1 | %init_intrinsic_param |
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2 | % |
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3 | %Initialization of the intrinsic parameters. |
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4 | %Runs as a script. |
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5 | % |
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6 | %INPUT: x_1,x_2,x_3,...: Feature locations on the images |
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7 | % X_1,X_2,X_3,...: Corresponding grid coordinates |
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8 | % |
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9 | %OUTPUT: fc: Camera focal length |
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10 | % cc: Principal point coordinates |
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11 | % kc: Distortion coefficients |
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12 | % alpha_c: skew coefficient |
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13 | % KK: The camera matrix (containing fc, cc and alpha_c) |
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14 | % |
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15 | %Method: Computes the planar homographies H_1, H_2, H_3, ... and computes |
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16 | % the focal length fc from orthogonal vanishing points constraint. |
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17 | % The principal point cc is assumed at the center of the image. |
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18 | % Assumes no image distortion (kc = [0;0;0;0]) |
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19 | % |
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20 | %Note: The row vector active_images consists of zeros and ones. To deactivate an image, set the |
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21 | % corresponding entry in the active_images vector to zero. |
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22 | % |
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23 | % |
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24 | %Important function called within that program: |
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25 | % |
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26 | %compute_homography.m: Computes the planar homography between points on the grid in 3D, and the image plane. |
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27 | % |
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28 | % |
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29 | %VERY IMPORTANT: This function works only with 2D rigs. |
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30 | %In the future, a more general function will be there (working with 3D rigs as well). |
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31 | |
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32 | |
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33 | if ~exist('two_focals_init'), |
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34 | two_focals_init = 0; |
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35 | end; |
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36 | |
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37 | if ~exist('est_aspect_ratio'), |
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38 | est_aspect_ratio = 1; |
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39 | end; |
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40 | |
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41 | check_active_images; |
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42 | |
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43 | if ~exist(['x_' num2str(ind_active(1)) ]), |
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44 | click_calib; |
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45 | end; |
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46 | |
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47 | |
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48 | fprintf(1,'\nInitialization of the intrinsic parameters - Number of images: %d\n',length(ind_active)); |
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49 | |
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50 | |
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51 | % Initialize the homographies: |
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52 | |
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53 | for kk = 1:n_ima, |
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54 | eval(['x_kk = x_' num2str(kk) ';']); |
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55 | eval(['X_kk = X_' num2str(kk) ';']); |
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56 | if (isnan(x_kk(1,1))), |
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57 | if active_images(kk), |
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58 | fprintf(1,'WARNING: Cannot calibrate with image %d. Need to extract grid corners first.\n',kk) |
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59 | fprintf(1,' Set active_images(%d)=1; and run Extract grid corners.\n',kk) |
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60 | end; |
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61 | active_images(kk) = 0; |
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62 | end; |
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63 | if active_images(kk), |
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64 | eval(['H_' num2str(kk) ' = compute_homography(x_kk,X_kk(1:2,:));']); |
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65 | else |
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66 | eval(['H_' num2str(kk) ' = NaN*ones(3,3);']); |
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67 | end; |
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68 | end; |
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69 | |
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70 | check_active_images; |
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71 | |
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72 | % initial guess for principal point and distortion: |
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73 | |
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74 | if ~exist('nx'), [ny,nx] = size(I); end; |
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75 | |
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76 | c_init = [nx;ny]/2 - 0.5; % initialize at the center of the image |
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77 | k_init = [0;0;0;0;0]; % initialize to zero (no distortion) |
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78 | |
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79 | |
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80 | |
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81 | % Compute explicitely the focal length using all the (mutually orthogonal) vanishing points |
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82 | % note: The vanihing points are hidden in the planar collineations H_kk |
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83 | |
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84 | A = []; |
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85 | b = []; |
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86 | |
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87 | % matrix that subtract the principal point: |
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88 | Sub_cc = [1 0 -c_init(1);0 1 -c_init(2);0 0 1]; |
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89 | |
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90 | for kk=1:n_ima, |
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91 | |
