2019-06-03-reconstruction

Posted on June 3, 2019
Structured light Q&A
  • phase shifting
    • algorithm for determining correspondence of the different phases
  • terminology
    • spatial sinusoids
      • black stripes have intensity of 1 and white stripes have intensity of 0 and they corresponds to spatial sinusoids
    • frequency
      • 1 pattern with varying width column stripes
    • shift N times
      • 1 pattern that is shifted by some N times, each by amount of phase
    • phase
      • each phase corresponds to a column stripe in a spatial sinusoids
  • where did the formula relating intensity and amplitude, offset, phase changes are ?
    • https://en.wikipedia.org/wiki/Phase_(waves)#Phase_shift
  • phase wrapping/unwrapping from interferometry paper (relation to phase shifting)
  • what is light transport coefficient a_{qc}
    • describes intensity of reflected light from point q that is received by point c?
  • why amplitude is a function of both frequency and amount of defocus?
  • why higher mean frequency -> resistance to global illumination
  • why frequency measured with respect to pixels
    • spatial frequency ?
    • w = 16 pixel period means how many 16 pixel in the image
  • 1991_automatic_processing_of_fringe_pattern_in_interger_interferometers
    • original paper explaining micro-phasing theory
    • goal
      • determine total phase difference of light waves without interference fringe counting
  • 2003_pattern_codification_strategies_in_structured_light_system
    • coded structured light
      • for recovering surface of objects
      • no location constraint
      • idea
        • project a light pattern
        • view the illuminated scene from one or more points of view
        • decoded points can be triangulated and 3D information obtained
      • patterns
        • the projected images are called patterns
    • stereo vision
      • view scene from two or more points of view and then finding correspondence between different images to triangulate the 3D position
    • coding strategies
      • patterns
        • designed to have codewords assigned to a set of pixels
        • f: codewords -> coordinates of pixel in pattern
          • codewords are numbers, i,e. grey levels, colors,
      • based on what to classify
        • what kind of codeword is used
        • if codeword encodes a single axis or two spatial axis
      • time-multiplexing strategy
        • patterns successively projected onto measuring surface
        • codeword for a pixel: sequence of illumination values
        • the good
          • accurate because
            • codeword basis tends to be small, so distinguishable
            • since pattern is successively projected, …
        • subclasses
          • binary codes
            • 0-1-1-0-1- …for 1 pattern axis
            • a sequence of m patterns,
              • 2^m stripes, i.e. codewords, using a binary code
              • codeword is a sequence of 0s and 1s from m patterns, first pattern is one contains most significant bit, 0-black, 1-white
          • n-ary
            • reduces number of patterns by means of increasing the number of intensity levels used to encode the stripes
            • multilevel Gray code
              • Gray code with alphabet of n symbols -> reduce number of patterns
                • i.e. n^m instead of 2^m stripes
          • gray code combined with phase shifting
            • same pattern projected several times, shifting it in certain direction in order to increase resolution
              • Gray code methods unambiguous
                • hamming distance of 1 -> good against noise
              • phase shift methods
                • high resolution
          • hybrid
  • 2012_micro_phase_shifting
    • http://www.cs.columbia.edu/CAVE/projects/micro_phase_shifting/
    • goal
      • shape recovery addressing global allumination + illumination defocus
    • problems & solutions
      • global illumination
        • project sinusoidal patterns with frequencies limited to a narrow frequency band, over which global illumination remain cosntant
      • defocus effects of projecter (limited FOV)
        • frequency in a narrow band,
          • so amplitudes for all frequencies are approximated the same, … single unknown
          • reduce number of input images for Micro PS
      • resolving depth ambiguities
        • fact
          • high freq sinusoids -> high resolution info, but in small depth range
          • use low freq sinusoids to disambiguate phase info over larger range
        • solution
          • emulate a low frequency sinusoid with a period equal to product of periods of several high-frequency sinusoids
    • phase shifting
      • phase corresponds to correspondence of projector pixels -> depth ..