CVML Final Exam Revision Guide

A compact "last-day before exam" guide. One page per chapter, plus templates and strategies.

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Strategy for the Real Exam

• First pass — easy points. Sweep through T/F questions. Skip if unsure (0 > −1).
• Second pass — numerical. Show every line, units consistent. Box your final answer.
• Third pass — short answer. 1–3 sentences using the precise technical term.
• Final pass — review flagged items for arithmetic and sign errors.

Time budget (90 min)

• 10 min for the high-weight numerical (Q2c convolution, Q7b stereo).
• 5 min per other numerical.
• 1 min per T/F (≈ 25 min in total).
• Remaining time on short-answer.

Strategy by question type

• Theory question (1–2 sentences). Use the precise technical term, give the purpose, then a one-line derivation/explanation. Don't ramble.
• Mathematical question. Restate the formula, identify all symbols, plug in numbers, simplify, give units. Box the answer.
• Coding question. Sketch pseudocode + key library calls (e.g. cv2.GaussianBlur, cv2.findHomography). Mention edge cases.
• Image / plot interpretation. Match high-level patterns: high disparity ⇒ close; bright Fourier dot off-centre ⇒ specific frequency direction; loss diverging ⇒ learning rate too high; etc.

Short answer templates

Define + Why + Equation + Example. "[Term] is …; this matters because …; mathematically …; e.g. in [application]."

Compare X vs Y. "Both X and Y aim to …; they differ in [criterion]; X is better when …; Y when …; example: …".

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Last-Minute Revision Checklist

• [ ] HSV: hue rotates colours; sat → grey; value → dark.
• [ ] Print = subtractive = CMYK; LED = additive = RGB.
• [ ] Aperture ↑ → DoF ↓ → image brighter.
• [ ] Barrel = wide-angle; pincushion = telephoto.
• [ ] Convolution mirrors the kernel before sliding.
• [ ] Gaussian smooths without ringing; box does ring; median kills salt-and-pepper.
• [ ] Sobel = central diff ⊗ Gaussian; Prewitt = ⊗ box.
• [ ] DoG ≈ LoG; both band-pass.
• [ ] Otsu maximises between-class variance; adaptive uses local stats.
• [ ] Concrete-wall trick: subtract heavy Gaussian-blurred copy.
• [ ] Z = b·f/d.
• [ ] Disparity = pixels; depth = metric.
• [ ] F is 3×3, rank 2, 7 DoF; E = K_Lᵀ F K_R = T_× · R; 5 DoF.
• [ ] Optical-flow equation: \(Ix\cdot u + Iy\cdot v + It = 0\).
• [ ] LK = local + structure tensor (Harris). Fails homogeneous.
• [ ] HS = global + smoothness.
• [ ] Backward warp = gather, no holes.
• [ ] Forward warp = scatter, holes & overlaps.
• [ ] Harris score \(R = \det (H) - k\cdot \operatorname{trace}(H)^{2}\), \(k \in [0.04, 0.06]\).
• [ ] SIFT 128-D, ratio test 0.6/0.8.
• [ ] Confusion matrix: Acc = TP+TN/Total, Sens = TP/(TP+FN), Spec = TN/(TN+FP).
• [ ] Epoch = one full pass over training data.
• [ ] Normalise after train/test split.
• [ ] More layers ≠ better.
• [ ] M = T·R·S reads right-to-left: scale, rotate, translate.
• [ ] Pivot rotation = T(P)·R(θ)·T(−P).
• [ ] Catmull-Rom = auto tangents \((P_{i+1} - P_{i-1})/2\), no overshoot.
• [ ] Hermite = position + manual tangent; can overshoot.
• [ ] TPS = "as smooth as possible" closed-form; can overlap.
• [ ] Morph in image space ⇒ NOT physically valid; rectify-then-interpolate is.
• [ ] Cross-dissolve = blend without warp.
• [ ] P = K·[R|T]; intrinsics K stay; extrinsics R,T change.
• [ ] RQ factorisation gives K and R from P[:,:3].
• [ ] Radial distortion is non-linear — never affine.
• [ ] NeRF input 5-D (xyz+θφ), output 4-D (RGB+σ).
• [ ] NeRFs use ray marching, NOT voxels, NOT meshes.
• [ ] Positional encoding kills MLP spectral bias.
• [ ] View direction enters at the penultimate layer (avoids shape-radiance ambiguity).

