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annotate OrthancStone/Resources/Computations/ComputeWarp.py @ 1739:9ac2a65d4172

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upgrade to year 2021
author Sebastien Jodogne <s.jodogne@gmail.com>
date Wed, 06 Jan 2021 17:50:00 +0100
parents 8563ea5d8ae4
children 3889ae96d2e9
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4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
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1 #!/usr/bin/python
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2
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3 # Stone of Orthanc
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4 # Copyright (C) 2012-2016 Sebastien Jodogne, Medical Physics
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5 # Department, University Hospital of Liege, Belgium
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6 # Copyright (C) 2017-2021 Osimis S.A., Belgium
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7 #
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8 # This program is free software: you can redistribute it and/or
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9 # modify it under the terms of the GNU Lesser General Public License
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10 # as published by the Free Software Foundation, either version 3 of
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11 # the License, or (at your option) any later version.
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12 #
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13 # This program is distributed in the hope that it will be useful, but
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14 # WITHOUT ANY WARRANTY; without even the implied warranty of
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15 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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16 # Lesser General Public License for more details.
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17 #
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18 # You should have received a copy of the GNU Lesser General Public
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19 # License along with this program. If not, see
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20 # <http://www.gnu.org/licenses/>.
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21
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22
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4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
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23 from sympy import *
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24 from sympy.solvers import solve
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25 import pprint
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26 import sys
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27
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28 init_printing(use_unicode=True)
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29
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
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30
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31 # Create a test 3D vector using homogeneous coordinates
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32 x, y, z, w = symbols('x y z w')
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33 p = Matrix([ x, y, z, w ])
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34
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35
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36 # Create a shear matrix, and a scale/shift "T * S" transform as in
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37 # Lacroute's thesis (Equation A.16, page 209)
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38 ex, ey, ew = symbols('ex ey ew')
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39 sx, sy, tx, ty = symbols('sx sy tx ty')
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40
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41 TS = Matrix([[ sx, 0, 0, tx ],
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42 [ 0, sy, 0, ty ],
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43 [ 0, 0, 1, 0 ],
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44 [ 0, 0, 0, 1 ]])
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45
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46 pureShear = Matrix([[ 1, 0, ex, 0 ],
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47 [ 0, 1, ey, 0 ],
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48 [ 0, 0, 1, 0 ],
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49 [ 0, 0, ew, 1 ]])
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50
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51
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52 # Create a general warp matrix, that corresponds to "M_warp" in
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53 # Equation (A.17) of Lacroute's thesis:
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54 ww11, ww12, ww13, ww14, ww21, ww22, ww23, ww24, ww31, ww32, ww33, ww34, ww41, ww42, ww43, ww44 = symbols('ww11 ww12 ww13 ww14 ww21 ww22 ww23 ww24 ww31 ww32 ww33 ww34 ww41 ww42 ww43 ww44')
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55
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56 WW = Matrix([[ ww11, ww12, ww13, ww14 ],
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57 [ ww21, ww22, ww23, ww24 ],
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58 [ ww31, ww32, ww33, ww34 ],
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59 [ ww41, ww43, ww43, ww44 ]])
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60
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61
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62 # Create the matrix of intrinsic parameters of the camera
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63 k11, k22, k14, k24 = symbols('k11 k22 k14 k24')
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64 K = Matrix([[ k11, 0, 0, k14 ],
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65 [ 0, k22, 0, k24 ],
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66 [ 0, 0, 0, 1 ]])
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68
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69 # The full decomposition is:
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70 M_shear = TS * pureShear
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71 M_warp = K * WW * TS.inv()
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72 AA = M_warp * M_shear
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73
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74 # Check that the central component "M_warp == K * WW * TS.inv()" that
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75 # is the left part of "A" is another general warp matrix (i.e. no
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76 # exception is thrown about incompatible matrix sizes):
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77 M_warp * p
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78
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79 if (M_warp.cols != 4 or
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80 M_warp.rows != 3):
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81 raise Exception('Invalid matrix size')
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82
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83
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84 # We've just shown that "M_warp" is a general 3x4 matrix. Let's call
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85 # it W:
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86 w11, w12, w13, w14, w21, w22, w23, w24, w41, w42, w43, w44 = symbols('w11 w12 w13 w14 w21 w22 w23 w24 w41 w42 w43 w44')
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87
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88 W = Matrix([[ w11, w12, w13, w14 ],
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89 [ w21, w22, w23, w24 ],
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90 [ w41, w43, w43, w44 ]])
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91
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92 # This shows that it is sufficient to study a decomposition of the
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93 # following form:
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94 A = W * M_shear
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95 print('\nA = W * M_shear =')
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96 pprint.pprint(A)
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97
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98 sys.stdout.write('\nW = ')
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99 pprint.pprint(W)
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100
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101 sys.stdout.write('\nM_shear = ')
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102 pprint.pprint(M_shear)
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103
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104
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105
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106 # Let's consider one fixed 2D point (i,j) in the intermediate
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107 # image. The 3D points (x,y,z,1) that are mapped to (i,j) must satisfy
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108 # the equation "(i,j) == M_shear * (x,y,z,w)". As "M_shear" is
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109 # invertible, we solve "(x,y,z,w) == inv(M_shear) * (i,j,k,1)".
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110
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111 i, j, k = symbols('i j k')
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112 l = M_shear.inv() * Matrix([ i, j, k, 1 ])
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113
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114 print('\nLocus for points imaged to some fixed (i,j,k,l) point in the intermediate image:')
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115 print('x = %s' % l[0])
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116 print('y = %s' % l[1])
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117 print('z = %s' % l[2])
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118 print('w = %s' % l[3])
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119
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120
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121 # By inspecting the 4 equations above, we see that the locus entirely
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122 # depends upon the "k" value that encodes the Z-axis
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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123
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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124 print('\nGlobal effect of the shear-warp transform on this locus:')
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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125 q = expand(A * l)
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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126 pprint.pprint(q)
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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127
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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128 print("\nWe can arbitrarily fix the value of 'k', so let's choose 'k=0':")
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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129 pprint.pprint(q.subs(k, 0))
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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130
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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131 print("\nThis gives the warp transform.")
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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132 print("QED: line after Equation (A.17) on page 209.\n")