Dimensionality reduction and sparse representations in computer vision

The proliferation of camera equipped devices, such as netbooks, smartphones and game stations, has led to a significant increase in the production of visual content. This visual information could be used for understanding the environment and offering a natural interface between the users and their surroundings. However, the massive amounts of data and the high computational cost associated with them, encumbers the transfer of sophisticated vision algorithms to real life systems, especially ones that exhibit resource limitations such as restrictions in available memory, processing power and bandwidth. One approach for tackling these issues is to generate compact and descriptive representations of image data by exploiting inherent redundancies. We propose the investigation of dimensionality reduction and sparse representations in order to accomplish this task. In dimensionality reduction, the aim is to reduce the dimensions of the space where image data reside in order to allow resource constrained systems to handle them and, ideally, provide a more insightful description. This goal is achieved by exploiting the inherent redundancies that many classes of images, such as faces under different illumination conditions and objects from different viewpoints, exhibit. We explore the description of natural images by low dimensional non-linear models called image manifolds and investigate the performance of computer vision tasks such as recognition and classification using these low dimensional models. In addition to dimensionality reduction, we study a novel approach in representing images as a sparse linear combination of dictionary examples. We investigate how sparse image representations can be used for a variety of tasks including low level image modeling and higher level semantic information extraction. Using tools from dimensionality reduction and sparse representation, we propose the application of these methods in three hierarchical image layers, namely low-level features, mid-level structures and high-level attributes. Low level features are image descriptors that can be extracted directly from the raw image pixels and include pixel intensities, histograms, and gradients. In the first part of this work, we explore how various techniques in dimensionality reduction, ranging from traditional image compression to the recently proposed Random Projections method, affect the performance of computer vision algorithms such as face detection and face recognition. In addition, we discuss a method that is able to increase the spatial resolution of a single image, without using any training examples, according to the sparse representations framework. In the second part, we explore mid-level structures, including image manifolds and sparse models, produced by abstracting information from low-level features and offer compact modeling of high dimensional data. We propose novel techniques for generating more descriptive image representations and investigate their application in face recognition and object tracking. In the third part of this work, we propose the investigation of a novel framework for representing the semantic contents of images. This framework employs high level semantic attributes that aim to bridge the gap between the visual information of an image and its textual description by utilizing low level features and mid level structures. This innovative paradigm offers revolutionary possibilities including recognizing the category of an object from purely textual information without providing any explicit visual example

Depth Estimation Using 2D RGB Images

Single image depth estimation is an ill-posed problem. That is, it is not mathematically possible to uniquely estimate the 3rd dimension (or depth) from a single 2D image. Hence, additional constraints need to be incorporated in order to regulate the solution space. As a result, in the first part of this dissertation, the idea of constraining the model for more accurate depth estimation by taking advantage of the similarity between the RGB image and the corresponding depth map at the geometric edges of the 3D scene is explored. Although deep learning based methods are very successful in computer vision and handle noise very well, they suffer from poor generalization when the test and train distributions are not close. While, the geometric methods do not have the generalization problem since they benefit from temporal information in an unsupervised manner. They are sensitive to noise, though. At the same time, explicitly modeling of a dynamic scenes as well as flexible objects in traditional computer vision methods is a big challenge. Considering the advantages and disadvantages of each approach, a hybrid method, which benefits from both, is proposed here by extending traditional geometric models’ abilities to handle flexible and dynamic objects in the scene. This is made possible by relaxing geometric computer vision rules from one motion model for some areas of the scene into one for every pixel in the scene. This enables the model to detect even small, flexible, floating debris in a dynamic scene. However, it makes the optimization under-constrained. To change the optimization from under-constrained to over-constrained while maintaining the model’s flexibility, ”moving object detection loss” and ”synchrony loss” are designed. The algorithm is trained in an unsupervised fashion. The primary results are in no way comparable to the current state of the art. Because the training process is so slow, it is difficult to compare it to the current state of the art. Also, the algorithm lacks stability. In addition, the optical flow model is extremely noisy and naive. At the end, some solutions are suggested to address these issues

Tensor Regression

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.Comment: 187 pages, 32 figures, 10 table

Learning to See with Minimal Human Supervision

Deep learning has significantly advanced computer vision in the past decade, paving the way for practical applications such as facial recognition and autonomous driving. However, current techniques depend heavily on human supervision, limiting their broader deployment. This dissertation tackles this problem by introducing algorithms and theories to minimize human supervision in three key areas: data, annotations, and neural network architectures, in the context of various visual understanding tasks such as object detection, image restoration, and 3D generation. First, we present self-supervised learning algorithms to handle in-the-wild images and videos that traditionally require time-consuming manual curation and labeling. We demonstrate that when a deep network is trained to be invariant to geometric and photometric transformations, representations from its intermediate layers are highly predictive of object semantic parts such as eyes and noses. This insight offers a simple unsupervised learning framework that significantly improves the efficiency and accuracy of few-shot landmark prediction and matching. We then present a technique for learning single-view 3D object pose estimation models by utilizing in-the-wild videos where objects turn (e.g., cars in roundabouts). This technique achieves competitive performance with respect to existing state-of-the-art without requiring any manual labels during training. We also contribute an Accidental Turntables Dataset, containing a challenging set of 41,212 images of cars in cluttered backgrounds, motion blur, and illumination changes that serve as a benchmark for 3D pose estimation. Second, we address variations in labeling styles across different annotators, which leads to a type of noisy label referred to as heterogeneous label. This variability in human annotation can cause subpar performance during both the training and testing phases. To mitigate this, we have developed a framework that models the labeling styles of individual annotators, reducing the impact of human annotation variations and enhancing the performance of standard object detection models. We have also applied this framework to analyze ecological data, which are often collected opportunistically across different case studies without consistent annotation guidelines. Through this application, we have obtained several insightful observations into large-scale bird migration behaviors and their relationship to climate change. Our next study explores the challenges of designing neural networks, an area that lacks a comprehensive theoretical understanding. By linking deep neural networks with Gaussian processes, we propose a novel Bayesian interpretation of the deep image prior, which parameterizes a natural image as the output of a convolutional network with random parameters and random input. This approach offers valuable insights to optimize the design of neural networks for various image restoration tasks. Lastly, we introduce several machine-learning techniques to reconstruct and edit 3D shapes from 2D images with minimal human effort. We first present a generic multi-modal generative model that bridges 2D images and 3D shapes via a shared latent space, and demonstrate its applications on versatile 3D shape generation and manipulation tasks. Additionally, we develop a framework for joint estimation of 3D neural scene representation and camera poses. This approach outperforms prior works and allows us to operate in the general SE(3) camera pose setting, unlike the baselines. The results also indicate this method can be complementary to classical structure-from-motion (SfM) pipelines as it compares favorably to SfM on low-texture and low-resolution images

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

LIPIcs, Volume 277, GIScience 2023, Complete Volume

LIPIcs, Volume 277, GIScience 2023, Complete Volum

12th International Conference on Geographic Information Science: GIScience 2023, September 12–15, 2023, Leeds, UK

No abstract available