Self-Supervised Shape and Appearance Modeling via Neural Differentiable Graphics

Inferring 3D shape and appearance from natural images is a fundamental challenge in computer vision. Despite recent progress using deep learning methods, a key limitation is the availability of annotated training data, as acquisition is often very challenging and expensive, especially at a large scale. This thesis proposes to incorporate physical priors into neural networks that allow for self-supervised learning. As a result, easy-to-access unlabeled data can be used for model training. In particular, novel algorithms in the context of 3D reconstruction and texture/material synthesis are introduced, where only image data is available as supervisory signal. First, a method that learns to reason about 3D shape and appearance solely from unstructured 2D images, achieved via differentiable rendering in an adversarial fashion, is proposed. As shown next, learning from videos significantly improves 3D reconstruction quality. To this end, a novel ray-conditioned warp embedding is proposed that aggregates pixel-wise features from multiple source images. Addressing the challenging task of disentangling shape and appearance, first a method that enables 3D texture synthesis independent of shape or resolution is presented. For this purpose, 3D noise fields of different scales are transformed into stationary textures. The method is able to produce 3D textures, despite only requiring 2D textures for training. Lastly, the surface characteristics of textures under different illumination conditions are modeled in the form of material parameters. Therefore, a self-supervised approach is proposed that has no access to material parameters but only flash images. Similar to the previous method, random noise fields are reshaped to material parameters, which are conditioned to replicate the visual appearance of the input under matching light

Feature Embedding by Template Matching as a ResNet Block

Convolution blocks serve as local feature extractors and are the key to success of the neural networks. To make local semantic feature embedding rather explicit, we reformulate convolution blocks as feature selection according to the best matching kernel. In this manner, we show that typical ResNet blocks indeed perform local feature embedding via template matching once batch normalization (BN) followed by a rectified linear unit (ReLU) is interpreted as arg-max optimizer. Following this perspective, we tailor a residual block that explicitly forces semantically meaningful local feature embedding through using label information. Specifically, we assign a feature vector to each local region according to the classes that the corresponding region matches. We evaluate our method on three popular benchmark datasets with several architectures for image classification and consistently show that our approach substantially improves the performance of the baseline architectures.Comment: Accepted at the British Machine Vision Conference 2022 (BMVC 2022

Rapid Spectral Parameter Prediction for Black Hole X-Ray Binaries using Physicalised Autoencoders

Black hole X-ray binaries (BHBs) offer insights into extreme gravitational environments and the testing of general relativity. The X-ray spectrum collected by NICER offers valuable information on the properties and behaviour of BHBs through spectral fitting. However, traditional spectral fitting methods are slow and scale poorly with model complexity. This paper presents a new semi-supervised autoencoder neural network for parameter prediction and spectral reconstruction of BHBs, showing an improvement of up to a factor of 2,700 in speed while maintaining comparable accuracy. The approach maps the spectral features from the numerous outbursts catalogued by NICER and generalises them to new systems for efficient and accurate spectral fitting. The effectiveness of this approach is demonstrated in the spectral fitting of BHBs and holds promise for use in other areas of astronomy and physics for categorising large datasets.Comment: 12 pages, 12 figure

DeFeat-Net: General Monocular Depth via Simultaneous Unsupervised Representation Learning

In the current monocular depth research, the dominant approach is to employ unsupervised training on large datasets, driven by warped photometric consistency. Such approaches lack robustness and are unable to generalize to challenging domains such as nighttime scenes or adverse weather conditions where assumptions about photometric consistency break down. We propose DeFeat-Net (Depth & Feature network), an approach to simultaneously learn a cross-domain dense feature representation, alongside a robust depth-estimation framework based on warped feature consistency. The resulting feature representation is learned in an unsupervised manner with no explicit ground-truth correspondences required. We show that within a single domain, our technique is comparable to both the current state of the art in monocular depth estimation and supervised feature representation learning. However, by simultaneously learning features, depth and motion, our technique is able to generalize to challenging domains, allowing DeFeat-Net to outperform the current state-of-the-art with around 10% reduction in all error measures on more challenging sequences such as nighttime driving

