Camera Obscura Image Formation (approximately) Vision infers world - PDF document

Camera Obscura Image Formation (approximately) • Vision infers world properties form images. • So we need to understand how images depend on these properties. • Two key elements "When images of illuminated objects ... penetrate through a – Geometry small hole into a very dark room ... you will see [on the opposi te – Light wall] these objects in their proper form and color, reduced in s ize – We consider only simple models of these ... in a reversed position, owing to the intersection of the ray s". Da Vinci http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html (Russell Naughton ) Jetty at Margate England, • Used to observe eclipses ( eg ., Bacon, 1214 - 1294) 1898. • By artists ( eg ., Vermeer). http://brightbytes.com/cosite/collection2.html (Jack and Beverly Wilgus ) Cameras Cameras Pinhole cameras • First photograph due to Niepce • Abstract camera • Pinhole cameras model - box with a work in practice • First on record shown in the book - small hole in it 1822 (Forsyth & Ponce) 1

Parallel lines meet Distant objects are smaller Common to draw image plane in front of the focal point. Moving the image plane merely scales the image. (Forsyth & Ponce) (Forsyth & Ponce) Vanishing points Properties of Projection • Points project to points • Each set of parallel lines meets at a different point • Lines project to lines – The vanishing point for this direction • Planes project to the whole image • Sets of parallel lines on the same plane lead to • Angles are not preserved collinear vanishing points. • Degenerate cases – The line is called the horizon for that plane – Line through focal point projects to a point. – Plane through focal point projects to line – Plane perpendicular to image plane projects to part of the image (with horizon). Take out paper and pencil 2

The equation of projection http://www. sanford - artedventures .com/create/tech_1pt_perspective.html (Forsyth & Ponce) Weak perspective (scaled The equation of projection orthographic projection) • Cartesian • Issue coordinates: – perspective effects, but not over the – We have, by similar ( x , y , z ) → ( f x z , f y scale of individual z ) triangles, that objects (x, y, z) - > (f x/z, f y/z, - f) – collect points into a group at about the – Ignore the third same depth, then coordinate, and get divide each point by the depth of its group (Forsyth & Ponce) The Equation of Weak Pros and Cons of These Perspective Models • Weak perspective much simpler math. → – Accurate when object is small and distant. ( x , y , z ) s ( x , y ) – Most useful for recognition. • Pinhole perspective much more • s is constant for all points. accurate for scenes. • Parallel lines no longer converge, they remain – Used in structure from motion. parallel. • When accuracy really matters, must model real cameras. 3

Cameras with Lenses Human Eye • Lens. • Fovea, and surround. (see The Island of the Colorblind by Oliver Sacks) http://www. cas . vanderbilt . edu /bsci111b/eye/human - eye. jpg (Forsyth & Ponce) CCD Cameras New Camera Design http://fizbin.eecs.lehigh.edu/~tboult/TRACK/LOTS.html (Terry Boult ) http:// huizen . ddsw . nl / bewoners / maan /imaging/camera/ccd1.gif Summary Light Source emits photons And then some reach the eye/camera. • Camera loses information about depth. – A model of the camera tells us what Photons travel in a straight line information is lost. • This will be important when we want to recover this information. Examples: – Motion: with multiple images. When they hit an object they: – Recognition: using a model. • bounce off in a new direction – Shape: how is boundary of smooth object • or are absorbed related to its image? • (exceptions later). 4

Modeling How Surfaces Basic fact: Light is linear Reflect Light • Double intensity of sources, double • First, language for describing light photons reaching eye. – Striking a surface; • Turn on two lights, and photons – Leaving a surface. reaching eye are same as sum of • Next, how do we model the relationship number when each light is on between the two. separately. – This depends on the material; – Eg ., cloth or mirror. Irradiance, E Radiance, L • Light power per unit area (watts per • Amount of light radiated from a surface square meter) incident on a surface. into a given solid angle per unit area (watts per square meter per steradian ). • If surface tilts away from light, same • Note: the area is the foreshortened area, as seen amount of light strikes bigger surface from the direction that the light is being emitted. (less irradiance). light light surface surface BRDF BRDF Not Always Appropriate BRDF BSSRDF (don’t ask) http://graphics.stanford.edu/papers/bssrdf/ (Jensen, Marschner , Levoy , Hanrahan ) 5

Special Cases: Lambertian Lambertian Examples 1 θ φ θ φ = f ( , , , ) k π i i e e • Albedo is fraction of light reflected. • Diffuse objects (cloth, matte paint). • Brightness doesn’t depend on viewpoint. Lambertian sphere as the light moves. • Does depend on angle between light and surface. (Steve Seitz) Scene θ φ ∝ θ Surface Light L ( , ) cos( ) normal e e (Oren and Nayar ) Specular surfaces Specular surfaces • Another important class of surfaces is • Brightness depends specular , or mirror - like. on viewing direction. – radiation arriving along a direction leaves along the specular direction – reflect about normal – some fraction is absorbed, some reflected – on real surfaces, energy usually goes (http://graphics.cs . ucdavis . edu / Graphi (http://graphics.cs . ucdavis . edu / Graphi into a lobe of directions csNotes /Shading/Shading.html) csNotes /Shading/Shading.html) Lambertian + specular Phong’s model • Two parameters: how shiny, what kind of shiny. • Advantages • Vision algorithms rarely depend on the exact shape of the – easy to manipulate specular lobe. – very often quite close true • Typically: • Disadvantages – very, very small --- mirror – some surfaces are not – small -- blurry mirror • e.g. underside of CD’s, feathers of many birds, – bigger -- see only light blue spots on many marine crustaceans and fish, sources as “ specularities ” most rough surfaces, oil films (skin!), wet surfaces – very big -- faint specularities (Forsyth & Ponce) – Generally, very little advantage in modelling • Phong’s model behaviour of light at a surface in more detail -- it is n δϑ ( ) quite difficult to understand behaviour of L+S – reflected energy falls off with cos surfaces (but in graphics???) 6

Lambertian+Specular+Ambient Modeling Light Sources • Ambient to be explained. • Light strikes a surface from every direction in front of the object. • Light in a scene can be complex: (http://graphics.cs . ucdavis . edu / GraphicsNotes /Shading/Shading.html) Can vary with direction. Also with position (from Langer and Zucker ) (from Debevec ) Simplest model: distant point And Along a Straight Line source • All light in scene comes from same direction. • With same intensity • Consequences: • Shadows are black. • Light represented as direction & intensity (from Narasimhan and Nayar ) Useful to use simplified models. 7

Lambertian + Point Source Ambient Component  l is direction of light • Assume each surface normal receives = •  l l l equal light from all directions.  l is intensity of light i = λ = λ • i max( 0 , ( l n ˆ ) a i is radiance ˆ l λ is albedo • Diffuse lighting, no cast shadows. Surface ˆ Light n is surface normal • Ambient + point source turns out to be normal good approximation to next model. Distant Light Conclusions • Projection loses info; we can understand this Sky with geometry. • Light reaching camera depends on surfaces and lighting; we can understand this with physics. • Light is function of direction. • Reflection also loses information. • Same at every scene point. • Our models are always simplified. • Point, elongated, diffuse. • Just because you can see doesn’t mean the relation between the world and images is intuitive. “(The world) saw shadows black until Monet discovered they were coloured ,…” Maugham, Of Human Bondage 8

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