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1# 

2# LSST Data Management System 

3# Copyright 2014 LSST Corporation. 

4# 

5# This product includes software developed by the 

6# LSST Project (http://www.lsst.org/). 

7# 

8# This program is free software: you can redistribute it and/or modify 

9# it under the terms of the GNU General Public License as published by 

10# the Free Software Foundation, either version 3 of the License, or 

11# (at your option) any later version. 

12# 

13# This program is distributed in the hope that it will be useful, 

14# but WITHOUT ANY WARRANTY; without even the implied warranty of 

15# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 

16# GNU General Public License for more details. 

17# 

18# You should have received a copy of the LSST License Statement and 

19# the GNU General Public License along with this program. If not, 

20# see <http://www.lsstcorp.org/LegalNotices/>. 

21# 

22 

23__all__ = ["MaskStreaksConfig", "MaskStreaksTask", "setDetectionMask"] 

24 

25import lsst.pex.config as pexConfig 

26import lsst.pipe.base as pipeBase 

27import lsst.kht 

28 

29import numpy as np 

30import scipy 

31import textwrap 

32import copy 

33from skimage.feature import canny 

34from sklearn.cluster import KMeans 

35import warnings 

36from dataclasses import dataclass 

37 

38 

39def setDetectionMask(maskedImage, forceSlowBin=False, binning=None, detectedPlane="DETECTED", 

40 badMaskPlanes=("NO_DATA", "INTRP", "BAD", "SAT", "EDGE"), detectionThreshold=5): 

41 """Make detection mask and set the mask plane 

42 

43 Creat a binary image from a masked image by setting all data with signal-to- 

44 noise below some threshold to zero, and all data above the threshold to one. 

45 If the binning parameter has been set, this procedure will be preceded by a 

46 weighted binning of the data in order to smooth the result, after which the 

47 result is scaled back to the original dimensions. Set the detection mask 

48 plane with this binary image. 

49 

50 Parameters 

51 ---------- 

52 maskedImage : `lsst.afw.image.maskedImage` 

53 Image to be (optionally) binned and converted 

54 forceSlowBin : bool (optional) 

55 Force usage of slower binning method to check that the two methods 

56 give the same result. 

57 binning : int (optional) 

58 Number of pixels by which to bin image 

59 detectedPlane : str (optional) 

60 Name of mask with pixels that were detected above threshold in image 

61 badMaskPlanes : set (optional) 

62 Names of masks with pixels that are rejected 

63 detectionThreshold : float (optional) 

64 Boundary in signal-to-noise between non-detections and detections for 

65 making a binary image from the original input image 

66 """ 

67 data = maskedImage.image.array 

68 weights = 1 / maskedImage.variance.array 

69 mask = maskedImage.getMask() 

70 

71 detectionMask = ((mask.array & mask.getPlaneBitMask(detectedPlane))) 

72 badPixelMask = mask.getPlaneBitMask(badMaskPlanes) 

73 badMask = (mask.array & badPixelMask) > 0 

74 fitMask = detectionMask.astype(bool) & ~badMask 

75 

76 fitData = np.copy(data) 

77 fitData[~fitMask] = 0 

78 fitWeights = np.copy(weights) 

79 fitWeights[~fitMask] = 0 

80 

81 if binning: 

82 # Do weighted binning: 

83 ymax, xmax = fitData.shape 

84 if (ymax % binning == 0) and (xmax % binning == 0) and (not forceSlowBin): 

85 # Faster binning method 

86 binNumeratorReshape = (fitData * fitWeights).reshape(ymax // binning, binning, 

87 xmax // binning, binning) 

88 binDenominatorReshape = fitWeights.reshape(binNumeratorReshape.shape) 

89 binnedNumerator = binNumeratorReshape.sum(axis=3).sum(axis=1) 

90 binnedDenominator = binDenominatorReshape.sum(axis=3).sum(axis=1) 

91 else: 

92 # Slower binning method when (image shape mod binsize) != 0 

93 warnings.warn('Using slow binning method--consider choosing a binsize that evenly divides ' 

94 f'into the image size, so that {ymax} mod binning == 0 ' 

95 f'and {xmax} mod binning == 0') 

