@PhDThesis{Smutny-TR-2014-11,
  IS = { zkontrolovano 11 Jan 2016 },
  UPDATE  = { 2015-06-26 },
author =      {Smutn{\' y}, Vladim{\'\i}r},
supervisor =  {Pajdla, Tom{\' a}{\v s}},
title =       {Light Propagation in Transparent Polyhedra},
school =      {Center for Machine Perception, K13133 FEE
               Czech Technical University},
address =     {Prague, Czech Republic},
year =        {2015},
month =       {March},
day =         {26},
type =        {{PhD Thesis CTU--CMP--2014--11}},
issn =        {1213-2365},
pages =       {126},
figures =     {},
authorship =  {100},
psurl       = {[Smutny-TR
-2014-11.pdf]},
project =     {SGS10/193/OHK3/2T/13, TACR TE01020197},
annote =      {Production of gemstones and fashion jewelry stones is a
                  multi-billion do llar industry.  The evaluation of
                  cut stones during their design, manufacturing, and
                  sale is necessary.  Computer vision is a natural
                  tool for this evaluation.  Cut gemstones are, due to
                  their manufacturing process, convex polyhedra. They
                  are manufactured mostly from clear or absorptive
                  transparent material.  This thesis advances two
                  methods we have developed previously. The first
                  approach starts with the geometrical model of the
                  jewelry stone complemented with the material
                  refraction index. A computer model of the stone is
                  illuminated by a beam of parallel rays and computer
                  simulation computes geometric and radiometric
                  parameters of the exiting beams. The features and
                  statistics are calculated on the simulation
                  results. These features are used for stone
                  evaluation or simulation results that can be
                  presented to experts.  The second approach compares
                  the result of the above simulation with physical
                  experiments. The differences between simulated and
                  laboratory experiments manifest the differences
                  between the stone model and its actual physical
                  shape. The computer model of the stone can be
                  modified according to these differences.  This
                  thesis contributes to both approaches. The
                  simulation of the light beam propagation is extended
                  to enable modeling of light absorbing
                  materials. Hence, it is possible to model stones
                  made from not only clear, but also light absorbing
                  transparent materials to color transparent stones,
                  which are common fashion jewelry stones. These
                  contributions have significantly extended the range
                  of the stones which can be modeled.  Methods for
                  reconstructing the actual shape of a stone by
                  comparing simulations with experimental results
                  requires solving the correspondence problem. The
                  thesis contributes to the solution of this problem
                  by defining features which can be extracted during
                  the simulation as well as in experimentally acquired
                  images.  The collimated light beam propagation in
                  polyhedral stones can be represented by a graph. It
                  gives further insight into the problem as well as a
                  tool for implementing the beam-tracing simulation
                  software.  A completely new approach developed in
                  this thesis is the method for simulating
                  omnidirectional illumination. The light source
                  coming from all directions is described here by a
                  mathematical model. Although the proposed method
                  enables the modeling only of reflection and
                  transmission during the first incidence, it is
                  possible to exten d it to other
                  reflections/transmissions in the
                  stone. Unfortunately the task becomes mathematically
                  difficult and calls for further
                  investigation. Nevertheless, our approac h opens the
                  space for further interesting research since it
                  removes the sampling issues of the previous methods
                  based on ray-tracing and beam-tracing. Furthermore,
                  our method completely solves the simulation of
                  stones which are translucent or which have the high
                  absorption coefficient.},
keywords =    {Computer vision, cut stones, inspection, dimensions measurement},
}