Sequential and adaptive Bayesian computation for inference and optimization

With the advent of cheap and ubiquitous measurement devices, today more data is measured, recorded, and archived in a relatively short span of time than all data recorded throughout history. Moreover, advances in computation have made it possible to model much more complicated phenomena and to use the vast amounts of data to calibrate the resulting high-dimensional models. In this thesis, we are interested in two fundamental problems which are repeatedly being faced in practice as the dimension of the models and datasets are growing steadily: the problem of inference in high-dimensional models and the problem of optimization for problems when the number of data points is very large. The inference problem gets difficult when the model one wants to calibrate and estimate is defined in a high-dimensional space. The behavior of computational algorithms in high-dimensional spaces is complicated and defies intuition. Computational methods which work accurately for inferring low-dimensional models, for example, may fail to generalize the same performance to high-dimensional models. In recent years, due to the significant interest in high-dimensional models, there has been a plethora of work in signal processing and machine learning to develop computational methods which are robust in high-dimensional spaces. In particular, the high-dimensional stochastic filtering problem has attracted significant attention as it arises in multiple fields which are of crucial importance such as geophysics, aerospace, control. In particular, a class of algorithms called particle filters has received attention and become a fruitful field of research because of their accuracy and robustness in low-dimensional systems. In short, these methods keep a cloud of particles (samples in a state space), which describe the empirical probability distribution over the state variable of interest. The particle filters use a model of the phenomenon of interest to propagate and predict the future states and use an observation model to assimilate the observations to correct the state estimates. The most common particle filter, called the bootstrap particle filter (BPF), consists of an iterative sampling-weighting-resampling scheme. However, BPFs also largely fail at inferring high-dimensional dynamical systems due to a number of reasons. In this work, we propose a novel particle filter, named the nudged particle filter (NuPF), which specifically aims at improving the performance of particle filters in high-dimensional systems. The algorithm relies on the idea of nudging, which has been widely used in the geophysics literature to tackle high-dimensional inference problems. In particular, in addition to standard sampling-weighting-resampling steps of the particle filter, we define a general nudging step based on the gradient of the likelihoods, which generalize some of the nudging schemes proposed in the literature. This step is based on modifying the particles, generated in the sampling step, using the gradients of the likelihoods. In particular, the nudging step moves a fraction of the particles to the regions under which they have high-likelihoods. This scheme results in significantly improved behavior in high-dimensional models. The resulting NuPF is able to track high-dimensional systems successfully. Unlike the proposed nudging schemes in the literature, the NuPF does not rely on Gaussianity assumptions and can be defined for a general likelihood. We analytically prove that, because we only move a fraction of the particles and not all of them, the algorithm has a convergence rate that matches standard Monte Carlo algorithms. More precisely, the NuPF has the same asymptotic convergence guarantees as the bootstrap particle filter. As a byproduct, we also show that the nudging step improves the robustness of the particle filter against model misspecification. In particular, model misspecification occurs when the true data-generating system and the model posed by the user of the algorithm differ significantly. In this case, a majority of computational inference methods fail due to the discrepancy between the modeling assumptions and the observed data. We show that the nudging step increases the robustness of particle filters against model misspecification. Specifically, we prove that the NuPF generates particle systems which have provably higher marginal likelihoods compared to the standard bootstrap particle filter. This theoretical result is attained by showing that the NuPF can be interpreted as a bootstrap particle filter for a modified state-space model. Finally, we demonstrate the empirical behavior of the NuPF with several examples. In particular, we show results on high-dimensional linear state-space models, a misspecified Lorenz 63 model, a high-dimensional Lorenz 96 model, and a misspecified object tracking model. In all examples, the NuPF infers the states successfully. The second problem, the so-called scability problem in optimization, occurs because of the large number of data points in modern datasets. With the increasing abundance of data, many problems in signal processing, statistical