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## Computer Vision

Lecturer: Dr J.G. Daugman

No. of lectures + examples classes: 15 + 1

Prerequisite courses: Mathematical Methods for Computer Science, Probability

Aims

The aims of this course are to introduce the principles, models and applications of computer vision, as well as some mechanisms used in biological visual systems that may inspire design of artificial ones. The course will cover: image formation, structure, and coding; edge and feature detection; neural operators for image analysis; texture, colour, stereo, and motion; wavelet methods for visual coding and analysis; interpretation of surfaces, solids, and shapes; data fusion; probabilistic classifiers; visual inference and learning. Several of these issues will be illustrated in the topic of face recognition.

Lectures

• Goals of computer vision; why they are so difficult. How images are formed, and the ill-posed problem of making 3D inferences from them about objects and their properties.

• Image sensing, pixel arrays, CCD cameras, framegrabbers. Elementary operations on image arrays; coding and information measures.

• Biological visual mechanisms from retina to cortex. Photoreceptor sampling; receptive field profiles; spike trains; channels and pathways. Neural image encoding operators.

• Mathematical operators for extracting image structure. Finite differences and directional derivatives. Filters; convolution; correlation. 2D Fourier domain theorems.

• Edge detection operators; the information revealed by edges. The Laplacian operator and its zero-crossings. Logan's Theorem.

• Multi-resolution representations. Active contours. 2D wavelets as visual primitives.

• Higher level visual operations in brain cortical areas. Multiple parallel mappings; streaming and divisions of labour; reciprocal feedback through the visual system.

• Texture, colour, stereo, and motion descriptors. Disambiguation and the achievement of invariances.

• Lambertian and specular surfaces. Reflectance maps. Image formation geometry. Discounting the illuminant when inferring 3D structure and surface properties.

• Shape representation. Inferring 3D shape from shading; surface geometry. Boundary descriptors; codons; superquadrics and the ``2.5-Dimensional" sketch.

• Perceptual psychology and visual cognition. Vision as model-building and graphics in the brain. Learning to see.

• Lessons from neurological trauma and visual deficits. Visual illusions and what they may imply about how vision works.

• Bayesian inference in vision; knowledge-driven interpretations. Classifiers. Probabilistic methods in vision.

• Object-centred coordinates. Appearance-based versus volumetric model-based vision.

• Vision as a set of inverse problems; mathematical methods for solving them: energy minimization, relaxation, regularization.

• Approaches to face detection, face recognition, and facial interpretation.

Objectives

At the end of the course students should

• understand visual processing from both ``bottom-up'' (data oriented) and ``top-down'' (goals oriented) perspectives

• be able to decompose visual tasks into sequences of image analysis operations, representations, specific algorithms, and inference principles

• understand the roles of image transformations and their invariances in pattern recognition and classification

• be able to analyse the robustness, brittleness, generalizability, and performance of different approaches in computer vision

• be able to describe key aspects of how biological visual systems encode, analyse, and represent visual information

• be able to think of ways in which biological visual strategies might be implemented in machine vision, despite the enormous differences in hardware

• understand in depth at least one major practical application problem, such as face recognition, detection, and interpretation