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.