Lec02 - Computer Vision Computer Lecture #2 Hossam...

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Unformatted text preview: Computer Vision Computer Lecture #2 Hossam Abdelmunim1 & Aly A. Farag2 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 1 2 Electerical and Computer Engineering Department, University of Louisville, Louisville, KY, USA ECE619/645 – Spring 2011 Geometric Primitives and Transformations Transformations • 2D Point – x=(x1,x2,1) • 2D Line – ax1+bx2+c=0 Geometric Primitives and Transformations Transformations • 3D Point – x=(x1,x2,x3,1) • 3D Line Derive the line equation shown above. Geometric Primitives and Transformations Transformations • 3D Plane – ax+by+cz+d=0; Derive the plane equation shown above. Transformation Matrix Transformation • Translation (Example in 2D) Transformation Matrix Transformation • Rotation Matrix (Example in 2D) Transformation Matrix Transformation • Scaling Matrix (Example in 3D) Projective Transformation Matrix Projective Hierarchy of Coordinate Transformations Transformations * *Homogeneous Scaling, rotation, and translation 3D to 2D Projection 3D What do we need? What we need to specify how 3D primitives (points) are projected onto the image plane. We can do this using a linear 3D to 2D projection matrix. Example Example Geometric Interpretation Geometric Perspective v's Parallel (orthogonal) Projection Perspective Projection Matrix Equation Equation Para-Perspective Projection Para-Perspective ...
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This note was uploaded on 01/12/2012 for the course ECE 618 taught by Professor Amini during the Spring '08 term at University of Louisville.

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