Humans perceive a lot of information about the three-dimensional structure in their environment by moving around it. When the observer moves, objects around them move different amounts depending on their distance from the observer. This is known as motion parallax, and from this depth information can be used to generate an accurate 3D representation of the world around them. In computer vision, we replicate this through geometric processing. Geometry is used to describe the structure and shape of the environment in which a camera is located. Geometric computer vision is, therefore, the process of determining the structure of the environment, and the position and orientation of the camera, and how the camera moves, with respect to the environment, through the analysis of camera image streams. It is commonly used in mobile robotics, vehicle autonomy and augmented reality. The module builds upon the machine vision modules already taught in the ECE department and complements the modules that teach semantic reasoning through machine learning. This module will be offered on the newly proposed part-time PPD in Computer Vision Systems (ID: 1681). In future, the module will be offered on a Part MEng in Intelligent Visual System and a Part MEng in Cognitive Robotics.

• Recap of Linear Algebra: Projective Geometry and Homogenous Coordinates • Feature/point Correspondences • Camera models and image formation • Applications of Multiple View Geometry - Automotive, Drone Flight, etc. • Epipolar Geometry and the Essential Matrix • Visual Odometry - Estimation and Properties of the Essential Matrix, 8-point algorithm, RANSAC • 3D Reconstruction of the scene - Midpoint, Direct Linear, "Optimal" • The uncalibrated camera case: Fundamental Matrix - generalization of the essential matrix, Euclidian/Metric/Affine/Projective reconstruction • Visual Simultaneous Localisation and Mapping • Introduction to optimisation algorithms, e.g. Levenberg Marquardt • Bundle Adjustment - multiple rays, multiple camera positions, builds from multiple view geometry • Windowed bundle adjustment, global bundle adjustment • Loop Closure - Bag of Words • Stereo Vision

On successful completion of this module, students will be able to: 1. Demonstrate an understanding of the fundamentals of camera projections and multiple view geometry 2. Demonstrate an understanding of visual simultaneous localization and mapping in applications such as mobile autonomous robotics 3. Critically evaluate different approaches in geometric computer vision for the task at hand 4. Demonstrate an understanding of the main areas in which geometric computer vision plays an important role

On successful completion of this module, students will be able to: 1. Differentiate from various design techniques that could be used and be able to justify an appropriate technique from geometric computer vision 2. Practice an objective approach to the selection of geometric computer vision methodologies to solve specific problems. 3. Effect a design of a geometric computer vision system to solve problems in robotics and vehicle autonomy 4. Contribute meaningfully to an engineering team project development on geometric computer vision systems

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The module will be delivered to part-time students in a completely online learning format, with online pre-recorded video lectures and live interactive Q+A tutorials. The students also complete a series of coding exercises in their own time with online moderator support.