Course Contents

Course Handout

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.

• INTRODUCTION
  • Characteristics and Categorization of Optimization Problems, Common Optimization problems in Computer Vision.


• RELEVANT OPTIMIZATION CONCEPTS AND METHODS
  • Constrained vs. unconstrained; Fibonacci and Golden-Section Search; QP, LP and NLP, Combinatorial, Stochastic and Semi-definite optimization algorithms; Min-Max algorithms;


• MULTIDIMENSIONAL GRADIENT METHODS
  • Steepest-Descent, Conjugate-Gradient, Newton, Gauss-Newton, Quasi-Newton, Sub-Gradient; Levenberg-Marquadrt (LM) Algorithm, Basis Pursuit and 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
  • Few selected topics from: Accelerated Proximal Gradient, ADMM, STAMP & SPADE; Manifold based optimization, L*-norms, Sparse representations and BOVWs, Multiple Kernel Learning (MKL), Latent and Multiple Instance (MI)-learning, Streaming Algorithms.


• IMAGE RECONSTRUCTION AND ANALYSIS
  • Denoising, Deblurring, Depth/motion from Defocus, Super-resolution, TV-ROF & Tikhonov regularization.


• CORRESPONDENCE PROBLEMS
  • Rectification, RANSAC, Bundle adjustment, Stratification and Auto-calibration, Iterative Closest Point (ICP), Spectral Graph matching.


• SEGMENTATION IN IMAGE/VIDEO
  • MRF, Max-flow & Min-Cut, Grab Cut, Spectral Clustering, Normalized Cut, Active contour, GMM, DPMM & Mean Shift Clustering, Particle filter and Subspace clustering.


• MODERN CV APPLICATIONS
  • Few 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; Deep Learning: SGD, Adam, Batch Learning.

References

Textbooks

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.

References

Richard Szeliski, Computer Vision: Algorithms and Applications, Springer-Verlag London Limited 2011.

Alan C. Bovik, Handbook of Image and Video Processing, ELSEVIER, ACADEMIC PRESS 2005.

Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge University Press 2004.

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, MIT Press 2002.

Ian Goodfellow, Yoshua Bengio and Aaron Courville, Deep Learning, MIT Press 2016.

Lecture Slides

1	Linear Regression
2	Polar Parameters Estimation for LSQ
3	Gradient Descent and it's variations
4	Optimization Methods
5	Super-Resolution Edge Reconstruction + Restoration
6	Filtering
7	ICCV Tutorial on Graph Cuts
8	Mathematical Image Processing
9	Scene Modelling, Recognition and Tracking
10	RANSAC
11	Simulated Annealing
12	Steepest Descent vs. Gradient Descent
13	Monasse Rectification

Assignment

Announcement

Tentative schedule for the Jan-May 2024 Semester

Marks Distribution

• Seminars : 20
• TPA : 30
• Tutorials : 10
• End Sem: 40

Tutorial Dates

• Tutorial1 : TBD
• Tutorial2 : TBD

Seminar Dates:

• TBD

TPA Deadline

• TBD

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Exams

• End-sem Exam : May 16, 2024