Course Map
A single schematic of the whole course: the geometric-vision pipeline up top, the six parts flowing from classical, proof-complete methods (Parts I–IV) into learning-based vision (Parts V–VI), the ten applications threaded throughout, and the four recurring throughlines. Click any part to jump to its lectures in the schedule.
How the Topics Connect
Beyond their linear order, the topics form a web of dependencies: linear algebra underwrites geometry, filtering feeds features, features drive matching and motion, and the whole classical toolkit becomes the inductive bias the learned models inherit — with every strand eventually meeting at the ten vision applications. This relationship map summarizes how the twenty-eight hours’ topics build on and reuse one another; colour marks the course part, and highlighted links name the key idea.
Overview
This course builds the fundamentals and principles of computer vision, then develops both classical and learning-based solutions across a wide range of applications. It begins with the mathematical groundwork and classical pipeline — image formation, features, and geometry — and moves into modern deep learning for vision, closing with advanced applications such as segmentation, depth estimation, neural radiance fields, and HDR imaging. Students from any discipline gain the foundational knowledge needed to build computer-vision models using OpenCV and PyTorch / Keras / TensorFlow.
Offered in Semester I of 2026–27 by Prof. Shanmuganathan Raman. Course materials, announcements, and assignments are managed through Google Classroom (join code dfrc4n7z).
Logistics
dfrc4n7zCourse Contents
Mathematical Basics
Classical Computer Vision
Learning for Computer Vision
Computer Vision Applications
Textbooks & References
- Foundations of Computer Visionfree online
- Robot Vision
- Multiple View Geometry in Computer Vision (2nd ed.)
- Deep Learning: Foundations and Conceptsfree online
- Understanding Deep Learningfree online
- Deep Learning: A Visual Approach
- Dive into Deep Learningfree online
- Deep Learningfree online
Learning Outcomes
By the end of the course, students will understand the fundamentals and principles of computer vision, and will be able to design and develop both classical and learning-based solutions for a variety of computer-vision applications. The tools covered are intended to help students across disciplines who need the foundational knowledge to build computer-vision models using OpenCV and PyTorch / Keras / TensorFlow.
Tentative Lecture Plan
Lecture Schedule
The course runs as twenty-eight lecture hours across six parts — classical, proof-complete methods first (Parts I–IV), then learning-based vision (Parts V–VI), with ten vision applications solved first by hand and then learned. A single-view Shape-from-X supplement (Lecture 18a) extends Hour 18. Per-lecture slides appear in the Slides column as each topic is covered; the course frontmatter deck — roadmaps, notation and conventions for all twenty-eight hours — is available now.
| Hr | Lecture | Slides | References |
|---|---|---|---|
| Part I · Foundations — Hours 1–3 | |||
| 1 | Introduction & image formationImage as a function; sampling, quantization & Nyquist; pinhole & perspective projection; lens & depth of field; the sensing pipeline — demosaicing, gamma, CRF. | Szeliski (2022); Hartley & Zisserman (2004) | |
| 2 | Linear algebra IFour subspaces; spectral theorem; SVD existence & Eckart–Young; rank, norms & conditioning; worked 2×2 SVD. | — | Trefethen & Bau (1997); Szeliski (2022) |
| 3 | Linear algebra IINormal equations & residual orthogonality; projection matrix; pseudo-inverse via SVD; homogeneous Ax = 0; minimum-norm & total least squares. | — | Trefethen & Bau (1997); Hartley & Zisserman (2004) |
| Part II · Filtering — Hours 4–6 | |||
| 4 | Convolution & LTI systemsSifting; LTI ⇒ convolution; FIR/IIR; BIBO stability; correlation & NCC; 2D separability; Toeplitz/circulant view. | — | Oppenheim & Schafer; Szeliski (2022) |
| 5 | Fourier analysisComplex exponentials as eigenfunctions; CTFT/DTFT/DFT/FFT; the convolution theorem; circular convolution; Gaussian self-duality; sampling & aliasing. | — | Bracewell; Oppenheim & Schafer |
| 6 | Image filteringBox & Gaussian filters; separability & integral images; derivative-of-Gaussian; median / bilateral / NL-means; anti-aliased pyramids; sharpening. | — | Gonzalez & Woods (2018); Szeliski (2022) |
| Part III · Features — Hours 7–10 | |||
| 7 | Gradients, edges, LoG & DoGFinite differences; Sobel separability; LoG closed form; heat equation; DoG ≈ LoG; structure tensor; Hough transform. | — | Marr & Hildreth (1980); Szeliski (2022) |
| 8 | Canny & HarrisCanny optimal detector, NMS & hysteresis; auto-correlation → structure tensor; R = det M − k·tr²M; rotation invariance. | — | Canny (1986); Harris & Stephens (1988) |
