Image formationMarc LevoyComputer Science DepartmentStanford UniversityCS 178, Spring 2011Begun 3/29/11. Finished 3/31/11.! Marc LevoyOutline!perspective•natural versus linear perspective•vanishing points!image formation•pinhole cameras•lenses!exposure•shutter speed•aperture•ISO!choosing a camera2! Marc LevoyThe 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 LevoyThe laws of perspective!natural perspective (Euclid, 3rd c. B.C.) 3a. More distant objects subtend smaller visual angles.4!1!2!2 > !1! Marc LevoyRoman wall paintings5from Villa Publius Fannius Synistor,Boscoreale, Pompeii (c. 40 B.C.)Still life with peaches, fromHerculaneum (before 79 A.D.)! Marc LevoyThe 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 LevoyThe laws of perspective!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!1!2!2 > !1y2 > y1y2y1pictureplane! Marc LevoyProjection onto picture plane(contents of whiteboard)8Filippo Brunelleschi,dome of the cathedral,Florence (1419)! Marc LevoyThe problem of drawing pavimento10Giovanni de Paolo, Birth of St. John the Baptist (1420)! Marc LevoyAlberti’s method (1435)11(Cole)Piero della Francesca, The Flagellation (c.1460)(Cole)! Marc LevoyVanishing points131-point(D’Amelio)2-point3-pointQ. How many vanishing points canthere be in a perspective drawing?! Marc Levoy!each direction of parallel lines will convergeto a unique vanishing pointExample of a 4th vanishing point14v.p. #3v.p. #1v.p. #2v.p. #4! Marc LevoyQ. 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!they appear smaller when you view the drawing,due to natural perspective (angles subtended at eye)15?! Marc LevoyRecap!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 converge16Questions?! Marc LevoySingle lens reflex camera (SLR)17Nikon F4(film camera)! Marc LevoyWhy not use sensors without optics?!each point on sensor would record the integral of light arriving from every point on subject!all sensor points would record similar colors(London)18! Marc LevoyPinhole camera(a.k.a. camera obscura)!linear perspective with viewpoint at pinhole!tilting the picture plane changes thenumber and location of vanishing points 19! Marc LevoyEquivalence of Dürer’s glass and camera obscura(contents of whiteboard)!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)20Dürer’s glasscamera obscura! Marc LevoyPinhole photography!no distortion•straight lines remain straight!infinite depth of field•everything is in focus(Bami Adedoyin)21! Marc LevoyEffect of pinhole size 22(London)! Marc LevoyEffect of pinhole size 23(London)! Marc LevoyReplacing the pinhole with a lens24(London)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.! Marc Levoy!parallel rays converge to a pointlocated at focal length f from lens!rays going through center of lens are not deviated•hence same perspective as pinholeGeometrical opticsf25! Marc LevoyGauss’ ray tracing construction!rays coming from points on a plane parallel to the lens are focused on another plane parallel to the lensobjectimage26! Marc Levoy!to focus on objectsat different distances,move sensor relative to lensChanging the focus distance27sensorffby convention, the “focus distance” is on the object side of the lensfocusdistanceGauss’s ray tracing construction isn’t sufficient to understand why focus distance (i.e. distance between the lens and scene) should decrease as the distance between 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.! Marc Levoy!weaker lenseshave longerfocal lengths!to stay in focus,move the sensorfurther back!focused imageof tree is locatedslightly beyondthe focal lengthChanging the focal length28(Kingslake)the tree would be in focus at the lens focal length only if it were infinitely far away! Marc Levoy!if the sensorsize is constant,the field of viewbecomes smallerChanging the focal length29FOV = 2 arctan (h / 2 f )FOVhf(Kingslake)! Marc LevoyFocal length and field of view30(London)FOV measured diagonally on a 35mm full-frame camera (24 ! 36mm)I rescanned this image from the 10th edition. The