CS6777 - Optimization Methods for Computer Vision Applications

#### Objectives:

In the recent past, algorithms of solving many ill-posed problems in the field of Computer Vision are derived from modern Optimization methods. Allied areas of Machine learning, Pattern recognition and Video processing have also seen a rise in the use of such methods. This course will provide an overview of the theories and hands-on practice, required by students and scholars who intend to specialize in this field, to solve complex problems in computer vision and associated fields of study.

#### Course Contents:

• INTRODUCTION : Characteristics and Categorization of Optimization Problems; Common Optimization problems in Computer Vision.
• RELEVANT OPTIMIZATION CONCEPTS AND METHODS : Constraint vs. unconstrained; Fibonacci Search, Golden-Section Search; QP, LP and Nonlinear programming,
Combinatorial optimization, Stochastic optimization, Semi-definite optimization; Min-Max algorithms;
• MULTIDIMENSIONAL GRADIENT METHODS : Steepest-Descent, Newton, Gauss-Newton, Quasi-Newton, Sub-Gradient, Conjugate-Gradient; Levenberg-Marquadrt(LM) Algorithm, Basis Pursuit & LASSO.
• CONSTRAINED OPTIMIZATION: Lagrange Multiplier, Karush–Kuhn–Tucker (KKT) conditions, First-Order and Second-Order Necessary Conditions for minima and maxima; Convex sets and functions, Convex optimization; Duality, IRLS.
• MODERN METHODS: Selected Topics form: Accelerated Proximal Gradient, ADMM, Manifold based optimization, L_*-norms, Sparse representations and BOVWs, Multiple Kernel Learning (MKL), Latent and Multiple Instance (MI)-Support Vector Machine (SVM).
• IMAGE RECONSTRUCTION AND ANALYSIS: Denoising, Debluring, Depth/motion from Defocus, Super-resolution.
• MULTI - VIEW GEOMETRY: RANSAC, Bundle adjustment, Stratification and Auto-calibration, Iterative Closest Point (ICP), Trifocal Tensor.
• SEGMENTATION : Markov Random Field, Grab Cut, Conditional Random Field, Active contour, ACO/PSO, PageRank.
• MODERN CV APPLICATIONS : Selected topics from: Intelligent Scissors, Inpainting, Stitching, Shape From X (SFX), Active Shape models (ASM, AAM), Saliency constraints, Retargeting, Video Stabilization, Domain Adaptation (Transfer Learning) for Object and event detection/categorization, Deformable part based models, Feature Selection.
Text Books:
• Marco Alexander Treiber, Optimization for Computer Vision: An Introduction to Core Concepts and Methods, Springer 2013.
• Andreas Antoniou and Wu-Sheng Lu, Practical Optimization: Algorithms and Engineering Applications, Springer 2007.
• Richard Szeliski, Computer Vision: Algorithms and Applications, Springer-Verlag London Limited, 2011.
Reference Books:
• Daphne Koller and Nir Friedman, Probabilistic Graphical Models - Principles and Techniques, The MIT Press, 2009.
• Bernhard Scholkopf and Alexander J. Smola, Learning with Kernels - Support Vector Machines, Regularization, Optimization and Beyond, ISBN- 978-0-262-19475-4, MIT Press, 2002.
• Alan C. Bovik, Handbook of Image and Video Processing, ISBN- 978-0123885623, ELSEVIER, ACADEMIC PRESS, 2005.
• Stephen Boyd and Lieven Vandenberghe, Convex Optimization, ISBN - 978-0-52183-378-3, Cambridge University Press, 2004.

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#### Parameters

 Credits Type Date of Introduction 3-1-0-4 Elective Jul 2014