3D Representation Learning for Shape Reconstruction and Understanding

The real world we are living in is inherently composed of multiple 3D objects. However, most of the existing works in computer vision traditionally either focus on images or videos where the 3D information inevitably gets lost due to the camera projection. Traditional methods typically rely on hand-crafted algorithms and features with many constraints and geometric priors to understand the real world. However, following the trend of deep learning, there has been an exponential growth in the number of research works based on deep neural networks to learn 3D representations for complex shapes and scenes, which lead to many cutting-edged applications in augmented reality (AR), virtual reality (VR) and robotics as one of the most important directions for computer vision and computer graphics. This thesis aims to build an intelligent system with dynamic 3D representations that can change over time to understand and recover the real world with semantic, instance and geometric information and eventually bridge the gap between the real world and the digital world. As the first step towards the challenges, this thesis explores both explicit representations and implicit representations by explicitly addressing the existing open problems in these areas. This thesis starts from neural implicit representation learning on 3D scene representation learning and understanding and moves to a parametric model based explicit 3D reconstruction method. Extensive experimentation over various benchmarks on various domains demonstrates the superiority of our method against previous state-of-the-art approaches, enabling many applications in the real world. Based on the proposed methods and current observations of open problems, this thesis finally presents a comprehensive conclusion with potential future research directions

The role of object instance re-identification in 3D object localization and semantic 3D reconstruction.

For an autonomous system to completely understand a particular scene, a 3D reconstruction of the world is required which has both the geometric information such as camera pose and semantic information such as the label associated with an object (tree, chair, dog, etc.) mapped within the 3D reconstruction. In this thesis, we will study the problem of an object-centric 3D reconstruction of a scene in contrast with most of the previous work in the literature which focuses on building a 3D point cloud that has only the structure but lacking any semantic information. We will study how crucial 3D object localization is for this problem and will discuss the limitations faced by the previous related methods. We will present an approach for 3D object localization using only 2D detections observed in multiple views by including 3D object shape priors. Since our first approach relies on associating 2D detections in multiple views, we will also study an approach to re-identify multiple object instances of an object in rigid scenes and will propose a novel method of joint learning of the foreground and background of an object instance using a triplet-based network in order to identify multiple instances of the same object in multiple views. We will also propose an Augmented Reality-based application using Google's Tango by integrating both the proposed approaches. Finally, we will conclude with some open problems that might benefit from the suggested future work

Differential geometric regularization for supervised learning of classifiers

We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to an estimator of the class probability P(y|\vec x). The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces rapid local oscillations and hence large volume of the estimator. This technique can be applied to regularize any classification function that satisfies two requirements: firstly, an estimator of the class probability can be obtained; secondly, first and second derivatives of the class probability estimator can be calculated. In experiments, we apply our regularization technique to standard loss functions for classification, our RBF-based implementation compares favorably to widely used regularization methods for both binary and multiclass classification.http://proceedings.mlr.press/v48/baia16.pdfPublished versio

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms

We present a technical survey on the state of the art approaches in data reduction and the coreset framework. These include geometric decompositions, gradient methods, random sampling, sketching and random projections. We further outline their importance for the design of streaming algorithms and give a brief overview on lower bounding techniques

Neighbourhood Consensus Networks

We address the problem of finding reliable dense correspondences between a pair of images. This is a challenging task due to strong appearance differences between the corresponding scene elements and ambiguities generated by repetitive patterns. The contributions of this work are threefold. First, inspired by the classic idea of disambiguating feature matches using semi-local constraints, we develop an end-to-end trainable convolutional neural network architecture that identifies sets of spatially consistent matches by analyzing neighbourhood consensus patterns in the 4D space of all possible correspondences between a pair of images without the need for a global geometric model. Second, we demonstrate that the model can be trained effectively from weak supervision in the form of matching and non-matching image pairs without the need for costly manual annotation of point to point correspondences. Third, we show the proposed neighbourhood consensus network can be applied to a range of matching tasks including both category- and instance-level matching, obtaining the state-of-the-art results on the PF Pascal dataset and the InLoc indoor visual localization benchmark.Comment: In Proceedings of the 32nd Conference on Neural Information Processing Systems (NeurIPS 2018