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Chapter Summaries — One Page Each

Chapter 01 — Image Acquisition

• Image = 2-D function, sampled to a pixel matrix.
• RGB additive, CMYK subtractive, HSV artistic, Lab perceptual.
• Pinhole projection \(p' = f \cdot p / z\) (similar triangles).
• Aperture ↑ → DoF ↓ + brighter; aperture ↓ → DoF ↑ + darker.
• Barrel distortion in wide-angle lenses; lines bow outward.
• CCD → streaking; CMOS → rolling shutter.
• Bayer pattern over-represents green.
• Gaussian noise: \(I_{noisy} = I + N(\mu , \sigma ^{2})\).
• Trial-exam: Q1a-d.

Chapter 02 — Filtering, Edges, Thresholding (20 pts)

• Convolution mirrors then slides kernel; correlation does not.
• Box (uniform), sinc (frequency cutoff), Gaussian (smooth, no ringing), median (salt-and-pepper).
• Sobel & Prewitt = first derivative (gradient); Laplacian = second derivative (zero-crossings = edges).
• DoG ≈ LoG (band-pass; SIFT scale space).
• Otsu = max between-class variance; adaptive = per-pixel local threshold for uneven illumination.
• Concrete-wall gradient removal: subtract heavily Gaussian-blurred image (high-pass).
• Manual convolution: stack kernel, multiply, sum, mind the sign and the mirroring.
• Power-spectrum reading: stripes ↔ perpendicular bright spots; DC at centre = average; high freq at periphery.
• Trial-exam: Q2a (Fourier match), Q2b (theory ×4), Q2c (numerical convolution), Q2d (filter category + more).

Chapter 04 — Machine Learning

• Perceptron \(y = a(\Sigma w_{i}x_{i} + b)\).
• ReLU hidden, softmax classification output, sigmoid binary, linear regression.
• Cross-entropy classification; MSE regression.
• Train / val / test split; normalise after splitting.
• K-fold CV for small data.
• CNN = conv + max-pool + dense + softmax; first layers learn Gabor-like filters.
• Confusion matrix: Acc = (TP+TN)/Total; Sens = TP/(TP+FN); Spec = TN/(TN+FP); Prevalence = (TP+FN)/Total.
• Epoch = one full pass over training data.
• More layers ≠ better; risk of overfitting; mitigations = dropout, early stopping, augmentation, regularisation.
• Trial-exam: Q3a-i, ii, iii (confusion matrix), Q3b (epoch), Q3c (3 T/F).

Chapter 05 — Features

• Pinhole \(p' = f \cdot p / z\). (Trial Q4a: \((10,5,3), f=2 \to (20/3, 10/3)\).)
• Good feature = unique, repeatable, invariant.
• Edge has 1 big eigenvalue; corner has 2.
• Harris score \(R = \det (H) - k\cdot \operatorname{trace}(H)^{2}\), \(k \in [0.04, 0.06]\).
• NCC scale-invariant; ZMNCC also offset-invariant. Both fail under non-linear lighting (specular, shadows, colour cast).
• SIFT 128-D, ratio test 0.6/0.8; rotation/scale/illumination invariant.
• Diagonals of Harris matrix encode squared gradient sums (NOT shear/rotation).
• Trial-exam: Q4a (numerical), Q4b (ZMNCC fix), Q4c (5 T/F).

Chapter 06 — Optical Flow

• OF equation: \(Ix\cdot u + Iy\cdot v + It = 0\) (one equation, two unknowns ⇒ aperture problem).
• Lucas-Kanade = local; uses structure tensor (= Harris matrix); fails in homogeneous regions.
• Horn-Schunck = global; adds smoothness term \(\lambda \cdot (\|\nabla u\|^{2} + \|\nabla v\|^{2})\); fills homogeneous; blurs edges.
• Backward warping = gather; no holes; standard for OF.
• Forward warping = scatter; can have holes & overlaps.
• Bilinear interpolation for sub-pixel lookup.
• Pyramidal coarse-to-fine for big motion.
• FlowNet 2.0 fast but still bad on occlusions / fine texture.
• Specular surfaces violate brightness constancy.
• Trial-exam: Q5a (backward warp), Q5b (5 T/F).

