Graduate Winter 2026 Upper Level Electives Grade: #

EECS 504: Foundations of Computer Vision provides a graduate-level foundation in computer vision by treating image analysis as a series of optimization problems, focusing on the mathematical modeling of visual invariants, feature extraction, and estimation techniques like camera calibration and stereo reconstruction.

Topic 1: Foundations of Mathematical Vision

This section covers the transition from raw pixels to structured geometric information. Through a series of high-level problem sets, I implemented the mathematical first principles of vision—including homography estimation, scale-space theory, and the statistical foundations of pattern recognition.

Project #1: Geometry, Filtering & Demosaicking
Python OpenCV Linear Least Squares Homography
  • Objective: Implementing core vision algorithms including homography-based projection, Bayer pattern reconstruction, and proving the rotation invariance of the Difference of Gaussians (DoG) operator.
  • Build: Developed a Linear Least Squares solver to estimate $3 \times 3$ homography matrices for image registration and authored a bilinear interpolation engine for Bayer Demosaicking to reconstruct full-color images from raw sensor data.
  • Functionality: Applied homography estimation to project virtual NFL-style "magic yellow lines" onto a football field with perspective correctness and achieved high-fidelity reconstruction of the "Orion" sculpture from mosaicked gray-scale inputs.
Project #2: Local Features, Scale Space & PCA
Python Harris Corners DoG Scale Space PCA / KNN
  • Objective: Extracting robust, scale-invariant features from images and implementing a statistical learning pipeline for digit classification.
  • Build: Architected a Harris Corner Detector using structure tensor eigenvalues and a Difference of Gaussians (DoG) scale-space pyramid. Developed a dimensionality reduction engine using Principal Component Analysis (PCA) to extract the most descriptive eigenvectors from the MNIST dataset.
  • Functionality: Performed multi-scale blob detection on biological and natural imagery (Drosophila, Sunflowers) and implemented a panoramic stitching pipeline using ORB features. Achieved high-accuracy digit classification ($>90\%$) by combining the PCA-reduced feature basis with a K-Nearest Neighbors (KNN) classifier.

Topic 2: Research & Advanced Applications

The capstone of the course involves translating academic research into functional software. Working in a small research group, this project focuses on locating state-of-the-art methods in literature and developing a custom solution for a novel computer vision challenge.

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