sharpness enhancement method for stereo images that incorporates binocular vision cues and depth information is presented. Perceptual evaluation and quantitative results based on the metric of interdifference deviation are reported; results of the proposed algorithm are competitive with state-of-the-art stereo algorithms.

Digital images and videos are produced every day in astonishing amounts. Consequently, the market-driven demand for higher quality content is constantly increasing which leads to the need of image quality assessment (IQA) methods. A training-free, no-reference image sharpness assessment method based on the singular value decomposition of perceptually-weighted normalized-gradients of relevant pixels in the input image is proposed. Results over six subject-rated publicly available databases show competitive performance when compared with state-of-the-art algorithms.