96 xarray = np.arange(xmax) 

97 yarray = np.arange(ymax) 

98 xmesh, ymesh = np.meshgrid(xarray, yarray) 

99 xbins = np.arange(0, xmax + binning, binning) 

100 ybins = np.arange(0, ymax + binning, binning) 

101 numerator = fitWeights * fitData 

102 binnedNumerator, *_ = scipy.stats.binned_statistic_2d(ymesh.ravel(), xmesh.ravel(), 

103 numerator.ravel(), statistic='sum', 

104 bins=(ybins, xbins)) 

105 binnedDenominator, *_ = scipy.stats.binned_statistic_2d(ymesh.ravel(), xmesh.ravel(), 

106 fitWeights.ravel(), statistic='sum', 

107 bins=(ybins, xbins)) 

108 binnedData = np.zeros(binnedNumerator.shape) 

109 ind = binnedDenominator != 0 

110 np.divide(binnedNumerator, binnedDenominator, out=binnedData, where=ind) 

111 binnedWeight = binnedDenominator 

112 binMask = (binnedData * binnedWeight**0.5) > detectionThreshold 

113 tmpOutputMask = binMask.repeat(binning, axis=0)[:ymax] 

114 outputMask = tmpOutputMask.repeat(binning, axis=1)[:, :xmax] 

115 else: 

116 outputMask = (fitData * fitWeights**0.5) > detectionThreshold 

117 

118 # Clear existing Detected Plane: 

119 maskedImage.mask.array &= ~maskedImage.mask.getPlaneBitMask(detectedPlane) 

120 

121 # Set Detected Plane with the binary detection mask: 

122 maskedImage.mask.array[outputMask] |= maskedImage.mask.getPlaneBitMask(detectedPlane) 

123 

124 

125@dataclass 

126class Line: 

127 """A simple data class to describe a line profile. The parameter `rho` 

128 describes the distance from the center of the image, `theta` describes 

129 the angle, and `sigma` describes the width of the line. 

130 """ 

131 rho: float 

132 theta: float 

133 sigma: float = 0 

134 

135 

136class LineCollection: 

137 """Collection of `Line` objects. 

138 

139 Parameters 

140 ---------- 

141 rhos : np.ndarray 

142 Array of `Line` rho parameters 

143 thetas : np.ndarray 

144 Array of `Line` theta parameters 

145 sigmas : np.ndarray (optional) 

146 Array of `Line` sigma parameters 

147 """ 

148 

149 def __init__(self, rhos, thetas, sigmas=None): 

150 if sigmas is None: 

151 sigmas = np.zeros(len(rhos)) 

152 

153 self._lines = [Line(rho, theta, sigma) for (rho, theta, sigma) in 

154 zip(rhos, thetas, sigmas)] 

155 

156 def __len__(self): 

157 return len(self._lines) 

158 

159 def __getitem__(self, index): 

160 return self._lines[index] 

161 

162 def __iter__(self): 

163 return iter(self._lines) 

164 

165 def __repr__(self): 

166 joinedString = ", ".join(str(line) for line in self._lines) 

167 return textwrap.shorten(joinedString, width=160, placeholder="...") 

168 

169 @property 

170 def rhos(self): 

171 return np.array([line.rho for line in self._lines]) 

172 

173 @property 

174 def thetas(self): 

175 return np.array([line.theta for line in self._lines]) 

176 

177 def append(self, newLine): 

178 """Add line to current collection of lines. 

179 

180 Parameters 

181 ---------- 

182 newLine : `Line` 

183 `Line` to add to current collection of lines 

184 """ 

185 self._lines.append(copy.copy(newLine)) 

186 

187 

188class LineProfile: 

189 """Construct and/or fit a model for a linear streak. 

190 

191 This assumes a simple model for a streak, in which the streak 

192 follows a straight line in pixels space, with a Moffat-shaped profile. The 

193 model is fit to data using a Newton-Raphson style minimization algorithm. 

194 The initial guess for the line parameters is assumed to be fairly accurate, 

195 so only a narrow band of pixels around the initial line estimate is used in 

196 fitting the model, which provides a significant speed-up over using all the 

197 data. The class can also be used just to construct a model for the data with 

198 a line following the given coordinates. 