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92 | if active_images(kk), |
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93 | |
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94 | eval(['Hkk = H_' num2str(kk) ';']); |
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95 | |
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96 | Hkk = Sub_cc * Hkk; |
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97 | |
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98 | % Extract vanishing points (direct and diagonals): |
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99 | |
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100 | V_hori_pix = Hkk(:,1); |
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101 | V_vert_pix = Hkk(:,2); |
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102 | V_diag1_pix = (Hkk(:,1)+Hkk(:,2))/2; |
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103 | V_diag2_pix = (Hkk(:,1)-Hkk(:,2))/2; |
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104 | |
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105 | V_hori_pix = V_hori_pix/norm(V_hori_pix); |
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106 | V_vert_pix = V_vert_pix/norm(V_vert_pix); |
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107 | V_diag1_pix = V_diag1_pix/norm(V_diag1_pix); |
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108 | V_diag2_pix = V_diag2_pix/norm(V_diag2_pix); |
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109 | |
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110 | a1 = V_hori_pix(1); |
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111 | b1 = V_hori_pix(2); |
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112 | c1 = V_hori_pix(3); |
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113 | |
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114 | a2 = V_vert_pix(1); |
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115 | b2 = V_vert_pix(2); |
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116 | c2 = V_vert_pix(3); |
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117 | |
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118 | a3 = V_diag1_pix(1); |
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119 | b3 = V_diag1_pix(2); |
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120 | c3 = V_diag1_pix(3); |
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121 | |
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122 | a4 = V_diag2_pix(1); |
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123 | b4 = V_diag2_pix(2); |
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124 | c4 = V_diag2_pix(3); |
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125 | |
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126 | A_kk = [a1*a2 b1*b2; |
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127 | a3*a4 b3*b4]; |
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128 | |
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129 | b_kk = -[c1*c2;c3*c4]; |
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130 | |
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131 | |
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132 | A = [A;A_kk]; |
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133 | b = [b;b_kk]; |
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134 | |
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135 | end; |
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136 | |
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137 | end; |
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138 | |
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139 | |
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140 | % use all the vanishing points to estimate focal length: |
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141 | |
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142 | |
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143 | % Select the model for the focal. (solution to Gerd's problem) |
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144 | if ~two_focals_init |
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145 | if b'*(sum(A')') < 0, |
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146 | two_focals_init = 1; |
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147 | end; |
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148 | end; |
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149 | |
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150 | |
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151 | |
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152 | if two_focals_init |
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153 | % Use a two focals estimate: |
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154 | f_init = sqrt(abs(1./(inv(A'*A)*A'*b))); % if using a two-focal model for initial guess |
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155 | else |
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156 | % Use a single focal estimate: |
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157 | f_init = sqrt(b'*(sum(A')') / (b'*b)) * ones(2,1); % if single focal length model is used |
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158 | end; |
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159 | |
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160 | |
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161 | if ~est_aspect_ratio, |
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162 | f_init(1) = (f_init(1)+f_init(2))/2; |
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163 | f_init(2) = f_init(1); |
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164 | end; |
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165 | |
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166 | alpha_init = 0; |
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167 | |
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168 | %f_init = sqrt(b'*(sum(A')') / (b'*b)) * ones(2,1); % if single focal length model is used |
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169 | |
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170 | |
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171 | % Global calibration matrix (initial guess): |
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172 | |
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173 | KK = [f_init(1) alpha_init*f_init(1) c_init(1);0 f_init(2) c_init(2); 0 0 1]; |
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174 | inv_KK = inv(KK); |
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175 | |
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176 | |
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177 | cc = c_init; |
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178 | fc = f_init; |
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179 | kc = k_init; |
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180 | alpha_c = alpha_init; |
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181 | |
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182 | |
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183 | fprintf(1,'\n\nCalibration parameters after initialization:\n\n'); |
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184 | fprintf(1,'Focal Length: fc = [ %3.5f %3.5f ]\n',fc); |
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185 | fprintf(1,'Principal point: cc = [ %3.5f %3.5f ]\n',cc); |
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186 | fprintf(1,'Skew: alpha_c = [ %3.5f ] => angle of pixel = %3.5f degrees\n',alpha_c,90 - atan(alpha_c)*180/pi); |
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187 | fprintf(1,'Distortion: kc = [ %3.5f %3.5f %3.5f %3.5f %5.5f ]\n',kc); |
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