inference, and machine learning turn into a large-scale optimization problems. For example, in signal processing, one might be interested in estimating a sparse signal given a large number of corrupted observations. Similarly, maximum-likelihood inference problems in statistics result in large-scale optimization problems. Another significant application domain is machine learning, where all important training methods are defined as optimization problems. To tackle these problems, computational optimization methods developed over the past decades are inefficient since they need to compute function evaluations or gradients over all the data for a single iteration. Because of this reason, a class of optimization methods, termed stochastic optimization methods, have emerged. The algorithms of this class are designed to tackle problems which are defined over a big number of data points. In short, these methods utilize a subsample of the dataset in order to update the parameter estimate and do so iteratively until some convergence criterion is met. However, there is a major difficulty that has to be addressed: Although the convergence theory for these algorithms is understood, they can have unstable behavior in practice. In particular, the most commonly used stochastic optimization method, namely the stochastic gradient descent, can diverge easily if its step-size is poorly set. Over the years, practitioners have developed a number of rules of thumb to alleviate stability issues. We argue in this thesis that one way to develop robust stochastic optimization methods is to frame them as inference methods. In particular, we show that stochastic optimization schemes can be recast as inference methods and can be understood as inference algorithms. Framing the problem as an inference problem opens the way to compare these methods to the optimal inference algorithms and understand why they might be failing or producing unstable behavior. In this vein, we show that there is an intrinsic relationship between a class of stochastic optimization methods, called incremental proximal methods, and Kalman (and extended Kalman) filters. The filtering approach to stochastic optimization results in an automatic calibration of the step-size, which removes the instability problems depending on the step-sizes. The probabilistic interpretation of stochastic optimization problems also paves the way to develop new optimization methods based on strategies which are popular in the inference literature. In particular, one can use a set of sampling methods in order to solve the inference problem and hence obtain the global minimum. In this manner, we propose a parallel sequential Monte Carlo optimizer (PSMCO), which is aiming at solving stochastic optimization problems. The PSMCO is designed as a zeroth order method which does not use gradients. It only uses subsets of the data points in order to move at each iteration. The PSMCO obtains an estimate of a global minimum at each iteration by utilizing a cheap kernel density estimator. We prove that the resulting estimator converges to a global minimum almost surely as the number of Monte Carlo samples tends to infinity. We also empirically demonstrate that the algorithm is able to reconstruct multiple global minima and solve difficult global optimization problems. By further exploiting the relationship between inference and optimization, we also propose a probabilistic and online matrix factorization method, termed the dictionary filter to solve large-scale matrix factorization problems. Matrix factorization methods have received significant interest from the machine learning community due to their expressive representations of high-dimensional data and interpretability of their estimates. As the majority of the matrix factorization methods are defined as optimization problems, they suffer from the same issues as stochastic optimization methods. In particular, when using stochastic gradient descent, one might need to try and err many times before deciding to use a step-size. To alleviate these problems, we introduce a matrix-variate probabilistic model for which inference results in a matrix factorization scheme. The scheme is online, in the sense that it only uses a single data point at a time to update the factors. The algorithm bears relationship with optimization schemes, namely with the incremental proximal method defined over a matrix-variate cost function. By way of intuition we developed for the optimization-inference relationship, we devise a model which results in similar update rules for matrix factorization as for the incremental proximal method. However, the probabilistic updates are more stable and efficient. Moreover, the algorithm does not have a step-size parameter to tune, as its role is played by the posterior covariance matrix. We demonstrate the utility of the algorithm on a missing data problem and a video processing problem. We show that the algorithm can be successfully used in machine learning problems and several promising extensions of the method can be constructed easily.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Ricardo Cao Abad.- Secretario: Michael Peter Wiper.- Vocal: Nicholas Paul Whitele

