computer vision lecture #2 hossam abdelmunim 1 & aly a. farag 2 1 computer & systems...
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Computer VisionComputer VisionLecture #2Lecture #2
Hossam Abdelmunim1 & Aly A. Farag2
1Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt
2Electerical and Computer Engineering Department, University of Louisville, Louisville, KY, USA
ECE619/645 – Spring 2011
Geometric Primitives and Geometric Primitives and TransformationsTransformations
Geometric Primitives and Geometric Primitives and TransformationsTransformations
• 2D Point– x=(x1,x2,1)
• 2D Line– ax1+bx2+c=0
Geometric Primitives and Geometric Primitives and TransformationsTransformations
Geometric Primitives and Geometric Primitives and TransformationsTransformations
• 3D Point– x=(x1,x2,x3,1)
• 3D Line
Derive the line equation shown above.
Geometric Primitives and Geometric Primitives and TransformationsTransformations
Geometric Primitives and Geometric Primitives and TransformationsTransformations
• 3D Plane– ax+by+cz+d=0;
Derive the plane equation shown above.
Transformation MatrixTransformation MatrixTransformation MatrixTransformation Matrix
• Translation (Example in 2D)
Transformation MatrixTransformation MatrixTransformation MatrixTransformation Matrix
• Rotation Matrix (Example in 2D)
Transformation MatrixTransformation MatrixTransformation MatrixTransformation Matrix
• Scaling Matrix (Example in 3D)
Projective Transformation MatrixProjective Transformation MatrixProjective Transformation MatrixProjective Transformation Matrix
Hierarchy of Coordinate Hierarchy of Coordinate TransformationsTransformations
Hierarchy of Coordinate Hierarchy of Coordinate TransformationsTransformations
*Homogeneous Scaling, rotation, and translation
*
3D to 2D Projection3D to 2D Projection3D to 2D Projection3D to 2D Projection
What do we need?What do we need?What do we need?What do we need?
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.
ExampleExampleExampleExample
Geometric InterpretationGeometric InterpretationGeometric InterpretationGeometric Interpretation
Perspective v's Parallel (orthogonal) Projection
Perspective Projection Matrix Perspective Projection Matrix EquationEquation
Perspective Projection Matrix Perspective Projection Matrix EquationEquation
Para-Perspective ProjectionPara-Perspective ProjectionPara-Perspective ProjectionPara-Perspective Projection