[37] | 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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