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python/structen.py 14.5 KB
 ```1 2 3 4 5 6 7``` `````` # -*- coding: utf-8 -*- """ Created on Sun Mar 12 21:54:40 2017 @author: david """ `````` ```8 9``` `````` import numpy as np import scipy as sp `````` ```10 11 12 13``` `````` import scipy.ndimage import progressbar import glob `````` `14` `````` def st2(I, s=1, dtype=np.float32): `````` ```15 16 17 18``` `````` #calculates the 2D structure tensor for an image using a gaussian window with standard deviation s #calculate the gradient `````` `19` `````` dI = np.gradient(I.astype(dtype)) `````` `20` `````` `````` ```21 22 23 24``` `````` #calculate the dimensions of the tensor field field_dims = [dI[0].shape[0], dI[0].shape[1], 3] #allocate space for the tensor field `````` `25` `````` Tg = np.zeros(field_dims, dtype=dtype) `````` ```26 27 28 29 30 31 32 33``` `````` #calculate the gradient components of the tensor ti = 0 for i in range(2): for j in range(i + 1): Tg[:, :, ti] = dI[j] * dI[i] ti = ti + 1 `````` ```34 35 36 37``` `````` #if the user does not want a blurred field if(s == 0): return Tg `````` `38` `````` #blur the tensor field `````` `39` `````` T = np.zeros(field_dims, dtype=dtype) `````` ```40 41 42 43 44 45 46``` `````` for i in range(3): T[:, :, i] = scipy.ndimage.filters.gaussian_filter(Tg[:, :, i], [s, s]) return T `````` ```47 48``` `````` def st3(I, s=1, v=[1, 1, 1], dtype=np.float32): #calculate the structure tensor field for the 3D input image I given the window size s and voxel size v `````` `49` `````` #check the format for the window size `````` `50` `````` `````` `51` `````` v = np.array(v) `````` `52` `````` print("\nCalculating gradient...") `````` `53` `````` dI = np.gradient(I.astype(dtype), v[0], v[1], v[2]) `````` ```54 55 56 57``` `````` #calculate the dimensions of the tensor field field_dims = [dI[0].shape[0], dI[0].shape[1], dI[0].shape[2], 6] #allocate space for the tensor field `````` `58` `````` Tg = np.zeros(field_dims, dtype=np.float32) `````` ```59 60 61 62 63 64 65 66 67 68 69 70 71``` `````` #calculate the gradient components of the tensor ti = 0 print("Calculating tensor components...") bar = progressbar.ProgressBar() bar.max_value = 6 for i in range(3): for j in range(i + 1): Tg[:, :, :, ti] = dI[j] * dI[i] ti = ti + 1 bar.update(ti) #blur the tensor field `````` `72` `````` T = np.zeros(field_dims, dtype=np.float32) `````` ```73 74 75 76``` `````` print("\nConvolving tensor field...") bar = progressbar.ProgressBar() bar.max_value = 6 `````` ```77 78``` `````` sigma = s / v print(sigma) `````` `79` `````` for i in range(6): `````` `80` `````` T[:, :, :, i] = scipy.ndimage.filters.gaussian_filter(Tg[:, :, :, i], sigma) `````` ```81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111``` `````` bar.update(i+1) return T def st(I, s=1): if I.ndim == 3: return st3(I, s) elif I.ndim == 2: return st2(I, s) else: print("Image must be 2D or 3D") return def sym2mat(T): #Calculate the full symmetric matrix from a list of lower triangular elements. #The lower triangular components in the input field T are assumed to be the # final dimension of the input matrix. # | 1 2 4 7 | # | 0 3 5 8 | # | 0 0 6 9 | # | 0 0 0 10 | in_s = T.shape #get the number of tensor elements n = in_s[T.ndim - 1] #calculate the dimension of the symmetric matrix `````` `112` `````` d = int(0.5 * (np.sqrt(8. * n + 1.) - 1.)) `````` ```113 114 115 116 117``` `````` #calculate the dimensions of the output field out_s = list(in_s)[:-1] + [d] + [d] #allocate space for the output field `````` `118` `````` R = np.zeros(out_s) `````` ```119 120 121 122 123 124 125 126 127 128 129``` `````` ni = 0 for i in range(d): for j in range(i + 1): R[..., i, j] = T[..., ni] if i != j: R[..., j, i] = T[..., ni] ni = ni + 1 return R `````` `130` `````` def vec(S, vector=0): `````` `131` `````` `````` ```132 133 134``` `````` if(S.ndim != 3): print("ERROR: a 2D slice is expected") return `````` ```135 136 137 138 139 140``` `````` #convert the field to a full rank-2 tensor T = sym2mat(S); del(S) #calculate the eigenvectors and eigenvalues `````` `141` `````` l, v = np.linalg.eig(T) `````` ```142 143 144 145 146``` `````` #get the dimension of the tensor field d = T.shape[2] #allocate space for the vector field `````` ```147 148 149``` `````` V = np.zeros([T.shape[0], T.shape[1], 3]) #arrange the indices for each pixel from smallest to largest eigenvalue `````` ```150 151 152``` `````` idx = l.argsort() for di in range(d): `````` `153` `````` b = idx[:, :, -1-vector] == di `````` ```154 155 156``` `````` V[b, 0:d] = v[b, :, di] return V `````` `157` `````` `````` ```158 159 160 161 162 163 164 165 166 167 168 169 170``` `````` def loadstack(filemask): #Load an image stack as a 3D grayscale array #get a list of all files matching the given mask files = [file for file in glob.glob(filemask)] #calculate the size of the output stack I = scipy.misc.imread(files[0]) X = I.shape[0] Y = I.shape[1] Z = len(files) #allocate space for the image stack `````` `171` `````` M = np.zeros([X, Y, Z]).astype('float32') `````` ```172 173 174 175 176 177 178 179 180 181 182 183``` `````` #create a progress bar bar = progressbar.ProgressBar() bar.max_value = Z #for each file for z in range(Z): #load the file and save it to the image stack M[:, :, z] = scipy.misc.imread(files[z], flatten="True").astype('float32') bar.update(z+1) return M `````` ```184 185``` `````` #calculate the anisotropy of a structure tensor given the tensor field S def anisotropy3(S): `````` ```186 187 188 189``` `````` Sf = sym2mat(S) #calculate the eigenvectors and eigenvalues `````` `190` `````` l, v = np.linalg.eig(Sf) `````` ```191 192``` `````` #store the sorted eigenvalues `````` `193` `````` ls = np.sort(l) `````` ```194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210``` `````` l0 = ls[:, :, 0] l1 = ls[:, :, 1] l2 = ls[:, :, 2] #calculate the linear anisotropy Cl = (l2 - l1)/(l2 + l1 + l0) #calculate the planar anisotropy Cp = 2 * (l1 - l0) / (l2 + l1 + l0) #calculate the spherical anisotropy Cs = 3 * l0 / (l2 + l1 + l0) #calculate the fractional anisotropy l_hat = (l0 + l1 + l2)/3 fa_num = (l2 - l_hat) ** 2 + (l1 - l_hat) ** 2 + (l0 - l_hat) ** 2; fa_den = l0 ** 2 + l1 ** 2 + l2 ** 2 `````` `211` `````` FA = np.sqrt(3./2.) * np.sqrt(fa_num) / np.sqrt(fa_den) `````` ```212 213 214``` `````` return FA, Cl, Cp, Cs `````` ```215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242``` `````` #calculate the fractional anisotropy def fa(S): Sf = sym2mat(S) #calculate the eigenvectors and eigenvalues l, v = np.linalg.eig(Sf) #store the sorted eigenvalues ls = np.sort(l) l0 = ls[:, :, 0] l1 = ls[:, :, 1] #if this is a 2D