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 ParaPPCP=L1NormMinimization(NuSupSize,PosiM,CoPM,HoriStickM,VertStickM,PosiDepthScale,Center,CoPEstDepth,EstDepHoriStick,EstDepVertStick,YPointer,RayAllM,RayAllOriM,FarestDist,ClosestDist) |
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40 | |
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41 | %% we first form the A, x and b for which it is |Ax-b|_1 |
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42 | |
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43 | A1=sparse(diag([PosiDepthScale; Center*CoPEstDepth; EstDepHoriStick; EstDepVertStick])*[PosiM;CoPM;HoriStickM;VertStickM]); |
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44 | b=[PosiDepthScale;zeros(size(CoPM,1),1);zeros(size(HoriStickM,1),1);zeros(size(VertStickM,1),1)]; |
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45 | A2=sparse([-RayAllM;RayAllM;-RayAllOriM;RayAllOriM;diag([zeros(length(YPointer),1);YPointer;zeros(length(YPointer),1)])]); |
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46 | c=[-1/FarestDist*ones(size(RayAllM,1),1);1/ClosestDist*ones(size(RayAllM,1),1);-1/FarestDist*ones(size(RayAllOriM,1),1);1/ClosestDist*ones(size(RayAllOriM,1),1);zeros(3*NuSupSize,1)]; |
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47 | |
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48 | %A=diag(VarM/BandWith;Center*CoPEstDepth;EstDepHoriStick;EstDepVertStick)*[PosiM;CoPM1-CoPM2;HoriStickM_i-HoriStickM_j;VertStickM_i-VertStickM_j]; |
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49 | %b=[ones(size(PosiM,1),1); zeros(size(A,1)-size(PosiM,1),1)]; |
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50 | |
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51 | %% Now we also include the other constraints on ParaPPCP and form a modified A' and b' |
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52 | %PPCP_Ycood=[zeros(NuSupSize,1) ones(NuSupSize,1) zeros(NuSupSize,1)]; |
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53 | %Ap=[RayAllM zeros(3*NuSupSize);-RayAllM zeros(3*NuSupSize);RayAllOriM zeros(3*NuSupSize);-RayAllOriM zeros(3*NuSupSize);PPCP_Ycood zeros(3*NuSupSize);A -eye(3*NuSupSize); -A -eye(3*NuSupSize)]; |
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54 | %bp=[zeros(size(Ap,1)-size(b,1),1);b;-b]; |
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55 | |
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56 | %% So now we have the problem in the form, minimize 1^ty, s.t. Ap [x;y] <= bp |
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57 | M1=size(A1,1); |
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58 | % incS1=1:M1; |
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59 | M2=size(A2,1); |
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60 | % incS2=1:M2; |
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61 | % xy=pcg(sparse([A1 -eye(M1); -A1 -eye(M1); A2 zeros(M2)]),[b;-b;c]); |
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62 | % x=xy(1:3*NuSupSize);%ones(3*NuSupSize,1); |
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63 | % y=xy(3*NuSupSize+1:end);%ones(M1,1); |
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64 | x=ones(3*NuSupSize,1); |
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65 | y=ones(M1,1); |
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66 | % [x,y,flag]=warmStart(A1,A2,b,c,M1,M2,NuSupSize); |
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67 | m=M1*2+M2; |
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68 | t=1000; |
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69 | epsilon=1e-5; |
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70 | mu=100; |
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71 | alpha=0.2; |
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72 | beta=0.5; |
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73 | %% may be later I can implement backtracking line search, as of now, working with small alpha; |
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74 | |
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75 | while((m/t)>epsilon) |
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76 | goOn=boolean(1); |
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77 | while(goOn) |
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78 | %D1=sparse(diag(1./([t1].^2))); |
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79 | %D2=sparse(diag(1./([t2].^2))); |
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80 | % size(b) |
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81 | % size(A1) |
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82 | % size(x) |
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83 | t1=b-A1*x+y+epsilon/t; |
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84 | it1=1./t1; |
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85 | it1s=1./(t1.^2); |
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86 | t2=-b+A1*x+y+epsilon/t; |
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87 | it2=1./t2; |
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88 | it2s=1./(t2.^2); |
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89 | t3=c-A2*x+epsilon/t; |
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90 | t4=(it1s-it2s); |
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91 | t5=(it1s+it2s); |
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92 | D=spdiags((2./([y.^2 + (b-A1*x).^2])),0,M1,M1); |
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93 | D3=spdiags(1./(t3.^2),0,M2,M2); |
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94 | g1=A1'*[it1-it2]-A2'*[1./t3]; |
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95 | g2=t*ones(M1,1)-it1-it2; |
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96 | %g=g1+A1'*(D1-D2)*inv(D1+D2)*g2; |
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97 | g=g1+A1'*[(t4./t5).*g2]; |
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98 | % DeltaxNt=cgs(A1'*D*A1+A2'*D3*A2,-g); |
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99 | DeltaxNt=pcg(A1'*D*A1+A2'*D3*A2,-g);%cgs(A1'*D*A1+A2'*D3*A2,-g); |
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100 | % DeltaxNt=-pinv(A1'*D*A1+A2'*D3*A2)*g; |
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101 | DeltayNt=((t4.*(A1*DeltaxNt))-g2)./t5; |
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102 | x=x+alpha*DeltaxNt; |
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103 | y=y+alpha*DeltayNt; |
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104 | toler=norm(DeltaxNt./x) |
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105 | if(toler<epsilon) |
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106 | goOn=boolean(0); |
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107 | end |
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108 | end |
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109 | t=mu*t; |
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110 | end |
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111 | |
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112 | |
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113 | |
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114 | |
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115 | |
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116 | |
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117 | %% The Hessian is given by A'*diag(d)^2 * A |
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118 | %% where d_i = 1/(bi-ai^tx) |
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119 | %d=(1./(bp-Ap*x)); |
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120 | %H=A'*diag(d.^2)*A; |
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121 | %g=A'*d; |
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122 | %deltaX=pcg(H,-g); |
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123 | |
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