CVML Exam Master Index — SS 2025¶
A single navigable map of every chapter, lecture section, code file, exercise, trial-exam question, and important formula/algorithm.
1. Chapters Overview¶
| # | Chapter | Trial-exam pts | Difficulty | Prerequisites |
|---|---|---|---|---|
| 01 | Image Acquisition | 10 | 🟢 Easy–Med | Basic linear algebra |
| 02 | Digital Image Processing (Filtering, Edges, Thresholding) | 20 | 🟡 Med–Hard | Convolution arithmetic, Fourier intuition |
| 04 | Machine Learning Basics | 10 | 🟡 Medium | Linear algebra, derivatives |
| 05 | Features | 10 | 🟡 Medium | Chapter 02 (gradients) |
| 06 | Optical Flow | 10 | 🟡 Medium | Chapters 02, 05 |
| 07 | Parametric Transformations & Scattered Data Interpolation | 10 | 🟡 Medium | Linear algebra |
| 08 | Epipolar Geometry & Depth | 10 | 🔴 Hard | Chapters 05, 07 |
| 09 | Video Matching, Morphing & View Synthesis | 10 | 🟢 Med | Chapters 07, 08 |
| 10 | Camera Calibration / Structure from Motion | 10 | 🟡 Medium | Chapters 07, 08 |
| 11 | Neural Radiance Fields | 10 | 🟢 Easy (T/F) | Chapter 04 |
(There is no Chapter 03 — the lecture set merges "Filtering" and "Edges & Thresholding" into a single combined Chapter 02.)
2. Files in this Output Folder¶
Chapter_01_Image_Acquisition.md/.pdfChapter_02_Filtering_Edges_Thresholding.md/.pdfChapter_04_Machine_Learning.md/.pdfChapter_05_Features.md/.pdfChapter_06_Optical_Flow.md/.pdfChapter_07_Parametric_Transformations.md/.pdfChapter_08_Epipolar_Geometry_and_Depth.md/.pdfChapter_09_Morphing_View_Synthesis.md/.pdfChapter_10_Camera_Calibration.md/.pdfChapter_11_Neural_Radiance_Fields.md/.pdfCVML_Trial_Exam_Analysis.md/.pdfCVML_Final_Exam_Revision.md/.pdfCVML_Deep_Question_Bank.md/.pdfCVML_Coding_Visualization_Practice.md/.pdfCVML_Exam_Master_Index.md/.pdf00_Processing_Plan.md(planning document; preserves the topic-wise plan you saw before the chapters were generated)
3. Per-Chapter Cross-Reference¶
Chapter 01 — Image Acquisition¶
- PDF sections: digital image, color spaces, light spectrum, sensors, pinhole camera, depth of field, lens distortions, noise, normalization.
- Code:
Ex/2/sheet2/img_processing.py,python_intro.py. - Exercises: Sheet 2.
- Trial-exam: Q1a-d.
- Must-know formulas: \(p' = f \cdot p / z\); normalization \(N = (I - a) / (b - a)\).
- Must-know algorithm: pinhole projection; vignetting correction.
- Important visualisations: colour-space wheel, barrel distortion sketch, DoF demo.
Chapter 02 — Digital Image Processing¶
- PDF sections: sampling theorem, Fourier transform, hybrid images, box / sinc / Gaussian filters, separability, border handling, image pyramids; gradient, Prewitt, Sobel, Gabor, Laplacian, LoG, DoG; histograms; Otsu; local thresholding; background subtraction.
- Code:
Ex/3/sheet3/1.py – 5.py,image_filtering.py,utils.py. - Exercises: Sheet 3.
- Trial-exam: Q2a (Fourier), Q2b-i to Q2b-iv (theory), Q2c (numerical convolution), Q2d (filter category).
- Must-know formulas: convolution, separability, Sobel kernel, Gaussian formula, DoG ≈ LoG.
- Must-know algorithms: Gaussian smoothing, Sobel/Canny, Otsu, adaptive thresholding.
- Visualisations: power spectrum, side-by-side filter outputs, histogram, threshold mask.
Chapter 04 — Machine Learning¶
- PDF sections: AI vs ML vs DL, perceptron, activations, gradient descent, hyperparameters, splits, K-fold, architectures (MLP, CNN, RNN, autoencoder, GAN, ResNet), CNN convolution, augmentation, confusion matrix, accuracy/sensitivity/specificity, fallacy of accurate tests.
