Linear Algebra:  n- dimensional Euclidean spaces, linear transformation, Matrices, Eigen values and Eigen vectors, Generalised  inverses, SVD.

Numerical Methods: Numerical Solution of nonlinear equations, Direct and iterative methods to solve system of linear equations, Numerical integration – Trapezoidal and Simpson’s rule, Interpolation, Splines and curve fitting, Numerical solution of ODE –Euler’s method and 4th order Runge- Kutta Method.

Introduction: Basics of geometrics, Projection and coordinate system, Camera calibration - representation of digital images B/W, RGB, HIS, CCD cameras, time delay integration, spectral sensitivity of CCD sensor, geometry problem of CCD image - , image measurement, coordinate system, image movement, image transformation, geometric and radiometric transformation - Vertical aerial photographs: Parallax, Stereo model - Tilted photos: Rectification, Mathematical photogrammetric principles, Analog vs Analytical vs Digital models - Orientation: Interior, Relative, Absolute - Collinearity and Copla

Electromagnetic radiation and its interaction with matter, Spectral signatures, image formation remote sensors and platforms, resolutions, radiometric and geometric distortions, thermal remote sensing, spectral indices, classification techniques, image transformations, intensity transformations, spatial filtering, image formats, noise reduction, image segmentation.Introduction to Geographic Information System (GIS) - Hardware, Software, Data types and models-Spatial data quality, Thematic maps, Symbolization, Scale and generalization - Co-ordinate systems, Map projections and visualization

Electromagnetic radiation and its interaction with matter, Spectral signatures, image formation remote sensors and platforms, resolutions, radiometric and geometric distortions, thermal remote sensing, spectral indices, classification techniques, image transformations, intensity transformations, spatial filtering, image formats, noise reduction, image segmentation.

Basics of Topology; complexes on data; homology; topological Persistence; computing Betti numbers; reconstruction from data; topology inference from data; computing optimized homology cycles; reeb graphs from data; topology of Laplace operators, spectra approximation.

Greedy and dynamic programming algorithms; Kruskals algorithm for minimum spanning trees; the folklore algorithm for the longest common subsequence of two strings; Dijstras algorithm and other algorithms for the shortest path problem; divide-and-conqueror and checkpoint algorithms; the Hirshbergs algorithm for aligning sequences in linear space; quick sorting; the Knuth-Morrison-Pratt algorithm; suffix trees; data structures: chained lists, reference lists, hash- ing; the Chomsky-hierarchy of grammars; parsing algorithms; connections to the automaton theory; Turing-machines; complexity and

The reinforcement learning problem; tabular & approximate solution methods: dynamic programming, Monto-Carlo Methods, temporal difference learning, eligibility traces; planning and learning; dimensions of reinforcement learning.

Graphical Models: Basic graph concepts; Bayesian Networks; conditional independence; Markov Networks; Inference: variable elimination, belief propagation, max-product, junction trees, loopy belief propogation, expectation propogation, sampling; structure learning; learning with missing data.

Deep Learning: recurrent networks; probabilistic neural nets; Boltzmann machines; RBMs; sigmoid belief nets; CNN; autoencoders; deep reinforcement learning; generative adversarial net- works; structured deep learning; applications.

Image Formation Models, Monocular imaging system, Orthographic & Perspective Projection ,
Camera model and Camera calibration , Binocular imaging systems Image Processing and Feature
Extraction , Image representations (continuous and discrete), Edge detection, Motion Estimation ,
Regularization theory, Optical computation , Stereo Vision , Motion estimation , Structure from
motion Shape Representation and Segmentation , Deformable curves and surfaces , Snakes and
active contours , Level set representations , Fourier and wavelet descriptors