Chapter 07 — Parametric Transformations

• DoF: Euclidean 3, similarity 4, affine 6, projective 8.
• \(M = T \cdot R \cdot S\) — read right-to-left (scale, rotate, translate).
• Pivot rotation: \(T(P) \cdot R(\theta ) \cdot T(-P)\).
• Homogeneous coords (x, y, 1) make translation expressible as a matrix multiply.
• Homography: 3×3, 8 DoF, fit via DLT from ≥ 4 correspondences.
• Bézier curve has degree-(n−1) basis polynomials; cubic uses 4 control points.
• Hermite = positions + tangents (overshoots possible).
• Catmull-Rom = auto tangents \((P_{i+1}-P_{i-1})/2\), never overshoots, interpolates all control points.
• TPS = closed-form smoothest warping; integrand of Hessian² = continuous Harris matrix; can overlap; straight lines bend.
• Trial-exam: Q6a (decomposition), Q6b (3-step rotation), Q6c (Catmull-Rom vs Hermite).

Chapter 08 — Epipolar Geometry & Depth

• \(Z = b \cdot f / d\) — depth from disparity.
• Disparity in pixels; depth in metric units.
• F: 3×3, rank 2, 7 DoF. \(x'^{T} F x = 0\).
• E: 5 DoF; \(E = K_{L}^{T} F K_{R} = T_\times \cdot R\). SVD recovers (R, T).
• Rectification puts epipolar lines on scan-lines ⇒ 1-D search for stereo matches.
• Block matching: SAD, SSD, NCC; Census + Hamming robust to lighting.
• Smoothness models: Potts; intensity-adaptive Potts; truncated linear.
• Graph cuts (α-expansion) ≈ optimal global stereo.
• Trial-exam: Q7a (depth from stereo), Q7b-i/ii/iii (numerical setup), Q7c (optical axis & epipolar line).

Chapter 09 — Morphing / View Synthesis

• Cross-dissolve = blend, no geometric alignment.
• Morphing = warp + cross-dissolve.
• Image-space morph is not physically valid; rectify-then-interpolate is.
• Trial-exam formula: \(\hat{x} = H_{1}^{-1} (H_{1} x + t \cdot (H_{2} x' - H_{1} x))\) — rectify, interpolate, un-rectify.
• Sand-Teller video matching uses parallax similarity + motion magnitude.
• Virtual video camera = space-time cube + tetrahedralisation + view morph.
• Trial-exam: Q8a (formula), Q8b (rectification benefit), Q8c (3 T/F).

Chapter 10 — Camera Calibration

• Intrinsics K (5 numbers): \(f_{x}, f_{y}, o_{x}, o_{y}, s\). Don't change with camera motion.
• Extrinsics [R | T]: 6 numbers; change every motion.
• \(P = K \cdot [R | T]\) — 11 DoF.
• RQ factorisation of P[:, :3] gives K and R; \(T = K^{-1} \cdot P[:, 4]\).
• \(E = K_{L}^{T} F K_{R} = T_\times \cdot R\); recover (R, T) via SVD.
• Triangulation (linear) recovers 3-D point from two views.
• Bundle adjustment minimises total re-projection error jointly over cameras + points.
• Radial distortion is non-linear; affine cannot correct it.
• Trial-exam: Q9a (intrinsics extraction), Q9b (parameter types), Q9c (3 T/F).

Chapter 11 — Neural Radiance Fields

• \((x, y, z, \theta , \phi ) \to (R, G, B, \sigma )\) — small MLP, 9 layers, 256 channels.
• Volume rendering: \(\alpha _{i} = 1 - \exp (-\sigma _{i} \cdot \delta _{i})\); alpha-composite front-to-back.
• Hierarchical sampling: coarse uniform + fine via importance.
• Positional encoding \(\gamma (p) = (\sin 2^{0}\pi p, \cos 2^{0}\pi p, \ldots )\) overcomes spectral bias.
• View direction enters at the penultimate layer to avoid shape-radiance ambiguity.
• Training requires multiple posed images of a static scene.
• No voxel grid, no explicit mesh.
• Slow: 3-day train, 1-min/frame inference (vanilla).
• NeRF++ for unbounded scenes; NeRF in the Wild for tourist photos.
• Trial-exam: Q10 (5 T/F).

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High-Probability Exam Topics (based on trial exam + exercises)

• Numerical convolution with a 1-D kernel (Q2c).
• Confusion-matrix arithmetic (Q3a).
• Pinhole projection arithmetic (Q4a).
• Matrix decomposition \(M = T\cdot R\cdot S\) (Q6a).
• Stereo 3-D reconstruction (Q7b).
• T/F questions everywhere — memorise the rules.
• Theory short-answers: Gaussian / DoG / global vs local thresholding / view morphing / intrinsics vs extrinsics.