- Code:
Ex/4/sheet4/pt_object_recognition.py,pt_object_detection.py. - Exercises: Sheet 4 task 3 + 4.
- Trial-exam: Q3a-i, Q3a-ii, Q3a-iii, Q3b, Q3c.
- Must-know formulas: softmax, cross-entropy, gradient-descent update, accuracy/sensitivity/specificity.
- Must-know algorithms: gradient descent, back-propagation.
- Visualisations: loss curve, decision boundary, confusion matrix.
Chapter 05 — Features¶
- PDF sections: pinhole refresher, correspondence problem, descriptors, Euclidean/L1/Mahalanobis, NCC, ZMNCC, Shi-Tomasi, Harris, scale space, normalised Laplacian, Harris-Laplace, LoG, DoG, dominant orientation, SIFT, SURF, FAST, GLOH, DAISY, AR markers.
- Code:
Ex/4/sheet4/feature_detection.py,pt_object_*.py. - Exercises: Sheet 4 task 1 + 2.
- Trial-exam: Q4a, Q4b, Q4c.
- Must-know formulas: Harris score \(R = \det (H) - k\cdot \operatorname{trace}(H)^{2}\); pinhole \(p' = f\cdot p/z\).
- Must-know algorithms: Harris corner, SIFT, ratio test.
- Visualisations: Harris ellipse for flat/edge/corner regions; SIFT keypoint matches.
Chapter 06 — Optical Flow¶
- PDF sections: apparent vs real motion, brightness-constancy, structure tensor, Lucas-Kanade, image pyramids, iterative warping, Horn-Schunck, gradient-constancy, anisotropic smoothness, occlusion, SIFT-flow, FlowNet, FlowNet 2.0.
- Code: none in repo (no Sheet 5).
- Trial-exam: Q5a, Q5b.
- Must-know formulas: OF equation \(Ix\cdot u + Iy\cdot v + It = 0\).
- Must-know algorithms: Lucas-Kanade, Horn-Schunck, pyramidal OF.
- Visualisations: colour-coded flow field; backward vs forward warp.
Chapter 07 — Parametric Transformations¶
- PDF sections: transformation taxonomy, translation/rotation/scaling/shearing, three-step pivot rotation, homogeneous coordinates, homography, DLT, forward/backward warping, circle/line, De Casteljau, Bézier, Hermite, Catmull-Rom, thin-plate splines.
- Code: none directly (homographies appear in
epipolar_geometry.py). - Trial-exam: Q6a, Q6b, Q6c.
- Must-know formulas: rotation matrix, T(P)·R(θ)·T(−P), Bézier polynomials.
- Must-know algorithms: DLT homography fit, TPS solve.
- Visualisations: before/after square under T·R·S; 4 control-point Bézier; TPS warped grid.
Chapter 08 — Epipolar Geometry & Depth¶
- PDF sections: triangulation, rectification, epipolar geometry, fundamental matrix, 8-point algorithm, disparity vs depth, block matching, Birchfield-Tomasi, census transform, dynamic programming, graph cuts, deep stereo, monocular depth.
- Code:
Ex/6/sheet6/epipolar_geometry.py,stereo_depth.py,pt_depth.py. - Exercises: Sheet 6.
- Trial-exam: Q7a, Q7b-i, Q7b-ii, Q7b-iii, Q7c.
- Must-know formulas: \(Z = b\cdot f/d\); \(x'^{T} F x = 0\).
- Must-know algorithms: rectification, block matching, dynamic programming, graph cuts.
- Visualisations: disparity map, epipolar lines, point cloud.
Chapter 09 — Morphing / View Synthesis¶
- PDF sections: Sand-Teller video matching, cross-dissolve, projective alignment, Beier-Neely line morphing, virtual video camera, view morphing, Seitz-Dyer rectification trick.
- Code: none directly (morphing uses §07 / §08 components).
- Trial-exam: Q8a, Q8b, Q8c.
- Must-know formulas: view-morph \(\hat{x} = H_{1}^{-1} (H_{1} x + t \cdot (H_{2} x' - H_{1} x))\).
- Must-know algorithms: triangulation morphing, view morphing.