| 9 | Scale space & blobsScale-space axioms; diffusion-equation proof; Gaussian/Laplacian pyramids; characteristic scale; DoG scale-space extrema. | — | Lindeberg (1994) |
| 10 | SIFT / SURF / ORBDoG keypoints; sub-pixel & edge rejection; orientation; 128-D descriptor; the ratio test; SURF; FAST/BRIEF/ORB; RANSAC count. | — | Lowe (2004) |
| Part IV · Geometry, Motion & Light — Hours 11–18 (+ 18a) | |||
| 11 | Projective geometry of the planeHomogeneous points & lines; incidence, join & meet; the line at infinity; conics; the cross-ratio. | — | Hartley & Zisserman (2004), Ch. 2 |
| 12 | Transformations & the homographyProjective transformations; the homography (8 DOF); the transformation hierarchy. | — | Hartley & Zisserman (2004) |
| 13 | DLT & robust estimationDirect Linear Transform; Hartley normalization; robust fitting with RANSAC. | — | Hartley & Zisserman (2004), §4; Szeliski (2022) |
| 14 | Camera models & calibrationP = K[R | t]; intrinsics & extrinsics; camera centre; calibration; image of the absolute conic. | — | Hartley & Zisserman (2004), Ch. 6 |
| 15 | Epipolar geometry: F & EThe epipolar constraint; essential & fundamental matrices; epipoles & epipolar lines. | — | Hartley & Zisserman (2004), Ch. 9 |
| 16 | Multi-view stereo & SfMTriangulation; multi-view stereo; structure from motion; scene reconstruction. | — | Szeliski (2022); Hartley & Zisserman (2004) |
| 17 | Optical flow + synthesisBrightness-constancy (OFCE); Lucas–Kanade; coarse-to-fine flow; course synthesis. | — | Lucas & Kanade (1981); Szeliski (2022) |
| 18 | Photometric stereo & shapePhotometric stereo; shape from light; inverse rendering. | — | Forsyth & Ponce (2012); Szeliski (2022) |
| 18a | Shape-from-X supplementA companion to Hour 18 — four single-view shape cues: depth from focus; depth from defocus (coded apertures, dual pixels, deep optics); shape from interreflections (direct–global separation); shape from polarization (normals from angle & degree of polarization). | — | Nayar–Ikeuchi–Kanade (1991); Levin et al. (2007); Atkinson & Hancock (2006); Kadambi et al. (2015) |
| Part V · Learning for Vision — Hours 19–23 | |||
| 19 | Neural nets & the MLPDiscriminative vs. generative models; the perceptron & the XOR problem; activations; universal approximation; backpropagation; SGD, initialization & vanishing gradients; nets as distribution transformers. | — | Prince (2023); Bishop & Bishop (2024) |
| 20 | Generalization, regularization & optimizersBias–variance & the over/under-fitting curve; capacity & double descent; train/val/test; L2/L1, dropout, early stopping, augmentation; batch & layer norm; momentum, RMSProp, Adam; LR schedules. | — | Prince (2023); Goodfellow, Bengio & Courville (2016) |
| 21 | Convolutional neural networksLocality, weight sharing & translation equivariance; receptive fields; pooling; LeNet → VGG → ResNet; transfer learning; CNNs as image-to-image; the ViT bridge. | — | Torralba, Isola & Freeman (2024); Prince (2023) |
| 22 | Generative models & the VAELatent-variable generators g(z, y); autoencoders; variational inference & the ELBO; the reparameterization trick; the VAE & β-VAE; density vs. energy models; a map of GANs, flows & diffusion. | — | Torralba, Isola & Freeman (2024); Bishop & Bishop (2024) |
| 23 | Computer-vision applicationsOne backbone, many heads — classification, semantic segmentation (FCN/U-Net), detection (Faster R-CNN/YOLO); homography, depth & optical-flow estimation; restoration & super-resolution; relighting; NeRF; HDR. | — | Torralba, Isola & Freeman (2024); Szeliski (2022) |
| Part VI · Advanced Paradigms — Hours 24–28 | |||
| 24 | Generative Adversarial NetworksThe adversarial game; minimax & the optimal discriminator → JS divergence; the non-saturating loss; mode collapse; WGAN; DCGAN, cGAN, pix2pix, CycleGAN, SRGAN, StyleGAN; FID. | — | Goodfellow et al. (2014); Torralba, Isola & Freeman (2024) |
| 25 | TransformersTokens & attention; scaled dot-product self-attention; multi-head attention; the transformer block; ViT — “CNNs in disguise”; positional encodings; DETR, Swin, SegFormer, DPT. | — | Torralba, Isola & Freeman (2024) |
| 26 | Diffusion modelsForward noising; predicting the added noise; reverse sampling (DDPM/DDIM); U-Net & time embedding; classifier-free guidance; latent diffusion; cross-attention text-to-image; ControlNet. | — | Ho et al. (2020); Torralba, Isola & Freeman (2024) |
| 27 | Flow modelsExact likelihood; change of variables & the log-det Jacobian; coupling layers (RealNVP); Glow 1×1 convolutions; continuous flows (Neural ODE); flow matching; SRFlow, compression, anomalies. | — | Torralba, Isola & Freeman (2024) |
| 28 | Representation & self-supervised learningEncoders & embeddings; autoencoders; pretext tasks; contrastive InfoNCE; alignment & uniformity; SimCLR, MoCo, BYOL; MAE; CLIP, zero-shot & open-vocabulary vision. | — | Torralba, Isola & Freeman (2024) |