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Image Formation

Image Formation. Light can change the image and appearances (images from D. Jacobs) What is the relation between pixel brightness and scene radiance? What is the relation between pixel brightness and scene reflectance ?. Camera Obscura.

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Image Formation

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  1. Image Formation Light can change the image and appearances (images from D. Jacobs) What is the relation between pixel brightness and scene radiance? What is the relation between pixel brightness and scene reflectance ? Computer Vision

  2. 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) Computer Vision

  3. Used to observe eclipses (eg., Bacon, 1214-1294) • By artists (eg., Vermeer). Computer Vision

  4. Cameras Jetty at Margate England, 1898. http://brightbytes.com/cosite/collection2.html (Jack and Beverly Wilgus) • First photograph due to Niepce • First on record shown in the book - 1822 Computer Vision

  5. Pinhole cameras • Abstract camera model - box with a small hole in it • Pinhole cameras work in practice Computer Vision

  6. Light And then some reach the eye/camera. Source emits photons Photons travel in a straight line • When they hit an object they: • bounce off in a new direction • or are absorbed • (exceptions later). Computer Vision

  7. 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). Irradiance, E light surface Computer Vision

  8. 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. Radiance, L light surface Computer Vision

  9. solid angle subtended by a small patch of area A. L - radiance is the amount of light radiated from a surface per solid angle (power per unit area per unit solid angle emitted from a surface.) E - irradiance is the amount of light falling in a surface (power per unit area incident in a surface.) Image Formation R dA Computer Vision

  10. Same solid angle Surface Radiance and Image Irradiance dA Pinhole Camera Model f z dI Computer Vision

  11. Solid angle subtended by the lens, as seen by the patch dA Power from patch dA through the lens Thus, we conclude Surface Radiance and Image Irradiance dA d f z dI Computer Vision

  12. The irradiance at the image pixel is converted into the brightness of the pixel • Image Irradiance is proportional to Scene Radiance • Scene distance, z, does not affect/reduce image brightness (the model is too simplified, since in practice it does.) • The angle of the scene patch with respect to the view (a) reduces the brightness by the . In practice the effect is even stronger. Summary Computer Vision

  13. The Bidirectional Reflectance Distribution Function (BRDF) BRDF - How bright a surface appears when viewed from one direction while light falls on it from another. Usually f depends only on , : true for matte surfaces and specularly reflecting surfaces. Computer Vision

  14. dA Extended Light Sources and BRDF Light source radiance arriving through solid angle dW Power arriving at patch dA from dW Foreshortening thus the irradiance arriving at patch dA is The radiance of a patch dA at direction is thus, given by Computer Vision

  15. Special Cases of BRDF • Lambertian Surfaces(matte)- appears equally bright from all viewing • directions and reflects all incident light, absorbing none, i.e. the • BRDF is constant and . What constant f ? Thus, the total “reflected power” from patch dA becomes Foreshortening since Using that and for Lambertian surfaces we finally obtain Computer Vision

  16. Special Cases of BRDF • Specular Surfaces (mirrors) – reflects all light arriving from the • direction into the direction . The BRDF is in this case • proportional to the product of two impulses, and • .What is the factor of proportionality ? and for specular surfaces we finally obtain Computer Vision

  17. Lambertian Surface Brightness How bright will a Lambertian surface be when it is illuminated by a point source of radiance E? and by a “sky” of uniform radiance E? For a point source the irradiance at the surface is and the radiance must then be Familiar cosine or “Lambert’s law” of reflection from matte surfaces (surfaces covered with finely powdered transparent materials such as barium sulfate or magnesium carbonate), and can approximate paper, snow and matte paint. Finally, for a “sky” of uniform radiance E we obtain Computer Vision

  18. Special Cases: Lambertian Examples Lambertian sphere as the light moves. (Steve Seitz) Scene (Oren and Nayar) Computer Vision

  19. Lambertian+Specular (http://graphics.cs.ucdavis.edu/GraphicsNotes/Shading/Shading.html) Computer Vision

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