- Visualisations: morph timeline (t = 0, 0.25, 0.5, 0.75, 1.0); rectified-then-interpolated example.
Chapter 10 — Camera Calibration¶
- PDF sections: intrinsic vs extrinsic, radial distortion model, coordinate-system math, forward imaging model, calibration matrix K, projection matrix P = K [R|T], calibration via checkerboard, RQ factorisation, uncalibrated stereo, essential matrix, triangulation, bundle adjustment, multi-view stereo, photo-tourism, smartphone portrait mode.
- Code:
Ex/6/sheet6/epipolar_geometry.py. - Exercises: Sheet 6 (related to stereo / fundamental matrix).
- Trial-exam: Q9a, Q9b, Q9c.
- Must-know formulas: \(P = K \cdot [R | T]\); \(E = K_{L}^{T} F K_{R} = T_\times \cdot R\).
- Must-know algorithms: DLT camera calibration, RQ factorisation, triangulation, bundle adjustment.
- Visualisations: 3-D reconstruction with camera frustums.
Chapter 11 — Neural Radiance Fields¶
- PDF sections: image-based vs physics-based rendering, rendering equation, volume rendering, NeRF MLP, hierarchical sampling, positional encoding, shape-radiance ambiguity, NeRF++, NeRF in the wild.
- Code: none in repo.
- Trial-exam: Q10 (5 T/F).
- Must-know formulas: alpha compositing along ray, positional encoding \(\gamma (p)\).
- Must-know algorithms: ray marching with hierarchical sampling.
- Visualisations: rendered novel views; depth maps.
4. Suggested Study Order¶
Given the trial-exam weights and concept dependencies:
- Chapter 01 (Image Acquisition) — quick foundation, easy points.
- Chapter 02 (Filtering / Edges / Thresholding) — heaviest weight, master convolution arithmetic.
- Chapter 04 (ML) — confusion matrix and basic perceptron arithmetic; quick.
- Chapter 05 (Features) — pinhole projection + Harris/SIFT memorisation.
- Chapter 06 (Optical Flow) — concise theory + 5 T/F.
- Chapter 07 (Parametric) — practice the matrix-decomposition mechanics.
- Chapter 08 (Epipolar / Depth) — practice numerical reconstruction question.
- Chapter 09 (Morphing) — practice writing the formula explanation in 4 sentences.
- Chapter 10 (Calibration) — intrinsic vs extrinsic mantra + RQ factorisation.
- Chapter 11 (NeRF) — last; just memorise the five T/F facts.
5. Important Formulas (one-page summary)¶
- Pinhole projection: \(p' = f \cdot p / z\).
- Normalisation: \(N = (I - a) / (b - a)\).
- Convolution: \((W * I)(x) = \Sigma W(i) \cdot I(x - i)\). Mirror the kernel.
- Sobel: \(S_{x}\) and \(S_{y} = S_{x}^{T}\). Magnitude: \(|\nabla I| = \sqrt{S_{x}^{2} + S_{y}^{2}}\).
- Gaussian: \(G(x, y) = (1 / (2\pi \sigma ^{2})) \cdot \exp (- (x^{2} + y^{2}) / (2 \sigma ^{2}))\).
- Otsu: maximise \(\sigma ^{2}_{B}(\tau ) = w_{0} w_{1} (\mu _{0} - \mu _{1})^{2}\).
- Softmax: \(\sigma _{i} = e^{x_{i}} / \Sigma _{j} e^{x_{j}}\).
- Cross-entropy: \(L = - \Sigma _{i} y_{i} \log p_{i}\).
- Confusion matrix: Acc = TP+TN/Total, Sens = TP/(TP+FN), Spec = TN/(TN+FP).
- Harris score: \(R = \det (H) - k \cdot \operatorname{trace}(H)^{2}\), \(k \in [0.04, 0.06]\).
- NCC = cosine similarity; ZMNCC = Pearson correlation.
- Optical flow: \(Ix\cdot u + Iy\cdot v + It = 0\).
- Lucas-Kanade: structure tensor = Harris matrix.
- Horn-Schunck: add smoothness term \(\lambda \cdot (\|\nabla u\|^{2} + \|\nabla v\|^{2})\).
- Bilinear interp: mix four neighbouring pixel values.
- Rotation matrix 2-D: \(R(\theta ) = [[\cos , -\sin ], [\sin , \cos ]]\).
