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lecture2 - Course overview 1 Geometry 2 Low Mid-level...

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Course overview 1. Geometry 2. Low & Mid-level vision 3. High level vision
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Course overview 1. Geometry 2. Low & Mid-level vision 3. High level vision - How to extract 3d information? - Which cues are useful? - What are the mathematical tools?
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Linear Algebra & Geometry why is linear algebra useful in computer vision? Some of the slides in this lecture are courtesy to Prof. Octavia I. Camps, Penn State University References: -Any book on linear algebra! -[HZ] – chapters 2, 4
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Why is linear algebra useful in computer vision? • Representation 3D points in the scene 2D points in the image • Coordinates will be used to Perform geometrical transformations – Associate 3D with 2D points • Images are matrices of numbers Find properties of these numbers
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Agenda 1. How did you like the movie? 2. Basics definitions and properties 3. Geometrical transformations 4. Application: removing perspective distortion
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P = [x,y,z] Vectors (i.e., 2D or 3D vectors) Image 3D world p = [x,y]
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Vectors (i.e., 2D vectors) ) , ( 2 1 x x = v P x1 x1 x2 x2 θ v Magnitude: Magnitude: 2 2 2 1 || || x x + = v Orientation: Orientation: = 1 2 1 tan x x θ = || || , || || || || 2 1 v v v v x x Is a unit vector Is a unit vector If If 1 || || = v , , v Is a UNIT vector Is a UNIT vector
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