Saral Shiksha Yojna
Courses/Computer Vision

Computer Vision

CSE471
Prof. Makarand Tapaswi + Prof. Charu Sharma•Spring 2025-26•4 credits
Sample Papers/Mock Paper 10 — Numerical Calculation Marathon (show all working)

Mock Paper 10 — Numerical Calculation Marathon (show all working)

Duration: 180 min • Max marks: 100

Section A — Quick Calculations (2 marks each, 20 marks)

20 marks
  1. 1.Conv output size: input 100×100, kernel 5×5, stride 3, padding 0.2 m
  2. 2.Conv layer C_in=64, C_out=128, kernel 3×3 — total params (with bias)?2 m
  3. 3.IoU between 1D segments [10, 30] and [20, 40].2 m
  4. 4.Compute Dice given IoU = 0.6.2 m
  5. 5.F1 with Precision = 0.75, Recall = 0.6.2 m
  6. 6.σ for a 5×5 Gaussian where corners ≈ 1% of centre.2 m
  7. 7.ViT-B/16 on 384×384 image — sequence length entering Transformer (with CLS)?2 m
  8. 8.Time complexity of QKᵀ for Q ∈ ℝ^{N×d_k}.2 m
  9. 9.LSTM with input dim 100, hidden dim 256 — total parameters (4 gates, each with W, U, b).2 m
  10. 10.OpenPose outputs 56 heatmap channels. How many keypoints K and limbs L if K + 2L = 56?2 m

Section B — Multi-Step Calculations (5-6 marks each, 40 marks)

40 marks
  1. 1.CNN forward trace. Input 64×64 grayscale. L1 conv 16@5×5 s=1 p=2; L2 ReLU; L3 maxpool 2 s=2; L4 conv 32@3×3 s=1 p=1; L5 ReLU; L6 maxpool 2 s=2; L7 conv 64@3×3 s=2 p=1; L8 FC 10. (a) Spatial dims per layer. (b) Params per conv/FC (with bias). (c) Total params.6 m
  2. 2.Receptive field at L7 output of the network from Q11 (in original pixels).6 m
  3. 3.NMS trace. Boxes A(0.95), B(0.85), C(0.75), D(0.65). Pairwise IoUs: AB 0.6, AC 0.3, AD 0.1, BC 0.7, BD 0.2, CD 0.55. Threshold 0.5.5 m
  4. 4.PR curve. 5 ground truths, 8 detections by score: TP, FP, TP, TP, FP, TP, FP, TP. (a) Cumulative P-R table. (b) AP via 11-point interpolation.6 m
  5. 5.Transformer block params: D=1024, 16 heads (d_k=64), FFN expansion 4×. Compute exact.5 m
  6. 6.Morphology numerical trace. 7×7 binary image; SE = 3×3 cross. Compute erosion, dilation, opening, closing.6 m
  7. 7.Backprop through y = Wx + b. W = [[1,2],[3,4],[5,6]], x = [1, 2]ᵀ, b = [1, 2, 3]ᵀ; upstream ∂L/∂y = [1, 0, 1]ᵀ. Compute (a) y; (b) ∂L/∂W; (c) ∂L/∂x; (d) ∂L/∂b.5 m

Section C — Complex Numerical Problems (10 marks each, 40 marks)

40 marks
  1. 1.Full CNN backprop. Image 4×4 x = [1..16] row-major; conv 3×3 w = [[1,0,-1],[2,0,-2],[1,0,-1]] (Sobel-X-like), stride 1, no padding → y 2×2; then ReLU, then avg pool 2×2 → scalar z. Target 0, L = (z − target)²/2. (a) Forward y, ReLU(y), z. (b) dL/dz. (c) dL/dy and dL/dw.10 m
  2. 2.Otsu's method numerical. Histogram p(0)=0.2, p(1)=0.1, p(2)=0.05, p(3)=0.15, p(4)=0.5. Find optimal Otsu threshold among {0.5, 1.5, 2.5, 3.5}.10 m
  3. 3.Self-attention numerical walkthrough. 3 tokens X = [[1,0], [0,1], [1,1]]; D=2; W_Q=W_K=W_V=I. Compute (a) Q, K, V; (b) QKᵀ; (c) scaled by √d_k; (d) softmax row-wise; (e) output = Attn·V.10 m
  4. 4.Homography numerical. Correspondences (0,0)→(0,0), (10,0)→(20,0), (0,10)→(0,20), (10,10)→(20,20). (a) Set up linear system. (b) Solve H. (c) Apply to (5,5). (d) Interpretation.10 m

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