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annotate OrthancStone/Resources/Computations/ComputeWarp.py @ 1871:7053b8a0aaec

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author Sebastien Jodogne <s.jodogne@gmail.com>
date Tue, 11 Jan 2022 11:18:48 +0100
parents 3889ae96d2e9
children 07964689cb0b
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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
1871
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6 # Copyright (C) 2017-2022 Osimis S.A., Belgium
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7 # Copyright (C) 2021-2022 Sebastien Jodogne, ICTEAM UCLouvain, Belgium
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8 #
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9 # This program is free software: you can redistribute it and/or
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10 # modify it under the terms of the GNU Lesser General Public License
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11 # as published by the Free Software Foundation, either version 3 of
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12 # the License, or (at your option) any later version.
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13 #
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14 # This program is distributed in the hope that it will be useful, but
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15 # WITHOUT ANY WARRANTY; without even the implied warranty of
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16 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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17 # Lesser General Public License for more details.
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18 #
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19 # You should have received a copy of the GNU Lesser General Public
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20 # License along with this program. If not, see
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21 # <http://www.gnu.org/licenses/>.
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22
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23
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4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
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24 from sympy import *
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25 from sympy.solvers import solve
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26 import pprint
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27 import sys
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28
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29 init_printing(use_unicode=True)
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30
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
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31
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32 # Create a test 3D vector using homogeneous coordinates
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33 x, y, z, w = symbols('x y z w')
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34 p = Matrix([ x, y, z, w ])
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35
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36
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37 # Create a shear matrix, and a scale/shift "T * S" transform as in
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38 # Lacroute's thesis (Equation A.16, page 209)
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39 ex, ey, ew = symbols('ex ey ew')
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40 sx, sy, tx, ty = symbols('sx sy tx ty')
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41
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42 TS = Matrix([[ sx, 0, 0, tx ],
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43 [ 0, sy, 0, ty ],
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44 [ 0, 0, 1, 0 ],
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45 [ 0, 0, 0, 1 ]])
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46
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47 pureShear = Matrix([[ 1, 0, ex, 0 ],
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48 [ 0, 1, ey, 0 ],
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49 [ 0, 0, 1, 0 ],
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50 [ 0, 0, ew, 1 ]])
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51
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52
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53 # Create a general warp matrix, that corresponds to "M_warp" in
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54 # Equation (A.17) of Lacroute's thesis:
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55 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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56
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57 WW = Matrix([[ ww11, ww12, ww13, ww14 ],
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58 [ ww21, ww22, ww23, ww24 ],
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59 [ ww31, ww32, ww33, ww34 ],
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60 [ ww41, ww43, ww43, ww44 ]])
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61
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62
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63 # Create the matrix of intrinsic parameters of the camera
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64 k11, k22, k14, k24 = symbols('k11 k22 k14 k24')
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65 K = Matrix([[ k11, 0, 0, k14 ],
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66 [ 0, k22, 0, k24 ],
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67 [ 0, 0, 0, 1 ]])
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68
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69
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70 # The full decomposition is:
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71 M_shear = TS * pureShear
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72 M_warp = K * WW * TS.inv()
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73 AA = M_warp * M_shear
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74
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75 # Check that the central component "M_warp == K * WW * TS.inv()" that
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76 # is the left part of "A" is another general warp matrix (i.e. no
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77 # exception is thrown about incompatible matrix sizes):
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78 M_warp * p
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79
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80 if (M_warp.cols != 4 or
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81 M_warp.rows != 3):
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82 raise Exception('Invalid matrix size')
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83
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84
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85 # We've just shown that "M_warp" is a general 3x4 matrix. Let's call
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86 # it W:
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87 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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88
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89 W = Matrix([[ w11, w12, w13, w14 ],
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90 [ w21, w22, w23, w24 ],
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91 [ w41, w43, w43, w44 ]])
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92
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93 # This shows that it is sufficient to study a decomposition of the
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94 # following form:
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95 A = W * M_shear
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96 print('\nA = W * M_shear =')
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97 pprint.pprint(A)
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98
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99 sys.stdout.write('\nW = ')
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100 pprint.pprint(W)
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101
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102 sys.stdout.write('\nM_shear = ')
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103 pprint.pprint(M_shear)
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104
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105
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106
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107 # Let's consider one fixed 2D point (i,j) in the intermediate
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108 # image. The 3D points (x,y,z,1) that are mapped to (i,j) must satisfy
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109 # the equation "(i,j) == M_shear * (x,y,z,w)". As "M_shear" is
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110 # invertible, we solve "(x,y,z,w) == inv(M_shear) * (i,j,k,1)".
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111
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112 i, j, k = symbols('i j k')
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113 l = M_shear.inv() * Matrix([ i, j, k, 1 ])
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114
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115 print('\nLocus for points imaged to some fixed (i,j,k,l) point in the intermediate image:')
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116 print('x = %s' % l[0])
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117 print('y = %s' % l[1])
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118 print('z = %s' % l[2])
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119 print('w = %s' % l[3])
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120
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121
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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122 # By inspecting the 4 equations above, we see that the locus entirely
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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123 # depends upon the "k" value that encodes the Z-axis
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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124
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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125 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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126 q = expand(A * l)
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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127 pprint.pprint(q)
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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128
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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129 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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130 pprint.pprint(q.subs(k, 0))
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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131
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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132 print("\nThis gives the warp transform.")
4abddd083374 ShearWarpProjectiveTransform::ApplyAxial()
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
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133 print("QED: line after Equation (A.17) on page 209.\n")