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Computer Vision Fundamentals: Epipolar Geometry and Image Segmentation - CAP 5415 Fall 2004

This course material from Dr. Alper Yilmaz at the University of Central Florida covers essential aspects of computer vision, including epipolar geometry, essential and fundamental matrices, the 8-point algorithm, and graph cuts for image segmentation. Students will learn to tackle challenges such as optical flow computation using the Lucas-Kanade method and the implementation of advanced segmentation techniques. The curriculum includes practical assignments and theoretical insights designed to deepen understanding of computer vision concepts within practical programming contexts.

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Computer Vision Fundamentals: Epipolar Geometry and Image Segmentation - CAP 5415 Fall 2004

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  1. CAP 5415 Computer VisionFall 2004 Dr. Alper Yilmaz Univ. of Central Florida www.cs.ucf.edu/courses/cap5415/fall2004 Office: CSB 250 Alper Yilmaz, Fall 2004 UCF

  2. RecapEpipolar Geometry • Essential matrix • Fundamental matrix P xl Pl xr Pr Cl Cr epipole epipole Alper Yilmaz, Fall 2004 UCF

  3. Recap8-Point Algorithm • N≥8 corresponding points in both images • Normalize and scale coordinates • Construct an observation matrix • Compute OTO and its eigenspace decomposition • Select min eigenvalued eigenvector as solution • Enforce rank 2 constraint • Compute SVD and set smallest singular value to 0 Alper Yilmaz, Fall 2004 UCF

  4. J. Shi and J. Malik, “Normalized Cuts & Image Segmentation,” IEEE Trans. of PAMI, Aug 2000. RecapGraph Cuts for Image Segmentation • Let all pixels be nodes of a graph • Compute similarity between each node to all other nodes of graph • Construct weight matrix W and diagonal cost matrix D • Compute eigenvector of (D-W) • Use the eigenvector with second smallest eigenvalue to segment image to 2 segments • Iteratively do these steps Alper Yilmaz, Fall 2004 UCF

  5. RecapDrawbacks of Minimum Normalized Cut • Huge storage requirement • Takes a lot of time • Bias towards partitioning into equally sized segments Alper Yilmaz, Fall 2004 UCF

  6. Mid Term 2 - 24 November 2004 • Hough Transform • Line, circle fitting • Generalized Hough transform • Interest point, corner detectors • Pixel based optical flow • Token based optical flow • Global motion • Shape from motion • Geometry of a stereo camera pair • Stereopsis • Fundamental matrix (estimation) • Graph based image segmentation Alper Yilmaz, Fall 2004 UCF

  7. Programming AssignmentDue date 3 December 2004 • Implement Lucas&Kanade method for computing optical flow. • Build Gaussian pyramid • Start from lowest resolution compute optical flow for each pixel • Go to next pyramid level by projecting computed optical flows • You need to replicate optical flow for erased pixels • Warp image intensities using the optical flow vector • Display flow vectors using quiver plot (plot every 5 pixel as a vector) • Deliverables • Report including all pyramid level images and flow vectors of each pyramid level along with source code Alper Yilmaz, Fall 2004 UCF

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