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The final exam for Visión por Computador is a written development exam (examen de desarrollo). It tests your ability to reason through problems rather than recall definitions — expect multi-step derivations, diagram interpretation, and short analytical arguments. The exam typically includes questions spanning three main areas: computational geometry, deep learning architectures, and ethics/fairness in AI. Below you will find past exams, a NotebookLM course assistant, and topic summaries to guide your review.

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Exam format

  • Type: Written, open-ended development questions (no multiple choice)
  • Coverage: Chapters 2, 3, and 4 — geometry, deep learning, and ethics
  • What is expected: Show your work; partial credit is given for correct reasoning even if the final answer is wrong
  • Mathematical tools: You are expected to apply matrix operations, SVD decomposition, homogeneous coordinates, and loss function formulations

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Past exams

Exam 2023 — Questions

Development questions from the 2023 final exam. Use these to practice writing full solutions under time constraints.

Exam 2023 — Solutions

Official solutions for the 2023 exam. Compare your reasoning against these after attempting the questions.

Exam 2024 — Questions

Development questions from the 2024 final exam. The 2024 paper includes more deep learning-focused questions.

Exam 2024 — Solutions

Official solutions for the 2024 exam.

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NotebookLM course assistant

The course has a dedicated NotebookLM notebook loaded with the course materials. You can ask it questions about any topic covered in the course and it will answer using the actual source documents. This is a useful tool for checking your understanding of a concept or exploring connections between topics — but do not rely on it as a substitute for working through the past exams yourself.

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Topic summaries

Use these summaries to identify gaps in your preparation. Each accordion covers one chapter.
This chapter is the heaviest in terms of mathematical content and typically accounts for the largest share of exam questions.Homogeneous coordinates
  • Points and lines in 2D are represented as 3-vectors; planes and points in 3D as 4-vectors.
  • The intersection of two lines l and m is the cross product l × m.
  • The line through two points p and q is the cross product p × q.
2D and 3D transformations
  • Know the hierarchy: Euclidean → similarity → affine → projective.
  • Each transformation is represented as a matrix acting on homogeneous coordinates.
  • Composition of transformations = multiplication of matrices.
Homographies
  • A homography is a 3×3 invertible matrix H mapping one projective plane to another.
  • Estimated from at least 4 point correspondences using the Direct Linear Transform (DLT).
  • DLT reduces to solving a homogeneous linear system Ah = 0, where the solution is the singular vector of A corresponding to the smallest singular value (SVD).
Camera calibration
  • The camera matrix P = K[R|t] encodes intrinsic (K) and extrinsic (R, t) parameters.
  • Calibration recovers K from known 3D–2D point correspondences, again via SVD.
  • Non-linear distortion parameters (radial, tangential) are estimated separately.
  • RANSAC is used to robustly estimate geometric models in the presence of outliers.
Epipolar geometry
  • Two cameras viewing the same scene share an epipolar constraint: p'ᵀFp = 0.
  • The fundamental matrix F (3×3, rank 2) encodes the relative geometry of the two cameras.
  • Estimated from 8 or more point correspondences using the 8-point algorithm and SVD.
  • Epipolar lines let you reduce stereo matching from 2D search to 1D search.
This chapter covers the main neural network architectures used in computer vision today.Convolutional neural networks (CNNs)
  • Convolution layers learn local spatial filters; pooling layers downsample feature maps.
  • Common architectures: LeNet, VGG, ResNet, EfficientNet.
  • Training: forward pass → loss → backpropagation → gradient descent.
  • Transfer learning: freeze pretrained weights, fine-tune the final layers on your dataset.
Object detection — YOLO
  • YOLO divides the image into a grid and predicts bounding boxes + class probabilities per cell.
  • Loss combines localization loss, confidence loss, and classification loss.
  • Non-maximum suppression (NMS) removes duplicate detections.
Facial analysis
  • Face detection, alignment, recognition, and attribute prediction are separate sub-tasks.
  • Modern face recognition systems (e.g., AdaFace) use metric learning (cosine similarity) on embeddings.
Segmentation — UNet
  • UNet uses an encoder–decoder architecture with skip connections.
  • Skip connections preserve spatial detail that is lost during downsampling.
  • Trained with pixel-wise cross-entropy or dice loss.
Generative models — GANs
  • A GAN consists of a generator G and discriminator D trained adversarially.
  • Training objective: G tries to fool D; D tries to distinguish real from fake.
  • Common failure modes: mode collapse, training instability.
Transformers and Vision Transformers (ViT)
  • Transformers use self-attention to model long-range dependencies without convolutions.
  • ViT splits an image into fixed-size patches, embeds them as tokens, and passes them through a standard Transformer encoder.
  • HuggingFace provides pretrained ViT models for rapid experimentation.
The ethics chapter is examined through both the E11 quiz and development questions in the final exam.Key concepts
  • Bias: Systematic errors in model predictions that disadvantage certain groups. Sources include biased training data, biased labels, and biased evaluation metrics.
  • Fairness: Multiple competing formal definitions (demographic parity, equalized odds, individual fairness). No single definition satisfies all desiderata simultaneously.
  • Explainability: Methods such as saliency maps, LIME, and MinPlus reveal which image regions drive a model’s prediction.
  • Adversarial attacks: Small, imperceptible perturbations to input images can cause confident misclassification.
  • Federated / swarm learning: Distributed training paradigms that avoid centralizing sensitive data.
What to know for the exam
  • Be able to define and distinguish bias, fairness, and discrimination.
  • Understand why fairness constraints can be in tension with accuracy.
  • Explain what a saliency map shows and what its limitations are.
  • Discuss at least one real-world case where a CV system caused harm due to bias.
Several mathematical tools appear across multiple chapters. Make sure you are comfortable with all of them.Homogeneous coordinates
  • Represent 2D points as (x, y, 1)ᵀ and 3D points as (X, Y, Z, 1)ᵀ.
  • Enable transformations (including projections) to be expressed as matrix multiplications.
Matrix decompositions
  • SVD (A = UΣVᵀ): Used throughout the course to solve homogeneous least-squares problems. The solution to min ‖Ah‖ subject to ‖h‖ = 1 is the last column of V.
  • QR decomposition: Used to extract the intrinsic matrix K from the camera matrix P.
  • Eigendecomposition: Used in PCA and in analyzing transformation matrices.
Least squares
  • Overdetermined system Ax ≈ b: solution is x = (AᵀA)⁻¹Aᵀb.
  • Homogeneous system Ax = 0: solution via SVD (smallest singular value).
  • Weighted and robust variants (RANSAC) handle outliers.
Calculus for deep learning
  • Chain rule for backpropagation.
  • Gradient of cross-entropy loss with softmax output.
  • Role of learning rate, momentum, and batch normalization in convergence.

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