Basic Principles of Imaging and Photometry Lecture #2
Basic Principles of Imaging and Photometry Lecture #2 Thanks to Shree Nayar, Ravi Ramamoorthi, Pat Hanrahan Computer Vision: Building Machines that See Lighting Camera Physical Models Computer Scene Scene Interpretation We need to understand the Geometric and Radiometric relations between the scene and its image. A Brief History of Images 1558 Camera Obscura, Gemma Frisius, 1558 A Brief History of Images 1558 1568 Lens Based Camera Obscura, 1568 A Brief History of Images 1558 1568 1837 Still Life, Louis Jaques Mande Daguerre, 1837 A Brief History of Images 1558 1568 1837 Silicon Image Detector, 1970 1970 A Brief History of Images 1558 1568 1837 Digital Cameras 1970 1995 Geometric Optics and Image Formation TOPICS TO BE COVERED : 1) Pinhole and Perspective Projection 2) Image Formation using Lenses 3) Lens related issues Pinhole and the Perspective Projection Is an image being formed (x,y) on the screen? YES! But, not a “clear” one. screen scene image plane r =(x, y, z) y optical effective focal length, f’ z axis pinhole x r'=(x', y', f ') r' r x' x y' y = = = f ' z f ' z f ' z Magnification A(x, y, z) B y d B(x +δx, y +δy, z) optical f’ z A axis Pinhole A’ d’ x planar scene image plane B’ A'(x', y', f ') B'(x'+δx', y'+δy', f ') From perspective projection: Magnification: x' x y' y d' (δx')2 + (δy')2 f ' = = m = = = f ' z f ' z d (δx)2 + (δy)2 z x'+δx' x +δx y'+δy' y +δy = = Area f ' z f ' z image = m2 Areascene Orthographic Projection Magnification: x' = m x y' = m y When m = 1, we have orthographic projection r =(x, y, z) r'=(x', y', f ') y optical z axis x z ∆ image plane z This is possible only when z >> ∆z In other words, the range of scene depths is assumed to be much smaller than the average scene depth.
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