Representation learning with structured invariance

Invariance is crucial for neural networks, enabling them to generalize effectively across variations of the input data by focusing on key attributes while filtering out irrelevant details. In this thesis, we study representation learning in neural networks through the lens of structured invariance. We start by studying the properties and limitations of the invariance that neural networks can learn from the data. Next, we develop a method to extract the structure of invariance learned by a neural network, providing a more nuanced analysis of the quality of learned invariance. In the next chapter, we focus on contrastive learning, demonstrating how more structured supervision results in a better quality of learned representations. The last two chapters that follow, focus on practical aspects of representation learning with structured invariance in computer vision

Minimizing Computational Resources for Deep Machine Learning: A Compression and Neural Architecture Search Perspective for Image Classification and Object Detection

Computational resources represent a significant bottleneck across all current deep learning computer vision approaches. Image and video data storage requirements for training deep neural networks have led to the widespread use of image and video compression, the use of which naturally impacts the performance of neural network architectures during both training and inference. The prevalence of deep neural networks deployed on edge devices necessitates efficient network architecture design, while training neural networks requires significant time and computational resources, despite the acceleration of both hardware and software developments within the field of artificial intelligence (AI). This thesis addresses these challenges in order to minimize computational resource requirements across the entire end-to-end deep learning pipeline. We determine the extent to which data compression impacts neural network architecture performance, and by how much this performance can be recovered by retraining neural networks with compressed data. The thesis then focuses on the accessibility of the deployment of neural architecture search (NAS) to facilitate automatic network architecture generation for image classification suited to resource-constrained environments. A combined hard example mining and curriculum learning strategy is developed to minimize the image data processed during a given training epoch within the NAS search phase, without diminishing performance. We demonstrate the capability of the proposed framework across all gradient-based, reinforcement learning, and evolutionary NAS approaches, and a simple but effective method to extend the approach to the prediction-based NAS paradigm. The hard example mining approach within the proposed NAS framework depends upon the effectiveness of an autoencoder to regulate the latent space such that similar images have similar feature embeddings. This thesis conducts a thorough investigation to satisfy this constraint within the context of image classification. Based upon the success of the overall proposed NAS framework, we subsequently extend the approach towards object detection. Despite the resultant multi-label domain presenting a more difficult challenge for hard example mining, we propose an extension to the autoencoder to capture the additional object location information encoded within the training labels. The generation of an implicit attention layer within the autoencoder network sufficiently improves its capability to enforce similar images to have similar embeddings, thus successfully transferring the proposed NAS approach to object detection. Finally, the thesis demonstrates the resilience to compression of the general two-stage NAS approach upon which our proposed NAS framework is based

Learned SPARCOM: Unfolded Deep Super-Resolution Microscopy

The use of photo-activated fluorescent molecules to create long sequences of low emitter-density diffraction-limited images enables high-precision emitter localization, but at the cost of low temporal resolution. We suggest combining SPARCOM, a recent high-performing classical method, with model-based deep learning, using the algorithm unfolding approach, to design a compact neural network incorporating domain knowledge. Our results show that we can obtain super-resolution imaging from a small number of high emitter density frames without knowledge of the optical system and across different test sets using the proposed learned SPARCOM (LSPARCOM) network. We believe LSPARCOM can pave the way to interpretable, efficient live-cell imaging in many settings, and find broad use in single-molecule localization microscopy of biological structures

Neural Radiance Fields: Past, Present, and Future

The various aspects like modeling and interpreting 3D environments and surroundings have enticed humans to progress their research in 3D Computer Vision, Computer Graphics, and Machine Learning. An attempt made by Mildenhall et al in their paper about NeRFs (Neural Radiance Fields) led to a boom in Computer Graphics, Robotics, Computer Vision, and the possible scope of High-Resolution Low Storage Augmented Reality and Virtual Reality-based 3D models have gained traction from res with more than 1000 preprints related to NeRFs published. This paper serves as a bridge for people starting to study these fields by building on the basics of Mathematics, Geometry, Computer Vision, and Computer Graphics to the difficulties encountered in Implicit Representations at the intersection of all these disciplines. This survey provides the history of rendering, Implicit Learning, and NeRFs, the progression of research on NeRFs, and the potential applications and implications of NeRFs in today's world. In doing so, this survey categorizes all the NeRF-related research in terms of the datasets used, objective functions, applications solved, and evaluation criteria for these applications.Comment: 413 pages, 9 figures, 277 citation