Computational Problem SolvingLaajuus (1 - 5 cr)

Objective

- Understand and apply mathematical and computational methods for reconstructing movement and drawings from video footage.
- Analyze camera perspectives, distortions, and projections to infer spatial relationships.
- Design, implement, and evaluate simulations and visual explainers.
- Apply optimization techniques such as local search, gradient descent, and neural networks to improve model accuracy.
- Implement the solution using a programming language (eg. JavaScript or Python).

Content

The course is structured around a single challenge: reconstructing a pen’s path from footage of its movement in front of colored balls. Through this, students will explore:
- Trilateration and geometric localization techniques.
- Perspective analysis and size scaling based on visual input.
- Camera modeling (pinhole camera, lens distortion).
- Map projections (Azimuthal equidistant, Lambert equal-area).
- Simulations and visual debugging (using JavaScript and Three.js).
- Optimization strategies: local search, gradient descent, and genetic algorithms.
- Neural network applications in spatial estimation.
- Signal and image processing techniques for segmentation and motion analysis.
- Problem decomposition and algorithm design for real-world-inspired scenarios.