tensor, calculate and return the coherence if(S.shape[2] == 3): C = ((l0 - l1) / (l0 + l1)) ** 2 return C #if this is a 3D tensor elif(S.shape[2] == 6): l2 = ls[:, :, 2] #calculate the fractional anisotropy l_hat = (l0 + l1 + l2)/3 fa_num = (l2 - l_hat) ** 2 + (l1 - l_hat) ** 2 + (l0 - l_hat) ** 2; fa_den = l0 ** 2 + l1 ** 2 + l2 ** 2 FA = np.sqrt(3./2.) * np.sqrt(fa_num) / np.sqrt(fa_den) return FA `````` ```243 244 245 246 247 248 249 250 251 252 253 254 255 256``` `````` #calculate the specified eigenvalue for the tensor field def eigenval(S, ev): Sf = sym2mat(S) #calculate the eigenvectors and eigenvalues l, v = np.linalg.eig(Sf) #store the sorted eigenvalues ls = np.sort(l) evals = ls[:, :, ev] return evals def amira(filename, T): `````` ```257 258 259 260 261 262 263 264 265 266``` `````` #generates a tensor field that can be imported into Amira # 0 dx dx ----> 0 # 1 dx dy ----> 1 # 2 dy dy ----> 3 # 3 dx dz ----> 2 # 4 dy dz ----> 4 # 5 dz dz ----> 5 #swap the 2nd and 3rd tensor components `````` `267` `````` A = np.copy(T) `````` ```268 269``` `````` A[..., 3] = T[..., 2] A[..., 2] = T[..., 3] `````` ```270 271``` `````` #roll the tensor axis so that it is the leading component `````` `272` `````` #A = numpy.rollaxis(A, A.ndim - 1) `````` `273` `````` A.tofile(filename) `````` ```274 275 276 277 278 279 280 281 282 283 284 285 286 287``` `````` print("\n", A.shape) def resample3(T, s=2): #resample a tensor field by an integer factor s #This function first convolves the field with a box filter and then # re-samples to create a smaller field #check the format for the window size if type(s) is not list: s = [s] * 3 elif len(s) == 1: s = s * 3 elif len(s) == 2: s.insert(1, s[0]) `````` `288` `````` s = np.array(s) `````` ```289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311``` `````` bar = progressbar.ProgressBar() bar.max_value = T.shape[3] #blur with a uniform box filter of size r for t in range(T.shape[3]): T[..., t] = scipy.ndimage.filters.uniform_filter(T[..., t], 2 * s) bar.update(t+1) #resample at a rate of r R = T[::s[0], ::s[1], ::s[2], :] return R def color3(prefix, T, vector='largest', aniso=True): #Saves a stack of color images corresponding to the eigenvector and optionally scaled by anisotropy bar = progressbar.ProgressBar() bar.max_value = T.shape[2] #for each z-axis slice for z in range(T.shape[2]): S = T[:, :, z, :] #get the slice V = st2vec(S, vector='smallest') #calculate the vector `````` `312` `````` C = np.absolute(V) #calculate the absolute value `````` ```313 314 315 316 317 318 319 320``` `````` if aniso == True: #if the image is scaled by anisotropy FA, Cl, Cp, Cs = anisotropy(S) #calculate the anisotropy of the slice if vector == 'largest': A = Cl elif vector == 'smallest': A = Cp else: #otherwise just scale by 1 `````` ```321 322``` `````` A = np.ones(T.shape[0], T.shape[1]) image = C * np.expand_dims(A, 3) `````` ```323 324 325``` `````` filename = prefix + str(z).zfill(4) + ".bmp" scipy.misc.imsave(filename, image) `````` ```326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438``` `````` bar.update(z + 1) def st2stack(T, outfile, **kwargs): eigenvector = False #initialize the colormap flags to false aniso_color = False aniso_alpha = False #image = False aniso_pwr = 1 cimage_pwr = 1 aimage_pwr = 1 anisostretch = 1 #set the contrast stretch parameter