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Comprehensive Review on Perspective Projection and Camera Calibration Techniques

This review covers topics like perspective projection, camera calibration, intrinsic and extrinsic camera parameters, shape from images, stereo constraints, correspondence problems, and disparity calculations. It delves into key concepts and algorithms used in recovering 3D information from images. The text provides insights on visual cues, shading, texture, motion, and their significance in determining depth perception. Essential theories such as epipolar constraints, correspondence algorithms, and window matching for stereo vision are discussed in detail. The review aims to enhance understanding of advanced imaging techniques for 3D reconstruction.

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Comprehensive Review on Perspective Projection and Camera Calibration Techniques

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  1. Structure from images

  2. Calibration

  3. Review: Pinhole Camera

  4. Review: Perspective Projection

  5. Review: Perspective Projection • Points go to Points • Lines go to Lines • Planes go to whole image or Half-planes • Polygons go to Polygons

  6. Review: Intrinsic Camera Parameters Y M Image plane C Z v X Focal plane m u

  7. Review: Extrinsic Parameters Y M Image plane Y C Z v X X Z Focal plane m u By Rigid Body Transformation:

  8. Estimating Camera Parameters Alper Yilmaz, CAP5415, Fall 2004

  9. Shape From Images

  10. Perspective cues

  11. Perspective cues

  12. Perspective cues

  13. Ames Room

  14. Ames Room Video

  15. Recovering 3D from images • What cues in the image provide 3D information?

  16. Visual cues • Shading Merle Norman Cosmetics, Los Angeles

  17. Visual cues • Shading • Texture The Visual Cliff, by William Vandivert, 1960

  18. Visual cues • Shading • Texture • Focus From The Art of Photography, Canon

  19. Visual cues • Shading • Texture • Focus • Motion

  20. Julesz: had huge impact because it showed that recognition not needed for stereo.

  21. Shape From Multiple Views

  22. 3D World Points • Camera Centers • Camera Orientations Multi-View Geometry Relates

  23. 3D World Points • Camera Centers • Camera Intrinsic Parameters • Image Points Multi-View Geometry Relates • Camera Orientations

  24. Stereo scene point image plane optical center

  25. Stereo • Basic Principle: Triangulation • Gives reconstruction as intersection of two rays • Requires • calibration • point correspondence

  26. Stereo Constraints p’ ? p Given p in left image, where can the corresponding point p’in right image be?

  27. Epipolar Line p’ Y2 X2 Z2 O2 Epipole Stereo Constraints M Image plane Y1 p O1 Z1 X1 Focal plane

  28. Epipolar Constraint

  29. P p p’ O’ O From Geometry to Algebra

  30. P p p’ O’ O From Geometry to Algebra

  31. Linear Constraint:Should be able to express as matrix multiplication.

  32. The Essential Matrix

  33. Correspondence

  34. Pin Hole Camera Model

  35. Basic Stereo Derivations Derive expression for Z as a function of x1, x2, f and B

  36. Basic Stereo Derivations

  37. Basic Stereo Derivations Disparity:

  38. We can always achieve this geometry with image rectification • Image Reprojection • reproject image planes onto common plane parallel to line between optical centers (Seitz)

  39. Rectification example

  40. Correspondence: Epipolar constraint.

  41. Correspondence Problem • Two classes of algorithms: • Correlation-based algorithms • Produce a DENSE set of correspondences • Feature-based algorithms • Produce a SPARSE set of correspondences

  42. Correspondence: Photometric constraint • Same world point has same intensity in both images. • Lambertian fronto-parallel • Issues: • Noise • Specularity • Foreshortening

  43. For each epipolar line For each pixel in the left image Improvement: match windows Using these constraints we can use matching for stereo • compare with every pixel on same epipolar line in right image • pick pixel with minimum match cost • This will never work, so:

  44. ? = g f Most popular Comparing Windows: For each window, match to closest window on epipolar line in other image.

  45. Minimize Sum of Squared Differences Maximize Cross correlation It is closely related to the SSD:

  46. Correspondence search Left Right • Slide a window along the right scanline and compare contents of that window with the reference window in the left image • Matching cost: SSD or normalized correlation scanline Matching cost disparity

  47. Correspondence search Left Right scanline SSD

  48. Correspondence search Left Right scanline Norm. corr

  49. Effect of window size W = 3 W = 20 • Smaller window + More detail • More noise • Larger window + Smoother disparity maps • Less detail • Fails near boundaries

  50. Stereo results • Data from University of Tsukuba Scene Ground truth (Seitz)

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