- Three-step pivot rotation: \(M = T(P) \cdot R(\theta ) \cdot T(-P)\).
- Homography: \(p' = H \cdot p\), fitted via DLT from ≥ 4 correspondences.
- Cubic Bézier: \(B(t) = \Sigma C(3, i) (1-t)^{3-i} t^i P_{i}\).
- Catmull-Rom tangent: \(P'_{i} = (P_{i+1} - P_{i-1}) / 2\).
- TPS RBF: \(\phi (r) = r^{2} \cdot \ln r\).
- Stereo depth: \(Z = b \cdot f / d\).
- Fundamental matrix: \(x'^{T} F x = 0\). F has 7 DoF, rank 2.
- Essential matrix: \(E = K_{L}^{T} F K_{R} = T_\times \cdot R\). 5 DoF.
- Projection matrix: \(P = K \cdot [R | T]\), 11 DoF. RQ-decompose
P[:, :3]to get K, R. - NeRF function: \((x, y, z, \theta , \phi ) \to (R, G, B, \sigma )\).
- Volume rendering alpha: \(\alpha _{i} = 1 - \exp (-\sigma _{i} \cdot \delta _{i})\).
- Positional encoding: \(\gamma (p) = (\sin 2^{0}\pi p, \cos 2^{0}\pi p, \ldots , \sin 2^{L-1}\pi p, \cos 2^{L-1}\pi p)\).
- View morph: \(\hat{x} = H_{1}^{-1} (H_{1} x + t \cdot (H_{2} x' - H_{1} x))\).
6. Important Algorithms (one-line each)¶
| Algorithm | Chapter | Use |
|---|---|---|
| Pinhole projection | 1, 5, 10 | World → image plane |
| Vignetting correction | 1 | Flat-field divide |
| Convolution / Sobel / Canny | 2 | Edge detection |
| Otsu / adaptive thresholding | 2 | Image binarisation |
| Gradient descent | 4 | Train neural networks |
| Backpropagation | 4 | Compute gradients |
| Harris-Stephens corner | 5 | Detect features |
| SIFT | 5 | Detect + describe scale-invariant features |
| Lucas-Kanade OF | 6 | Local optical flow |
| Horn-Schunck OF | 6 | Global optical flow |
| Pyramidal coarse-to-fine | 6 | Big-motion OF |
| DLT homography | 7 | Fit perspective transform |
| Bézier / Catmull-Rom / TPS | 7 | Smooth curves & warping |
| 8-point algorithm | 8 | Estimate fundamental matrix |
| Block matching / Census + Hamming | 8 | Stereo correspondence |
| Graph cuts / α-expansion | 8 | Global stereo optimisation |
| RQ factorisation | 10 | Recover K, R from P |
| Bundle adjustment | 10 | Joint SfM optimisation |
| Triangulation (linear) | 10 | 3-D point from 2 views |
| Volume rendering / ray marching | 11 | Render NeRF |
| Hierarchical sampling | 11 | Speed up NeRF |
7. Important Visualisations¶
| Visualisation | Chapter | Purpose |
|---|---|---|
| Colour-space wheels (RGB, HSV) | 1 | Understand additive vs subtractive |
| Barrel/pincushion distortion sketch | 1 / 10 | Lens distortion |
| 2-D power spectrum interpretations | 2 | Fourier intuition |
| Side-by-side noisy vs filtered images | 2 | Filter comparison |
| Histogram + Otsu threshold | 2 | Show automatic threshold |
| Loss-curve plot | 4 | Diagnose training |
| Confusion matrix heat-map | 4 | Multi-class evaluation |
| Harris ellipse on patch | 5 | Flat / edge / corner |
| SIFT-key-point match overlay | 5 | Feature matching |
| Colour-coded optical flow | 6 | Magnitude + direction |
| Image pyramid stack | 2/6 | Scale space |
| Bézier / Catmull-Rom / TPS curves | 7 | Spline behaviour |
| Disparity map with colour bar | 8 | Stereo result |
| Epipolar lines in pairs | 8 | Geometric matching |
| Morph timeline (t = 0…1) | 9 | Smooth transition |
| 3-D point cloud + camera frustums | 10 | SfM reconstruction |
| NeRF rendered novel views + depth | 11 | Image-based rendering |