From 713fee8d5851c1c9442812ff013017afab9e5042 Mon Sep 17 00:00:00 2001 From: HongjunLee Date: Thu, 18 Jun 2015 11:07:06 +0900 Subject: [PATCH] Epipolar and Triangulation Epipolar and Triangulation --- Homework_5.1/2D/001.P | 3 + Homework_5.1/2D/001.corners | 542 ++++++++++++++++++++++++++++ Homework_5.1/2D/001.lines | 489 ++++++++++++++++++++++++++ Homework_5.1/2D/002.P | 3 + Homework_5.1/2D/002.corners | 448 ++++++++++++++++++++++++ Homework_5.1/2D/002.lines | 581 +++++++++++++++++++++++++++++++ Homework_5.1/2D/003.P | 3 + Homework_5.1/2D/003.corners | 322 +++++++++++++++++ Homework_5.1/2D/003.lines | 455 ++++++++++++++++++++++++ Homework_5.1/2D/README-2D | 33 ++ Homework_5.1/2D/nview-corners | 575 ++++++++++++++++++++++++++++++ Homework_5.1/2D/nview-lines | 177 ++++++++++ Homework_5.1/3D/README-3D | 8 + Homework_5.1/3D/l3d | 177 ++++++++++ Homework_5.1/3D/p3d | 575 ++++++++++++++++++++++++++++++ Homework_5.1/camera.py | 74 ++++ Homework_5.1/figure_1.png | Bin 0 -> 333154 bytes 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b/Homework_5.1/2D/README-2D new file mode 100644 index 0000000..e868668 --- /dev/null +++ b/Homework_5.1/2D/README-2D @@ -0,0 +1,33 @@ + 2D geometry and matches + ----------------------- + +Files: + ###.corners Affine multiscale Harris corners. ASCII x y coordinates, one per line + ###.lines Line segments. ASCII x0 y0 x1 y1, one per line + + nview-corners Corner matches + nview-lines Line matches + + The image coordinate frame (to which files ###.corners and ###.lines refer) + is as follows: the top-left image pixel has coordinates (0,0), first axis + aims to the right, second axis aims down. + + +Match format: (e.g. nview-corners) + + Each row of the file corresponds to one 3d feature (these features are in files + p3d and l3d) and contains #images integers (one per view) indicating + which corner is the image of the 3D point in the associated + view. Views in which the point does not appear are marked with an asterisk. + + For example the line + 134 * 132 131 * * * * * * * * + indicates that this 3D point : + corresponds to corner 134 in view 1, + has no match in view 2, + corresponds to corner 132 in view 3, + corresponds to corner 131 in view 4, + and has no matches through the rest of the sequence. + + Note that indices of points and lines start from zero, and are indices into + the appropriate ".corners" or ".lines" files. \ No newline at end of file diff --git a/Homework_5.1/2D/nview-corners b/Homework_5.1/2D/nview-corners new file mode 100644 index 0000000..5955705 --- /dev/null +++ b/Homework_5.1/2D/nview-corners @@ -0,0 +1,575 @@ + 0 0 * + 1 1 * + 2 2 * + 3 3 * + 4 * 0 + 5 4 * + 6 * 1 + 7 * 2 + 8 * 3 + 9 * 4 + 10 * 5 + 11 5 * + 12 * 6 + 13 * 7 + 14 * 8 + 15 * 9 + 16 6 * + 17 * 10 + 18 7 * + 19 8 * + 20 * 11 + 21 * 12 + 22 * 13 + 23 * 14 + 24 9 * + 25 * 15 + 26 10 * + 27 11 * + 28 * 16 + 29 12 * + 30 * 17 + 31 13 * + 32 14 * 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132 + * 259 133 + * 260 134 + * 261 * + * 262 136 + * 263 137 + * 264 138 + * 265 139 + * 266 140 + * 267 141 + * 268 142 + * 269 143 + * 270 144 + * 271 145 + * 272 146 + * 273 147 + * 274 148 + * 275 149 + * 276 150 + * 277 151 + * 278 152 + * 279 153 + * 280 154 + * 281 155 + * 282 156 + * 283 157 + * 284 158 + * 285 159 + 380 286 160 + 381 287 161 + 382 288 162 + 383 289 163 + 384 290 164 + 385 291 165 + * 292 166 + 387 293 167 + 388 294 168 + 389 295 169 + 390 296 170 + 391 297 171 + 392 298 * + 393 299 173 + 394 300 174 + 395 301 175 + 396 302 176 + 397 303 177 + 398 304 178 + 399 305 179 + 400 306 180 + 401 * * + 402 308 182 + 403 309 183 + 404 310 184 + 405 311 185 + 406 * * + 407 313 187 + 408 314 188 + 409 315 189 + 410 316 190 + 411 317 191 + 412 318 192 + * 319 * + 414 320 194 + 415 321 195 + 416 322 196 + 417 323 197 + 418 324 198 + 419 325 199 + 420 326 200 + * * * + 422 328 202 + * 329 * + 424 330 204 + 425 331 205 + 426 332 206 + 427 333 207 + 428 334 208 + 429 335 209 