1. © 2004 by Davi GeigerComputer Vision February 2004 L1.1 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 ?

2. © 2004 by Davi GeigerComputer Vision February 2004 L1.2 http://www.acmi.net.au/AIC/CAMERA_OBSCURA.htmlhttp://www.acmi.net.au/AIC/CAMERA_OBSCURA.html (Russell Naughton) 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

3. © 2004 by Davi GeigerComputer Vision February 2004 L1.3 Used to observe eclipses (eg., Bacon, 1214-1294) By artists (eg., Vermeer).

4. © 2004 by Davi GeigerComputer Vision February 2004 L1.4 http://brightbytes.com/cosite/collection2.htm lhttp://brightbytes.com/cosite/collection2.htm l (Jack and Beverly Wilgus) Jetty at Margate England, 1898. Cameras First photograph due to Niepce First on record shown in the book - 1822

5. © 2004 by Davi GeigerComputer Vision February 2004 L1.5 Pinhole cameras Abstract camera model - box with a small hole in it Pinhole cameras work in practice

6. © 2004 by Davi GeigerComputer Vision February 2004 L1.6 Light 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). And then some reach the eye/camera.

7. © 2004 by Davi GeigerComputer Vision February 2004 L1.7 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

8. © 2004 by Davi GeigerComputer Vision February 2004 L1.8 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

9. © 2004 by Davi GeigerComputer Vision February 2004 L1.9 Image Formation R solid angle subtended by a small patch of area A. A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. )

10. © 2004 by Davi GeigerComputer Vision February 2004 L1.10 AA II z f Surface Radiance and Image Irradiance Same solid angle Pinhole Camera Model

11. © 2004 by Davi GeigerComputer Vision February 2004 L1.11 AA II z f d Surface Radiance and Image Irradiance Solid angle subtended by the lens, as seen by the patch  A Power from patch  A through the lens Thus, we conclude

12. © 2004 by Davi GeigerComputer Vision February 2004 L1.12 Summary 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 (  reduces the brightness by the. In practice the effect is even stronger.

13. © 2004 by Davi GeigerComputer Vision February 2004 L1.13 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.

14. © 2004 by Davi GeigerComputer Vision February 2004 L1.14 Extended Light Sources and BRDF Light source radiance arriving through solid angle  Power arriving at patch  A from  AA Foreshortening AA

15. © 2004 by Davi GeigerComputer Vision February 2004 L1.15 Extended Light Sources and BRDF thus the power arriving at patch  A is The radiance of a patch  A at direction is thus, given by AA

16. © 2004 by Davi GeigerComputer Vision February 2004 L1.16 Special Cases of BRDF 1.Lambertian Surfaces (matte)- appears equally bright from all viewing directions and reflects all incident light, absorbing none, i.e. the BRDF is constant and power arriving is the same as power leaving the surface or What is the constant f ? Thus, the total “reflected power” from patch  A becomes we finally obtain since Foreshortening Thus,

17. © 2004 by Davi GeigerComputer Vision February 2004 L1.17 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

18. © 2004 by Davi GeigerComputer Vision February 2004 L1.18 Special Cases: Lambertian Examples Scene (Oren and Nayar) Lambertian sphere as the light moves. (Steve Seitz)

19. © 2004 by Davi GeigerComputer Vision February 2004 L1.19 Special Cases of BRDF 1.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 ? we finally obtain and for specular surfaces

20. © 2004 by Davi GeigerComputer Vision February 2004 L1.20 Lambertian+Specular (http://graphics.cs.ucdavis.edu/GraphicsNotes/Shading/Shading.html)