Image formation CS 178 Spring 2011 Begun 3 29 11 Finished 3 31 11 Marc Levoy Computer Science Department Stanford University Outline perspective natural versus linear perspective vanishing points image formation pinhole cameras lenses exposure shutter speed aperture ISO 2 choosing a camera Marc Levoy The laws of perspective common assumptions 1 Light leaving an object travels in straight lines 2 These lines converge to a point at the eye natural perspective Euclid 3rd c B C 3a More distant objects subtend smaller visual angles 3 Marc Levoy The laws of perspective 2 2 1 1 natural perspective Euclid 3rd c B C 3a More distant objects subtend smaller visual angles 4 Marc Levoy Roman wall paintings from Villa Publius Fannius Synistor Boscoreale Pompeii c 40 B C 5 Still life with peaches from Herculaneum before 79 A D Marc Levoy The laws of perspective common assumptions 1 Light leaving an object travels in straight lines 2 These lines converge to a point at the eye natural perspective Euclid 3rd c B C 3a More distant objects subtend smaller visual angles linear perspective Filippo Brunelleschi 1413 3b A perspective image is formed by the intersection of these lines with a picture plane the canvas 6 Marc Levoy The laws of perspective 2 y2 y1 2 1 y2 y1 1 picture plane natural perspective Euclid 3rd c B C 3a More distant objects subtend smaller visual angles linear perspective Filippo Brunelleschi 1413 3b A perspective image is formed by the intersection of these lines with a picture plane the canvas 7 Marc Levoy Projection onto picture plane contents of whiteboard 8 Marc Levoy Filippo Brunelleschi dome of the cathedral Florence 1419 The problem of drawing pavimento Giovanni de Paolo Birth of St John the Baptist 1420 10 Marc Levoy Alberti s method 1435 Cole 11 Marc Levoy Cole Piero della Francesca The Flagellation c 1460 Vanishing points an c s t n i o p ing h s i n a v y g n man i w w a o r d H e Q ctiv e p s r e p a there be in 1 point 3 point 13 2 point D Amelio Marc Levoy Example of a 4th vanishing point v p 4 v p 2 v p 1 v p 3 14 each direction of parallel lines will converge to a unique vanishing point Marc Levoy Q Should the distant ends of a long facade be drawn smaller than its center in a perspective drawing no in linear perspective straight lines remain straight lines parallel to the picture plane do not converge 15 they appear smaller when you view the drawing due to natural perspective angles subtended at eye Marc Levoy Recap natural perspective visual angle subtended by a feature in the world linear perspective intersections of lines of sight with a picture plane the correct way to make a drawing on a flat surface vanishing points one per direction of line in the scene lines parallel to the picture plane do not converge Que s t ions 16 Marc Levoy Single lens reflex camera SLR 17 Nikon F4 film camera Marc Levoy Why not use sensors without optics London 18 each point on sensor would record the integral of light arriving from every point on subject all sensor points would record similar colors Marc Levoy Pinhole camera a k a camera obscura 19 linear perspective with viewpoint at pinhole tilting the picture plane changes the number and location of vanishing points Marc Levoy Equivalence of D rer s glass and camera obscura contents of whiteboard camera obscura D rer s glass 20 both devices compute 2D planar geometric projections i e projections along straight lines through a point and onto a plane the images differ only in scale and a reflection around the origin Marc Levoy Pinhole photography no distortion straight lines remain straight infinite depth of field everything is in focus Bami Adedoyin 21 Marc Levoy Effect of pinhole size London 22 Marc Levoy Effect of pinhole size London 23 Marc Levoy Replacing the pinhole with a lens As I mentioned in class but may not have made sufficiently clear a photographic camera produces the same linear perspective projection as a camera obscura In the photographic case a lens replaces the pinhole of the camera obscura and film or a digital sensor replaces the wall that receives the image in the camera obscura The advantage of a lens over a pinhole is that it lets in more light yet still makes a sharp image The precise location of the equivalent pinhole inside a photographic lens is a topic we will consider next week when we look at lens geometry One of the implications of this equivalence is that rotating a camera which tilts its sensor relative to the world has the same effect as tilting the wall in a cameara obscura or the glass plane in Durer s perspective glass it adds or removes vanishing points from the resulting perspective image London 24 Marc Levoy Geometrical optics parallel rays converge to a point located at focal length f from lens f rays going through center of lens are not deviated 25 hence same perspective as pinhole Marc Levoy Gauss ray tracing construction image object 26 rays coming from points on a plane parallel to the lens are focused on another plane parallel to the lens Marc Levoy Changing the focus distance f to focus on objects at different distances move sensor relative to lens f sensor Gauss s ray tracing construction isn t sufficient to understand why focus distance i e distance bet ween the lens and scene should decrease as the distance bet ween the lens and sensor increases We ll investigate this relationship next week and derive some formulas about it Also although I ve drawn the sensor as moving in this example in practice one moves the lens by focusing it The sensor is fixed inside the camera body and doesn t move by convention the focus distance is on the object side of the lens 27 focus distance Marc Levoy Changing the focal length 28 weaker lenses have longer focal lengths to stay in focus move the sensor further back focused image of tree is located slightly beyond the focal length Kingslake the tree would be in focus at the lens focal length only if it were infinitely far away Marc Levoy Changing the focal length if the sensor size is constant the field of view becomes smaller h FOV f Kingslake FOV 2 arctan h 2 f 29 Marc Levoy Focal length and field of view I rescanned this image from the 10th edition The drawn arc for 104 is now correct London 30 FOV measured diagonally on a 35mm full frame camera 24 36mm Marc Levoy Focal length and field of view London 31 FOV measured diagonally on a 35mm full frame camera 24 36mm Marc Levoy Changing the sensor size if the sensor size is smaller the field of view