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# Image formation

Image formation. ECE 847: Digital Image Processing. Stan Birchfield Clemson University. Cameras. First photograph due to Niepce Basic abstraction is the pinhole camera lenses required to ensure image is not too dark various other abstractions can be applied.

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## Image formation

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1. Image formation ECE 847:Digital Image Processing Stan Birchfield Clemson University

2. Cameras • First photograph due to Niepce • Basic abstraction is the pinhole camera • lenses required to ensure image is not too dark • various other abstractions can be applied F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

3. Image formation overview Image formation involves • geometry – path traveled by light • radiometry – optical energy flow • photometry – effectiveness of light to produce “brightness” sensation in human visual system • colorimetry – physical specifications of light stimuli that produce given color sensation • sensors – converting photons to digital form

4. Pinhole camera D. Forsyth, http://luthuli.cs.uiuc.edu/~daf/book/bookpages/slides.html

5. Parallel lines meet: vanishing point • each set of parallel lines (=direction) 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

6. Properties of projection: Points go to points Lines go to lines Planes go to whole image Polygons go to polygons Degenerate cases line through focal point to point plane through focal point to line k P p i C Q f q O j Perspective projection F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

7. Perspective projection (cont.) F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

8. 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 Weak perspective projection D. Forsyth, http://luthuli.cs.uiuc.edu/~daf/book/bookpages/slides.html

9. Weak perspective (cont.) F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

10. Orthographic projection Let Z0=1: F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

11. Pushbroom cameras

12. Pinhole size Pinhole too big - many directions are averaged, blurring the image Pinhole too small- diffraction effects blur the image Generally, pinhole cameras are dark, because a very small set of rays from a particular point hits the screen. D. Forsyth, http://luthuli.cs.uiuc.edu/~daf/book/bookpages/slides.html

13. The reason for lenses D. Forsyth, http://luthuli.cs.uiuc.edu/~daf/book/bookpages/slides.html

14. focal points The thin lens D. Forsyth, http://luthuli.cs.uiuc.edu/~daf/book/bookpages/slides.html

15. Focusing http://www.theimagingsource.com

16. Thick lens • thick lens has 6 cardinal points: • two focal points (F1 and F2) • two principal points (H1 and H2) • two nodal points (N1 and N2) • complex lens is formed by combining individual concave and convex lenses http://physics.tamuk.edu/~suson/html/4323/thick.html D. Forsyth, http://luthuli.cs.uiuc.edu/~daf/book/bookpages/slides.html

17. Complex lens All but the simplest cameras contain lenses which are actually composed of several lens elements http://www.cambridgeincolour.com/tutorials/camera-lenses.htm

18. Choosing a lens • How to select focal length: • x=fX/Z • f=xZ/X • Lens format should be >= CCD format to avoid optical flaws at the rim of the lens http://www.theimagingsource.com/en/resources/whitepapers/download/choosinglenswp.en.pdf

19. Lenses – Practical issues • standardized lens mount has two varieties: • C mount • CS mount • CS mount lenses cannot be used with C mount cameras http://www.theimagingsource.com/en/resources/whitepapers/download/choosinglenswp.en.pdf

20. Spherical aberration perfect lens actual lens On a real lens, even parallel rays are not focused perfectly http://en.wikipedia.org/wiki/Spherical_aberration

21. Chromatic aberration On a real lens, different wavelengths are not focused the same http://en.wikipedia.org/wiki/Chromatic_aberration

22. Radial distortion straight lines are curved: uncorrected corrected

23. Radial distortion (cont.) Two types: barrel distortion(more common) pincushion distortion barrel pincushion http://en.wikipedia.org/wiki/Image_distortion http://foto.hut.fi/opetus/260/luennot/11/atkinson_6-11_radial_distortion_zoom_lenses.jpg

24. Vignetting vignetting – reduction of brightness at periphery of image D. Forsyth, http://luthuli.cs.uiuc.edu/~daf/book/bookpages/slides.html

25. Normalized Image coordinates 1 O u=X/Z = dimensionless ! P F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

26. Pixel units Pixels are on a grid of a certain dimension f O u=k f X/Z = in pixels ! [f] = m (in meters) [k] = pixels/m P F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

27. Pixel coordinates We put the pixel coordinate origin on topleft f O u=u0 + k f X/Z P F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

28. Pixel coordinates in 2D 640 (0.5,0.5) i (u0,v0) 480 (640.5,480.5) j F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

29. skew Summary: Intrinsic Calibration 5 Degrees of Freedom ! F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

30. Camera Pose In order to apply the camera model, objects in the scene must be expressed in camera coordinates. Camera Coordinates World Coordinates Calibration target looks tilted from camera viewpoint. This can be explained as a difference in coordinate systems. F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

31. Rigid Body Transformations • Need a way to specify the six degrees-of-freedom of a rigid body. • Why are there 6 DOF? A rigid body is a collection of points whose positions relative to each other can’t change Fix one point, three DOF Fix second point, two more DOF (must maintain distance constraint) Third point adds one more DOF, for rotation around line F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

32. Notations • Superscript references coordinate frame • AP is coordinates of P in frame A • BP is coordinates of P in frame B • Example: F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

33. Translation F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

34. Translation • Using homogeneous coordinates, translation can be expressed as a matrix multiplication. • Translation is commutative F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

35. Rotation means describing frame A in The coordinate system of frame B F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

36. Rotation Orthogonal matrix! F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

37. Example: Rotation about z axis What is the rotation matrix? F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

38. Rotation in homogeneous coordinates • Using homogeneous coordinates, rotation can be expressed as a matrix multiplication. • Rotation is not communicative F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

39. Rigid transformations F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

40. Rigid transformations (con’t) • Unified treatment using homogeneous coordinates. F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

41. Projective Camera Matrix 5+6 DOF = 11 ! F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

42. Projective Camera Matrix 5+6 DOF = 11 ! F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

43. Columns & Rows of M m2P=0 O F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

44. Effect of Illumination Light source strength and direction has a dramatic impact on distribution of brightness in the image (e.g. shadows, highlights, etc.) (Subject 8 from the Yale face database due to P. Belhumeur et. al.) F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

45. Image formation • Light source emits photons • Absorbed, transmitted, scattered • fluorescence source Camera F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

46. Surfaces receives and emits • Incident light from lightfield • Act as a light source • How much light ? F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

47. Irradiance • Irradiance – amount of light falling on a surface patch • symbol=E, units = W/m2 dA F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

48. Radiosity • power leaving a point per area • symbol=B, units = W/m2 dA F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

49. Light = Directional • Light emitted varies w. direction F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

50. Steradians (Solid Angle) • 3D analogue of 2D angle A R F. Dellaert, http://www.cc.gatech.edu/~dellaert/vision/html/materials.html

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