1 | % * This code was used in the following articles:
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2 | % * [1] Learning 3-D Scene Structure from a Single Still Image,
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3 | % * Ashutosh Saxena, Min Sun, Andrew Y. Ng,
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4 | % * In ICCV workshop on 3D Representation for Recognition (3dRR-07), 2007.
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5 | % * (best paper)
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6 | % * [2] 3-D Reconstruction from Sparse Views using Monocular Vision,
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7 | % * Ashutosh Saxena, Min Sun, Andrew Y. Ng,
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8 | % * In ICCV workshop on Virtual Representations and Modeling
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9 | % * of Large-scale environments (VRML), 2007.
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10 | % * [3] 3-D Depth Reconstruction from a Single Still Image,
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11 | % * Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng.
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12 | % * International Journal of Computer Vision (IJCV), Aug 2007.
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13 | % * [6] Learning Depth from Single Monocular Images,
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14 | % * Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng.
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15 | % * In Neural Information Processing Systems (NIPS) 18, 2005.
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16 | % *
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17 | % * These articles are available at:
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18 | % * http://make3d.stanford.edu/publications
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19 | % *
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20 | % * We request that you cite the papers [1], [3] and [6] in any of
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21 | % * your reports that uses this code.
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22 | % * Further, if you use the code in image3dstiching/ (multiple image version),
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23 | % * then please cite [2].
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24 | % *
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25 | % * If you use the code in third_party/, then PLEASE CITE and follow the
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26 | % * LICENSE OF THE CORRESPONDING THIRD PARTY CODE.
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27 | % *
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28 | % * Finally, this code is for non-commercial use only. For further
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29 | % * information and to obtain a copy of the license, see
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30 | % *
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31 | % * http://make3d.stanford.edu/publications/code
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32 | % *
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33 | % * Also, the software distributed under the License is distributed on an
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34 | % * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
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35 | % * express or implied. See the License for the specific language governing
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36 | % * permissions and limitations under the License.
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37 | % *
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38 | % */
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39 | function [alphas] = recoverAlphasFromU(R) |
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40 | %[alphaOut, alphaUp, alphaRight, q] = recoverAlphas(cameraLoc, cameraAt, cameraUp, gripperOut, gripperUp) |
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41 | |
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42 | %up, right, out |
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43 | |
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44 | if size(R,2) == 9 %rotation matrix |
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45 | |
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46 | R = reshape(R, 3,3); |
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47 | displayFlag = 0; |
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48 | |
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49 | % Calculates the rotation about the three camera vectors: out, up, and right |
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50 | |
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51 | R = R'; % Makes rotation from image frame to gripper frame. |
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52 | |
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53 | q = [(sqrt( max( 0, 1 + R(1,1) + R(2,2) + R(3,3) ) ) / 2); |
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54 | (sqrt( max( 0, 1 + R(1,1) - R(2,2) - R(3,3) ) ) / 2); |
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55 | (sqrt( max( 0, 1 - R(1,1) + R(2,2) - R(3,3) ) ) / 2); |
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56 | (sqrt( max( 0, 1 - R(1,1) - R(2,2) + R(3,3) ) ) / 2)]; |
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57 | signMat = -1 + 2*(0 <= [1 ; |
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58 | (R(3,2) - R(2,3)); |
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59 | (R(1,3) - R(3,1)); |
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60 | (R(2,1) - R(1,2))]); |
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61 | q = q .* signMat; |
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62 | |
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63 | test = q(2)*q(3) + q(4)*q(1); |
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64 | if (test > 0.499) %% singularity at north pole |
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65 | alphaOut = -2 * atan2(q(2),q(1)); |
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66 | alphaUp = -pi/2; |
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67 | alphaRight = 0; |
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68 | elseif (test < -0.499) %% singularity at south pole |
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69 | alphaOut = 2 * atan2(q(2),q(1)); |
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70 | alphaUp = pi/2; |
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71 | alphaRight = 0; |
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72 | else |
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73 | sqx = q(2)*q(2); sqy = q(3)*q(3); sqz = q(4)*q(4); |
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74 | alphaRight = -atan2(2*q(3)*q(1)-2*q(2)*q(4) , 1 - 2*sqy - 2*sqz); |
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75 | alphaUp = -asin(2*test); |
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76 | alphaOut = -atan2(2*q(2)*q(1)-2*q(3)*q(4) , 1 - 2*sqx - 2*sqz); |
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77 | alphas = [alphaOut, alphaUp, alphaRight]; |
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78 | end |
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79 | |
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80 | elseif size(R,2) == 3 |
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81 | alphaOut = acos( R(1)); |
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82 | alphaRight = asin(R(2) / sqrt(1-R(1)^2)); |
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83 | alphaUp = acos(R(3) / sqrt(1-R(1)^2)); |
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84 | |
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85 | elseif size(R,2) == 1 |
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86 | alphaOut = zeros(size(R,1),1); |
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87 | alphaRight = zeros(size(R,1),1); |
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88 | alphaUp = zeros(size(R,1),1); |
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89 | |
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90 | elseif size(R,2) == 4 |
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91 | q = R; |
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92 | test = q(2)*q(3) + q(4)*q(1); |
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93 | if (test > 0.499) %% singularity at north pole |
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94 | alphaOut = -2 * atan2(q(2),q(1)); |
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95 | alphaUp = -pi/2; |
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96 | alphaRight = 0; |
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97 | elseif (test < -0.499) %% singularity at south pole |
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98 | alphaOut = 2 * atan2(q(2),q(1)); |
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99 | alphaUp = pi/2; |
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100 | alphaRight = 0; |
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101 | else |
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102 | sqx = q(2)*q(2); sqy = q(3)*q(3); sqz = q(4)*q(4); |
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103 | alphaRight = -atan2(2*q(3)*q(1)-2*q(2)*q(4) , 1 - 2*sqy - 2*sqz); |
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104 | alphaUp = -asin(2*test); |
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105 | alphaOut = -atan2(2*q(2)*q(1)-2*q(3)*q(4) , 1 - 2*sqx - 2*sqz); |
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106 | alphas = [alphaOut, alphaUp, alphaRight]; |
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107 | end |
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108 | |
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109 | alphaOut = acos( R(1)); |
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110 | alphaRight = asin(R(2) / sqrt(1-R(1)^2)); |
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111 | alphaUp = acos(R(3) / sqrt(1-R(1)^2)); |
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112 | |
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113 | end; |
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114 | |
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115 | alphas = [alphaOut, alphaUp, alphaRight]; |
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116 | return; |
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117 | |
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118 | |
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