Computer and Robot Vision Vol. 1, by R.M. Haralick and Linda G. Shapiro, Addison-Wesley, 1992, ISBN 0-201-10887-1.

Computer and Robot Vision

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian approximation and ensemble learning techniques are two most widely-used UQ methods in the literature. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning. Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods. Finally, we briefly highlight the fundamental research challenges faced by UQ methods and discuss the future research directions in this field.

A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "auto-diff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational uid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.

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Automatic differentiation in machine learning: a survey

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Using Algebraic Geometry

Visual localization is the task of accurate camera pose estimation in a known scene. It is a key problem in computer vision and robotics, with applications including self-driving cars, Structure-from-Motion, SLAM, and Mixed Reality. Traditionally, the localization problem has been tackled using 3D geometry. Recently, end-to-end approaches based on convolutional neural networks have become popular. These methods learn to directly regress the camera pose from an input image. However, they do not achieve the same level of pose accuracy as 3D structure-based methods. To understand this behavior, we develop a theoretical model for camera pose regression. We use our model to predict failure cases for pose regression techniques and verify our predictions through experiments. We furthermore use our model to show that pose regression is more closely related to pose approximation via image retrieval than to accurate pose estimation via 3D structure. A key result is that current approaches do not consistently outperform a handcrafted image retrieval baseline. This clearly shows that additional research is needed before pose regression algorithms are ready to compete with structure-based methods.

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Understanding the Limitations of CNN-Based Absolute Camera Pose Regression

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Grobner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Grobner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems.

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Beyond Grobner Bases: Basis Selection for Minimal Solvers

In this paper we present new techniques for constructing compact and robust minimal solvers for absolute pose estimation. We focus on the P4Pfr problem, but the methods we propose are applicable to a more general setting. Previous approaches to P4Pfr suffer from artificial degeneracies which come from their formulation and not the geometry of the original problem. In this paper we show how to avoid these false degeneracies to create more robust solvers. Combined with recently published techniques for Grobner basis solvers we are also able to construct solvers which are significantly smaller. We evaluate our solvers on both real and synthetic data, and show improved performance compared to competing solvers. Finally we show that our techniques can be directly applied to the P3.5Pf problem to get a non-degenerate solver, which is competitive with the current state-of-the-art.

Making Minimal Solvers for Absolute Pose Estimation Compact and Robust

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.

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A Clever Elimination Strategy for Efficient Minimal Solvers

To estimate the 6-DoF extrinsic pose of a pinhole camera with partially unknown intrinsic parameters is a critical sub-problem in structure-from-motion and camera localization. In most of existing camera pose estimation solvers, the principal point is assumed to be in the image center. Unfortunately, this assumption is not always true, especially for asymmetrically cropped images. In this paper, we develop the first exactly minimal solver for the case of unknown principal point and focal length by using four and a half point correspondences (P4.5Pfuv). We also present an extremely fast solver for the case of unknown aspect ratio (P5Pfuva). The new solvers outperform the previous state-of-the-art in terms of stability and speed. Finally, we explore the extremely challenging case of both unknown principal point and radial distortion, and develop the first practical non-minimal solver by using seven point correspondences (P7Pfruv). Experimental results on both simulated data and real Internet images demonstrate the usefulness of our new solvers.

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Camera Pose Estimation with Unknown Principal Point

To model radial distortion there are two main approaches; either the image points are undistorted such that they correspond to pinhole projections, or the pinhole projections are distorted such that they align with the image measurements. Depending on the application, either of the two approaches can be more suitable. For example, distortion models are commonly used in Structure-from-Motion since they simplify measuring the reprojection error in images. Surprisingly, all previous minimal solvers for pose estimation with radial distortion use undistortion models. In this paper we aim to fill this gap in the literature by proposing the first minimal solvers which can jointly estimate distortion models together with camera pose. We present a general approach which can handle rational models of arbitrary degree for both distortion and undistortion.

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Zuzana Kukelova

Papers

Beyond Grobner Bases: Basis Selection for Minimal Solvers

Making Minimal Solvers for Absolute Pose Estimation Compact and Robust

A Clever Elimination Strategy for Efficient Minimal Solvers

Camera Pose Estimation with Unknown Principal Point

Revisiting Radial Distortion Absolute Pose