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b/Homework_5.1/3D/README-3D @@ -0,0 +1,8 @@ + 3D reconstruction + ----------------- + +Files: + ###.P 3x4 camera projection matrix, one per image. + p3d 3D points. ASCII x y z coordinates, one per line + l3d 3D line segments. ASCII x0 y0 z0 x1 y1 z1 one per line + arec.wrl VRML 1.0 file with points, lines and cameras \ No newline at end of file diff --git a/Homework_5.1/3D/l3d b/Homework_5.1/3D/l3d new file mode 100644 index 0000000..4be8dc1 --- /dev/null +++ b/Homework_5.1/3D/l3d @@ -0,0 +1,177 @@ + 3.7987359e-01 4.3329707e+00 -1.1007211e+00 1.4465859e+00 4.3329707e+00 -1.1007211e+00 + 3.9280047e-01 4.3142323e+00 -3.1585982e+00 1.4631623e+00 4.3142323e+00 -3.1585982e+00 + 3.4808889e+00 9.0877155e-01 3.1793866e-01 4.3926394e+00 9.0877155e-01 3.1793866e-01 + 2.1721912e+00 4.3349486e+00 -1.7906553e-01 6.9948474e-01 4.3349486e+00 -1.7906553e-01 + 4.4699253e+00 2.6026220e+00 -2.6856990e-02 3.4769378e+00 2.6026220e+00 -2.6856990e-02 + 4.6000398e+00 2.3150873e+00 2.2039226e-01 5.3679147e+00 2.3150873e+00 2.2039226e-01 + 5.4898098e+00 2.5780271e+00 -3.9742258e-02 4.5942124e+00 2.5780271e+00 -3.9742258e-02 + 2.1737073e+01 -2.4897941e+01 -1.5633306e+01 2.4845167e+01 -2.4897941e+01 -1.5633306e+01 + 3.4538917e+00 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3.3407139e-02 + 4.3520343e+00 -6.0413290e-01 2.6309313e+00 + 5.3667670e+00 -2.8479408e-01 3.9365875e-02 + 3.1923853e+00 -6.2141059e+00 5.1624334e+00 + 1.4225223e+00 1.0465825e+00 -7.0223162e-02 diff --git a/Homework_5.1/camera.py b/Homework_5.1/camera.py new file mode 100644 index 0000000..1abf519 --- /dev/null +++ b/Homework_5.1/camera.py @@ -0,0 +1,74 @@ +from numpy import * +from scipy import linalg + + +class Camera(object): + """ Class for representing pin-hole cameras. """ + + def __init__(self,P): + """ Initialize P = K[R|t] camera model. """ + self.P = P + self.K = None # calibration matrix + self.R = None # rotation + self.t = None # translation + self.c = None # camera center + + + def project(self,X): + """ Project points in X (4*n array) and normalize coordinates. """ + + x = dot(self.P,X) + for i in range(3): + x[i] /= x[2] + return x + + + def factor(self): + """ Factorize the camera matrix into K,R,t as P = K[R|t]. """ + + # factor first 3*3 part + K,R = linalg.rq(self.P[:,:3]) + + # make diagonal of K positive + T = diag(sign(diag(K))) + if linalg.det(T) < 0: + T[1,1] *= -1 + + self.K = dot(K,T) + self.R = dot(T,R) # T is its own inverse + self.t = dot(linalg.inv(self.K),self.P[:,3]) + + return self.K, self.R, self.t + + + def center(self): + """ Compute and return the camera center. """ + + if self.c is not None: + return self.c + else: + # compute c by factoring + self.factor() + self.c = -dot(self.R.T,self.t) + return self.c + + + +# helper functions + +def rotation_matrix(a): + """ Creates a 3D rotation matrix for rotation + around the axis of the vector a. """ + R = eye(4) + R[:3,:3] = linalg.expm([[0,-a[2],a[1]],[a[2],0,-a[0]],[-a[1],a[0],0]]) + return R + + +def rq(A): + from scipy.linalg import qr + + Q,R = qr(flipud(A).T) + R = flipud(R.T) + Q = Q.T + + return R[:,::-1],Q[::-1,:] diff --git a/Homework_5.1/figure_1.png b/Homework_5.1/figure_1.png new file mode 100644 index 0000000000000000000000000000000000000000..ee64de4b9524e61db711025a3216db95d4ff37db GIT binary patch literal 333154 zcmeFY1yft!7dF}!N};&B6?cc=rKL!*;ts`%6Wp!1yK7sl6n7_Ba4YV?9fA}>Ai&M< zfA9Mt?##PqGD*(tb7r#l+H0*x68%M09{VlD+ZQihU@I!fYP@)XLigguD{XW%Vq7J^@MCX;%-oXWa|*8AhwrH18~Wnk1W99DSW(OTcN;NBj(``cL$X;^_Km zWc8NGM4wWL$T!(S(pcXzqQ4qY;U-x^5%0*#w?8;NdicXJwHTyj4fIsio;uZzU4II| z3(v1+IGOl!J`Nj!`D`re*>k=7-}t!MIggEpj~vONA74iOZ(zm0`rj3Na*Ee<|C_}x z`1ZZ*f5Xy-DENPKhNoFy{C5|A@=x^_|KFpEUi@#4Y=qqZeb9f4^ncgr|Hje(JtFx3 zKS?8d21+T6ekKR)=f*9PiYe=k zOo|~pfR0u6rxwUbJ#2g>BdD4W&Hn7X+fw>~RxJf}(Zj1HS+XF=B=8|&C#lpHA{@ZL z-&VutL8nR(cXCme7!aq#QGr-Wd;}2psJvrOK(W33@aBQSi;owBkLLNj<(WElo*#1G 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