Image formation (approximately) - UMD Department of Computer ...
Image Formation (approximately) Vision infers world properties form images. So we need to understand how images depend on these properties. Two key elements Geometry Light We consider only simple models of these
Camera Obscura "When images of illuminated objects ... penetrate through a small hole into a very dark room ... you will see [on the opposite wall] these objects in their proper form and color, reduced in size ... in a reversed position, owing to the intersection of the rays". Da Vinci http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html (Russell Naughton)
Used to observe eclipses (eg., Bacon, 1214-1294) By artists (eg., Vermeer). Jetty at Margate England, 1898. http://brightbytes.com/cosite/collection2.html (Jack and Beverly Wilgus)
Cameras First photograph due to Niepce First on record shown in the book 1822 Pinhole cameras Abstract camera model - box with a small hole in it
Pinhole cameras work in practice (Forsyth & Ponce) Distant objects are smaller (Forsyth & Ponce)
Parallel lines meet Common to draw image plane in front of the focal point. Moving the image plane merely scales the image. (Forsyth & Ponce) Vanishing points Each set of parallel lines meets at a different point
The vanishing point for this direction Sets of parallel lines on the same plane lead to collinear vanishing points. The line is called the horizon for that plane Properties of Projection
Points project to points Lines project to lines Planes project to the whole image Angles are not preserved Degenerate cases
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 http://www.sanford-artedventures.com/create/tech_1pt_perspective.html
The equation of projection (Forsyth & Ponce) 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 (x, y, z) ( f , f ) z z
Weak perspective (scaled orthographic projection) Issue perspective effects, but not over the scale of individual objects collect points into a group at about the same depth, then
divide each point by the depth of its group (Forsyth & Ponce) The Equation of Weak Perspective ( x, y , z ) s ( x, y ) s is constant for all points.
Parallel lines no longer converge, they remain parallel. Pros and Cons of These Models Weak perspective much simpler math. Accurate when object is small and distant. Most useful for recognition.
Pinhole perspective much more accurate for scenes. Used in structure from motion. When accuracy really matters, must model real cameras. Cameras with Lenses
(Forsyth & Ponce) 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 CCD Cameras http://huizen.ddsw.nl/bewoners/maan/imaging/camera/ccd1.gif New Camera Design
http://fizbin.eecs.lehigh.edu/~tboult/TRACK/LOTS.html (Terry Boult) Summary Camera loses information about depth. A model of the camera tells us what information is lost. This will be important when we want to recover this information. Examples:
Motion: with multiple images. Recognition: using a model. Shape: how is boundary of smooth object related to its image? Source emits photons Light
And then some reach the eye/camera. Photons travel in a straight line When they hit an object they: bounce off in a new direction
or are absorbed (exceptions later). Basic fact: Light is linear Double intensity of sources, double photons reaching eye. Turn on two lights, and photons reaching eye are same as sum of number when each light is on
separately. Modeling How Surfaces Reflect Light First, language for describing light Striking a surface; Leaving a surface. Next, how do we model the relationship
between the two. This depends on the material; Eg., cloth or mirror. Irradiance, E Light power per unit area (watts per square meter) incident on a surface. If surface tilts away from light, same amount of light strikes bigger surface (less irradiance).
light surface Radiance, L Amount of light radiated from a surface into a given solid angle per unit area (watts per square meter per steradian). Note: the area is the foreshortened area, as seen
from the direction that the light is being emitted. light surface BRDF BRDF Not Always Appropriate
Albedo is fraction of light reflected. Diffuse objects (cloth, matte paint). Brightness doesnt depend on viewpoint. Does depend on angle between light and surface. Surface normal
Light L( e , e ) cos( ) Lambertian Examples Lambertian sphere as the light moves. Scene
(Oren and Nayar) (Steve Seitz) Specular surfaces Another important class of surfaces is specular, or mirror-like. 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/
into a lobe of directions GraphicsNotes/Shading/ Shading.html) Specular surfaces Brightness depends on viewing direction. (http://graphics.cs.ucdavis.edu/ GraphicsNotes/Shading/
Shading.html) Phongs model Vision algorithms rarely depend on the exact shape of the specular lobe. Typically: very, very small --- mirror small -- blurry mirror
bigger -- see only light sources as specularities very big -- faint specularities Phongs model reflected energy falls off with (Forsyth & Ponce) n cos
Lambertian + specular Two parameters: how shiny, what kind of shiny. Advantages easy to manipulate very often quite close true Disadvantages some surfaces are not e.g. underside of CDs, feathers of many birds,
blue spots on many marine crustaceans and fish, most rough surfaces, oil films (skin!), wet surfaces Generally, very little advantage in modelling behaviour of light at a surface in more detail -- it is quite difficult to understand behaviour of L+S surfaces (but in graphics???) Lambertian+Specular+Ambient Ambient to be explained.
(http://graphics.cs.ucdavis.edu/GraphicsNotes/Shading/Shading.html) Modeling Light Sources Light strikes a surface from every direction in front of the object. Light in a scene can be complex: Can vary with direction.
(from Debevec) Also with position (from Langer and Zucker) And Along a Straight Line
(from Narasimhan and Nayar) Useful to use simplified models. Simplest model: distant point source All light in scene comes from same direction. With same intensity Consequences:
Shadows are black. Light represented as direction & intensity Lambertian + Point Source l is direction of light l l l
l is intensity of light i max(0, (l n ) i is radiance is albedo n is surface normal l Surface
normal Light Ambient Component Assume each surface normal receives equal light from all directions. i a
Diffuse lighting, no cast shadows. Ambient + point source turns out to be good approximation to next model. Distant Light Sky Light is function of direction. Same at every scene point.
Point, elongated, diffuse. Conclusions Projection loses info; we can understand this with geometry. Light reaching camera depends on surfaces and lighting; we can understand this with physics. Reflection also loses information. Our models are always simplified.
Just because you can see doesnt 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
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