Technical Report CIS9910

Title: Numerical Geometry of Images: Theory, Algorithms, and Applications
Authors: Ron Kimmel
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Abstract: Lecture notes for Advanced Topics in Computer Science: `Numerical Geometry of Images'The goal of this course is to introduce recent algorithms and numerical methods motivated by differential geometry, and apply them to various problems in Image Processing, Computer Vision, Robotic Navigation,and Computer Graphics. We learn about non-linear methods in image processing like image enhancement, color processing, video processing, and resolution enhancement. We explore new geometric methods in computer vision for 2D and 3D object segmentation, signatures for recognition, and 3D shape reconstruction from a single image. Next, we learn how the same mathematical machinery can be used to solve problems in other fields, like robotic navigation and mathematical morphology. During the semester I will present some open research problems: Some theoretical and mostly practical.
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