lec5 Image Formation and cameras

lec5 Image Formation and cameras - Image Formation Outline...

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1 CSE190A, Fall 06 Biometrics Image Formation and Cameras Biometrics CSE 190A Lecture 5 CSE190A, Fall 06 Biometrics Image Formation: Outline • Factors in producing images • Projection • Perspective • Vanishing points • Orthographic •L e n s e s •S e n s o r s • Quantization/Resolution • Illumination • Reflectance CSE190A, Fall 06 Biometrics Earliest Surviving Photograph • First photograph on record, “la table service” by Nicephore Niepce in 1822. • Note: First photograph by Niepce was in 1816. CSE190A, Fall 06 Biometrics Images are two-dimensional patterns of brightness values. They are formed by the projection of 3D objects. Figure from US Navy Manual of Basic Optics and Optical Instruments, prepared by Bureau of Naval Personnel. Reprinted by Dover Publications, Inc., 1969. CSE190A, Fall 06 Biometrics Effect of Lighting: Monet CSE190A, Fall 06 Biometrics Change of Viewpoint: Monet Haystack at Chailly at Sunrise (1865)
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2 CSE190A, Fall 06 Biometrics Pinhole Camera: Perspective projection • Abstract camera model - box with a small hole in it Forsyth&Ponce CSE190A, Fall 06 Biometrics Geometric properties of projection • Points go to points • Lines go to lines • Planes go to whole image or half-plane • Polygons go to polygons • Angles & distances not preserved • Degenerate cases: – line through focal point yields point – plane through focal point yields line CSE190A, Fall 06 Biometrics Parallel lines meet in the image • vanishing point Image plane CSE190A, Fall 06 Biometrics The equation of projection Cartesian coordinates: • We have, by similar triangles, that (x, y, z) -> (f x/z, f y/z, -f) • Ignore the third coordinate, and get ( x , y , z ) ( f x z , f y z ) CSE190A, Fall 06 Biometrics A Digression Homogenous Coordinates and Camera Matrices CSE190A, Fall 06 Biometrics Homogenous coordinates • Our usual coordinate system is called a Euclidean or affine coordinate system • Rotations, translations and projection in Homogenous coordinates can be expressed linearly as matrix multiplies Euclidean World 3D Homogenous World 3D Homogenous Image 2D Euclidean World 2D Convert Projection
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3 CSE190A, Fall 06 Biometrics Homogenous coordinates A way to represent points in a projective space 1. Add an extra coordinate e.g., (x,y) -> (x,y,1)=(u,v,w) 2. Impose equivalence relation such that ( λ not 0) (u,v,w) ≈ λ *(u,v,w) i.e., (x,y,1) ( λ x, λ y, λ ) 3. “Point at infinity” – zero for last coordinate e.g., (x,y,0) • Why do this? – Possible to represent points “at infinity” • Where parallel lines intersect • Where parallel planes intersect – Possible to write the action of a perspective camera as a matrix CSE190A, Fall 06 Biometrics Euclidean -> Homogenous-> Euclidean In 2-D • Euclidean -> Homogenous: (x, y) -> k (x,y,1) • Homogenous -> Euclidean: (u,v,w) -> (u/w, v/w) In 3-D • Euclidean -> Homogenous: (x, y, z) -> k (x,y,z,1) • Homogenous -> Euclidean: (x, y, z, w) -> (x/w, y/w, z/w) CSE190A, Fall 06 Biometrics The camera matrix Turn this expression into homogenous coordinates – HC’s for 3D point are (X,Y,Z,T) – HC’s for point in image are (U,V,W) U V W
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This note was uploaded on 02/14/2008 for the course CSE 190A taught by Professor Kriegman during the Fall '06 term at UCSD.

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lec5 Image Formation and cameras - Image Formation Outline...

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