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Image Formation Lecture 2 Motion in Robotics Evolution of the Eye - - PowerPoint PPT Presentation
Image Formation Lecture 2 Motion in Robotics Evolution of the Eye - - PowerPoint PPT Presentation
Image Formation Lecture 2 Motion in Robotics Evolution of the Eye Pin Hole Model + More than 50% of the human cortex involved in vision! What will we learn - Fundamentals of Image Formation Evolution of Biological Eye Projective
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Evolution of the Eye
Pin Hole Model
+ More than 50% of the human cortex “involved” in vision!
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What will we learn - Fundamentals of Image Formation
- Evolution of Biological Eye
- Projective Geometry
○ Pinhole Camera Model ○ Plumb-Bob Distortion Model
- Camera Calibration
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How do we see the world?
slides credit to Prof. Savarese
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Pinhole Camera
slides credit to Prof. Savarese
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First one to do it (that we know about…)
Leonardo da Vinci (1452-1519)
slides credit to Prof. Savarese
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Pinhole Camera Model
slides credit to Prof. Savarese
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Pinhole Camera Model
slides credit to Prof. Savarese
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Pinhole Camera Model
slides credit to Prof. Savarese
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Digital Image
j’ k’ u v
slides credit to Prof. Savarese
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Offset to Image Center
j’ k’ u v xc yc Projective Transformation
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Homogeneous Coordinates
slides credit to Prof. Savarese
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Projective Transformation with Homogeneous Coordinates K
slides credit to Prof. Savarese
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Exercise on Projective Geometry
Given the intrinsic camera matrix project the point
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Size of the Aperture
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Camera Lenses
slides credit to Prof. Savarese
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Problem: Radial Distortion
slides credit to Prof. Savarese
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Problem: Tangential Distortion
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Modeling Distortion: Plumb Bob Model
Radial distance Distortion parameters
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Intrinsic and Extrinsic Camera Parameters
Intrinsic Camera Parameters: Extrinsic Camera Parameters:
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Exercise on Projective Geometry
Given the intrinsic camera matrix and the 3D point
- n an object positioned at
- Wrt. the camera, estimate the projection of the point into the camera.
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Estimating Camera Parameters: Camera Calibration
- Move known pattern (size) in front of the
camera and collect images
- Detect point-corners on the pattern
○ Set of images -> set of corresponding points
- Estimate:
○ Camera-to-pattern poses ○ Camera parameters that minimize the reprojection error
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Calibration Procedure
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Calibration Procedure
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Calibration Procedure
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Calibration Procedure
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