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Last-Day Mantras (memorise these)

• "Pinhole: \(p' = f\cdot p/z\)."
• "Aperture ↑ → DoF ↓ → brighter."
• "Convolution mirrors. Box rings. Gaussian smooths. Median kills salt-and-pepper."
• "DoG ≈ LoG."
• "Otsu = automatic global; adaptive = per-pixel."
• "\(Z = b\cdot f/d\)."
• "F: 3×3, rank 2, 7 DoF. E removes K from F."
• "OF: \(Ix u + Iy v + It = 0\). LK fails homogeneous; HS smooths edges."
• "Backward warp = gather, no holes."
• "M = T·R·S right-to-left."
• "Catmull-Rom auto tangents, never overshoots."
• "P = K·[R|T]; RQ-decompose P[:,:3] for K, R."
• "Radial distortion is NEVER affine."
• "NeRF: 5-D in, 4-D out, ray-march, no voxels, no mesh."
• "Image-space morph is fake; rectify then interpolate."

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Key-Term Quick Reference (English ↔ বাংলা)

Topic	Term	বাংলা ব্যাখ্যা
1	focal length	লেন্স থেকে ইমেজ-প্লেনের দূরত্ব
1	aperture	লেন্সের আলো ঢোকার ছিদ্র
1	depth of field	কত দূর পর্যন্ত ছবি ঝকঝকে থাকে
1	barrel distortion	সরলরেখা বাইরের দিকে ফুলে যাওয়া (wide-angle)
1	hue / saturation / value	রঙের ধরন / তীব্রতা / উজ্জ্বলতা
1	noise	আসল মান আর মাপা মানের পার্থক্য
2	convolution	ছবির ওপর ছোট ম্যাট্রিক্স (kernel) বসিয়ে নতুন মান
2	smoothing	আশেপাশের গড় নিয়ে noise কমানো
2	edge detection	যেখানে intensity হঠাৎ বদলায় তা খোঁজা
2	threshold	যার উপরে 1, নিচে 0
2	low-/high-pass filter	ধীর পরিবর্তন রাখে / দ্রুত পরিবর্তন রাখে
4	loss function	মডেল কতটা ভুল করছে তার মাপ
4	learning rate	gradient ধাপের আকার
4	confusion matrix	কোন class কোনটার সাথে গুলিয়েছে
5	structure tensor	gradient-এর কোভ্যারিয়েন্স ম্যাট্রিক্স
5	scale space	বিভিন্ন blur স্তরে ছবির প্রতিনিধিত্ব
5	keypoint	ট্র্যাক করার মতো বিশেষ বিন্দু (corner)
6	optical flow	প্রতি পিক্সেলের আপাত গতিভেক্টর
6	brightness constancy	একই বিন্দুর রঙ দুই ফ্রেমে এক রকম থাকা
6	forward/backward warping	scatter (গর্ত হয়) / gather (নিরাপদ)
7	homography	projective 3×3 রূপান্তর, 8 DOF
7	homogeneous coordinates	(x, y, w) — শেষে w দিয়ে ভাগ
8	disparity / depth	পিক্সেল-ভিন্নতা d / গভীরতা Z = b·f/d
8	rectification	epipolar line-গুলোকে অনুভূমিক করা
8	fundamental / essential matrix	uncalibrated F (7 DOF) / calibrated E (5 DOF)
8	epipole / epipolar line	অন্য ক্যামেরার ছবি-বিন্দু / খোঁজার ১-D লাইন
9	cross-dissolve	শুধু রঙ মেশানো — ghost হয়
9	morphing / view interpolation	warp + blend / মাঝের দৃশ্য বানানো
10	intrinsic / extrinsic	ক্যামেরার ভেতরের K / ভঙ্গি R, t
10	calibration / projection matrix	K / P = K[R
10	bundle adjustment	সব ক্যামেরা + 3D বিন্দু একসাথে অপ্টিমাইজ
11	radiance field	F(x, y, z, θ, φ) → (r, g, b, σ)
11	volume rendering / ray marching	ray বরাবর নমুনা জমিয়ে রঙ
11	positional encoding	sin/cos দিয়ে উঁচু frequency শেখানো
11	spectral bias	MLP-এর কম-ফ্রিকোয়েন্সি শেখার প্রবণতা

Good luck. Ruhe bewahren — and Viel Erfolg!