1 / 40

Computer Vision

Computer Vision. Spring 2006 15-385,-685 Instructor: S. Narasimhan Wean 5403 T-R 3:00pm – 4:20pm Lecture #12. Midterm – March 9. Syllabus – until and including Lightness and Retinex Closed book, closed notes exam in class. Time: 3:00pm – 4:20pm Midterm review class next Tuesday (March 7)

zeno
Download Presentation

Computer Vision

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Computer Vision Spring 2006 15-385,-685 Instructor: S. Narasimhan Wean 5403 T-R 3:00pm – 4:20pm Lecture #12

  2. Midterm – March 9 Syllabus – until and including Lightness and Retinex Closed book, closed notes exam in class. Time: 3:00pm – 4:20pm Midterm review class next Tuesday (March 7) (Email me by March 6 specific questions) If you have read the notes and readings, attended all classes, done assignments well, it should be a walk in the park

  3. Mechanisms of Reflection source incident direction surface reflection body reflection surface • Surface Reflection: • Specular Reflection • Glossy Appearance • Highlights • Dominant for Metals • Body Reflection: • Diffuse Reflection • Matte Appearance • Non-Homogeneous Medium • Clay, paper, etc Image Intensity = Body Reflection + Surface Reflection

  4. Example Surfaces Surface Reflection: Specular Reflection Glossy Appearance Highlights Dominant for Metals Body Reflection: Diffuse Reflection Matte Appearance Non-Homogeneous Medium Clay, paper, etc Many materials exhibit both Reflections:

  5. Diffuse Reflection and Lambertian BRDF source intensity I incident direction normal viewing direction surface element • Surface appears equally bright from ALL directions! (independent of ) albedo • Lambertian BRDF is simply a constant : • Surface Radiance : source intensity • Commonly used in Vision and Graphics!

  6. Diffuse Reflection and Lambertian BRDF

  7. White-out: Snow and Overcast Skies CAN’T perceive the shape of the snow covered terrain! CAN perceive shape in regions lit by the street lamp!! WHY?

  8. Diffuse Reflection from Uniform Sky • Assume Lambertian Surface with Albedo = 1 (no absorption) • Assume Sky radiance is constant • Substituting in above Equation: Radiance of any patch is the same as Sky radiance !! (white-out condition)

  9. Specular Reflection and Mirror BRDF source intensity I specular/mirror direction incident direction normal viewing direction surface element • Valid for very smooth surfaces. • All incident light energy reflected in a SINGLE direction (only when = ). • Mirror BRDF is simply a double-delta function : specular albedo • Surface Radiance :

  10. Combing Specular and Diffuse: Dichromatic Reflection Observed Image Color = a x Body Color + b x Specular Reflection Color Klinker-Shafer-Kanade 1988 R Color of Source (Specular reflection) Does not specify any specific model for Diffuse/specular reflection G Color of Surface (Diffuse/Body Reflection) B

  11. Diffuse and Specular Reflection diffuse specular diffuse+specular

  12. Photometric Stereo Lecture #12

  13. Image Intensity and 3D Geometry • Shading as a cue for shape reconstruction • What is the relation between intensity and shape? • Reflectance Map

  14. Equation of plane or Let Surface normal Surface Normal surface normal

  15. Normal vector Source vector plane is called the Gradient Space (pq plane) • Every point on it corresponds to a particular surface orientation Gradient Space

  16. : source brightness : surface albedo (reflectance) : constant (optical system) Image irradiance: Let then Reflectance Map • Relates image irradiance I(x,y) to surface orientation (p,q) for given source direction and surface reflectance • Lambertian case:

  17. Reflectance Map (Lambertian) Iso-brightness contour cone of constant Reflectance Map • Lambertian case

  18. Reflectance Map iso-brightness contour • Lambertian case Note: is maximum when

  19. Diffuse peak Specular peak Reflectance Map • Glossy surfaces (Torrance-Sparrow reflectance model) diffuse term specular term

  20. Shape from a Single Image? • Given a single image of an object with known surface reflectance taken under a known light source, can we recover the shape of the object? • Given R(p,q) ( (pS,qS) and surface reflectance) can we determine (p,q) uniquely for each image point? NO

  21. Solution • Take more images • Photometric stereo • Add more constraints • Shape-from-shading (next class)

  22. Photometric Stereo

  23. Photometric Stereo Lambertian case: Image irradiance: • We can write this in matrix form:

  24. inverse Solving the Equations

  25. Least squares solution: Moore-Penrose pseudo inverse • Solve for as before More than Three Light Sources • Get better results by using more lights

  26. Color Images • The case of RGB images • get three sets of equations, one per color channel: • Simple solution: first solve for using one channel • Then substitute known into above equations to get • Or combine three channels and solve for

  27. Computing light source directions • Trick: place a chrome sphere in the scene • the location of the highlight tells you the source direction

  28. Specular Reflection - Recap • For a perfect mirror, light is reflected about N • We see a highlight when • Then is given as follows:

  29. Computing the Light Source Direction Chrome sphere that has a highlight at position h in the image • Can compute N by studying this figure • Hints: • use this equation: • can measure c, h, and r in the image N h H rN c C sphere in 3D image plane

  30. V2 V1 N Depth from Normals • Get a similar equation for V2 • Each normal gives us two linear constraints on z • compute z values by solving a matrix equation

  31. Limitations • Big problems • Doesn’t work for shiny things, semi-translucent things • Shadows, inter-reflections • Smaller problems • Camera and lights have to be distant • Calibration requirements • measure light source directions, intensities • camera response function

  32. Trick for Handling Shadows • Weight each equation by the pixel brightness: • Gives weighted least-squares matrix equation: • Solve for as before

  33. Original Images

  34. Results - Shape Shallow reconstruction (effect of interreflections) Accurate reconstruction (after removing interreflections)

  35. Results - Albedo No Shading Information

  36. Original Images

  37. Results - Shape

  38. Results - Albedo

  39. Results • Estimate light source directions • Compute surface normals • Compute albedo values • Estimate depth from surface normals • Relight the object (with original texture and uniform albedo)

  40. Next Class • Shape from Shading • Reading: Horn, Chapter 11.

More Related