alpha_channel = False alpha_image = False color_image = False for k,v in kwargs.items(): #for each argument if(k == "ev"): #if the user wants a colormap based on an eigenvector eigenvector = True #set the eigenvector flag to true ev = v #save the desired eigenvector if(k == "aniso"): #if the user wants to factor in anisotropy aniso = True #set the anisotropy flag to true aniso_channel = v #save the anisotropy channel if(k == "aniso_color"): aniso_color = v if(k == "aniso_alpha"): aniso_alpha = v if(k == "apwr"): #if the user wants to amplify the anisotropy aniso_pwr = v #set the anisotropy exponent if(k == "cipwr"): #if the user specifies the image power cimage_pwr = v if(k == "aipwr"): aimage_pwr = v if(k == "alphaimage"): Ia = v alpha_image = True if(k == "colorimage"): Ic = v color_image = True if(k == "anisostretch"): anisostretch = v if(k == "alpha"): alpha_channel = v bar = progressbar.ProgressBar() bar.max_value = T.shape[2] for i in range(0, T.shape[2]): #for i in range(0, 50): if(alpha_image or alpha_channel): img = np.ones([T.shape[0], T.shape[1], 4]) else: img = np.ones([T.shape[0], T.shape[1], 3]) if(eigenvector): V = st2vec(T[:, :, i], ev) #get the vector field for slice i corresponding to eigenvector ev img[:, :, 0:3] = V #update the image with the vector field information if(aniso): #if the user is requesting anisotropy be incorporated into the image FA, Cl, Cp, Cs = anisotropy(T[:, :, i]) #calculate the anisotropy of the tensors in slice i if(aniso_channel == "fa"): A = FA elif(aniso_channel == "l"): A = Cl elif(aniso_channel == "p"): A = Cp else: A = Cs if(aniso_alpha): print("rendering anisotropy to the alpha channel") img[:, :, 3] = A ** aniso_pwr * anisostretch if(aniso_color): print("rendering anisotropy to the color channel") img[:, :, 0:3] = img[:, :, 0:3] * np.expand_dims(A ** aniso_pwr, 3) * anisostretch if(alpha_image): img[:, :, 3] = Ia[:, :, i]/255 ** aimage_pwr if(color_image): img[:, :, 0:3] = img[:, :, 0:3] * (np.expand_dims(Ic[:, :, i], 3)/255) ** cimage_pwr #multiply the vector field by the image intensity #outname = outfile + str(i).zfill(3) + ".bmp" #get the file name to be saved outname = outfile.replace("*", str(i).zfill(3)) sp.misc.imsave(outname, np.ndarray.astype(np.abs(img)*255, "uint8")) #save the output image bar.update(i+1) #this function takes a 3D image and turns it into a stack of color images based on the structure tensor def img2stack(I, outfile, **kwargs): vs = [1, 1, 1] #set the default voxel size to 1 w = 5 for k,v in kwargs.items(): #for each argument if(k == "voxelsize"): #if the voxel size is specified if(len(v) == 1): #if the user just specifies one value vs = [v] * 3 #assume that the voxels are isotropic, create a list of 3 v's elif(len(v) == 2): #if the user specifies two values vs[0] = v[0] #assume that the voxels are isotropic along (x, y) and anisotropic along z vs[1] = v[0] vs[2] = v[1] elif(len(v) == 3): vs = v if(k == "window"): #if the user specifies a window size w = v T = st3(I, w, vs) #calculate the structure tensor st2stack(T, outfile, **kwargs) def stack2stack(infile_mask, outfile, **kwargs): I = loadstack(infile_mask) #load the file mask for k,v in kwargs.items(): #for each argument if(k == "ipwr"): img = I img2stack(I, outfile, image=img, **kwargs) #call the function to convert the image to an output ST stack ``````