Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering...
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Transcript of Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering...
![Page 1: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/1.jpg)
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
![Page 2: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/2.jpg)
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
![Page 3: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/3.jpg)
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.
![Page 4: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/4.jpg)
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.
![Page 5: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/5.jpg)
Transformation MatrixTransformation MatrixTransformation MatrixTransformation Matrix
• Translation (Example in 2D)
![Page 6: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/6.jpg)
Transformation MatrixTransformation MatrixTransformation MatrixTransformation Matrix
• Rotation Matrix (Example in 2D)
![Page 7: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/7.jpg)
Transformation MatrixTransformation MatrixTransformation MatrixTransformation Matrix
• Scaling Matrix (Example in 3D)
![Page 8: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/8.jpg)
Projective Transformation MatrixProjective Transformation MatrixProjective Transformation MatrixProjective Transformation Matrix
![Page 9: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/9.jpg)
Hierarchy of Coordinate Hierarchy of Coordinate TransformationsTransformations
Hierarchy of Coordinate Hierarchy of Coordinate TransformationsTransformations
*Homogeneous Scaling, rotation, and translation
*
![Page 10: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/10.jpg)
3D to 2D Projection3D to 2D Projection3D to 2D Projection3D to 2D Projection
![Page 11: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/11.jpg)
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.
![Page 12: Computer Vision Lecture #2 Hossam Abdelmunim 1 & Aly A. Farag 2 1 Computer & Systems Engineering Department, Ain Shams University, Cairo, Egypt 2 Electerical.](https://reader035.fdocuments.net/reader035/viewer/2022062322/56649ec05503460f94bcb9d3/html5/thumbnails/12.jpg)
ExampleExampleExampleExample
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Geometric InterpretationGeometric InterpretationGeometric InterpretationGeometric Interpretation
Perspective v's Parallel (orthogonal) Projection
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Perspective Projection Matrix Perspective Projection Matrix EquationEquation
Perspective Projection Matrix Perspective Projection Matrix EquationEquation
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Para-Perspective ProjectionPara-Perspective ProjectionPara-Perspective ProjectionPara-Perspective Projection