199 

200 Parameters 

201 ---------- 

202 data : np.ndarray 

203 2d array of data 

204 weights : np.ndarray 

205 2d array of weights 

206 line : `Line` (optional) 

207 Guess for position of line. Data far from line guess is masked out. 

208 Defaults to None, in which case only data with `weights` = 0 is masked 

209 out. 

210 """ 

211 

212 def __init__(self, data, weights, line=None): 

213 self.data = data 

214 self.weights = weights 

215 self._ymax, self._xmax = data.shape 

216 self._dtype = data.dtype 

217 xrange = np.arange(self._xmax) - self._xmax / 2. 

218 yrange = np.arange(self._ymax) - self._ymax / 2. 

219 self._rhoMax = ((0.5 * self._ymax)**2 + (0.5 * self._xmax)**2)**0.5 

220 self._xmesh, self._ymesh = np.meshgrid(xrange, yrange) 

221 self.mask = (weights != 0) 

222 

223 self._initLine = line 

224 self.setLineMask(line) 

225 

226 def setLineMask(self, line): 

227 """Set mask around the image region near the line 

228 

229 Parameters 

230 ---------- 

231 line : `Line` 

232 Parameters of line in the image 

233 """ 

234 if line: 

235 # Only fit pixels within 5 sigma of the estimated line 

236 radtheta = np.deg2rad(line.theta) 

237 distance = (np.cos(radtheta) * self._xmesh + np.sin(radtheta) * self._ymesh - line.rho) 

238 m = (abs(distance) < 5 * line.sigma) 

239 self.lineMask = self.mask & m 

240 else: 

241 self.lineMask = np.copy(self.mask) 

242 

243 self.lineMaskSize = self.lineMask.sum() 

244 self._maskData = self.data[self.lineMask] 

245 self._maskWeights = self.weights[self.lineMask] 

246 self._mxmesh = self._xmesh[self.lineMask] 

247 self._mymesh = self._ymesh[self.lineMask] 

248 

249 def _makeMaskedProfile(self, line, fitFlux=True): 

250 """Construct the line model in the masked region and calculate its 

251 derivatives 

252 

253 Parameters 

254 ---------- 

255 line : `Line` 

256 Parameters of line profile for which to make profile in the masked 

257 region 

258 fitFlux : bool 

259 Fit the amplitude of the line profile to the data 

260 

261 Returns 

262 ------- 

263 model : np.ndarray 

264 Model in the masked region 

265 dModel : np.ndarray 

266 Derivative of the model in the masked region 

267 """ 

268 invSigma = line.sigma**-1 

269 # Calculate distance between pixels and line 

270 radtheta = np.deg2rad(line.theta) 

271 costheta = np.cos(radtheta) 

272 sintheta = np.sin(radtheta) 

273 distance = (costheta * self._mxmesh + sintheta * self._mymesh - line.rho) 

274 distanceSquared = distance**2 

275 

276 # Calculate partial derivatives of distance 

277 drad = np.pi / 180 

278 dDistanceSqdRho = 2 * distance * (-np.ones_like(self._mxmesh)) 

279 dDistanceSqdTheta = (2 * distance * (-sintheta * self._mxmesh + costheta * self._mymesh) * drad) 

280 

281 # Use pixel-line distances to make Moffat profile 

282 profile = (1 + distanceSquared * invSigma**2)**-2.5 

283 dProfile = -2.5 * (1 + distanceSquared * invSigma**2)**-3.5 

284 

285 if fitFlux: 

286 # Calculate line flux from profile and data 

287 flux = ((self._maskWeights * self._maskData * profile).sum() 

288 / (self._maskWeights * profile**2).sum()) 

289 else: 

290 # Approximately normalize the line 

291 flux = invSigma**-1 

292 if np.isnan(flux): 

293 flux = 0 

294 

295 model = flux * profile 

296 

297 # Calculate model derivatives 

298 fluxdProfile = flux * dProfile 

299 fluxdProfileInvSigma = fluxdProfile * invSigma**2 

300 dModeldRho = fluxdProfileInvSigma * dDistanceSqdRho 

301 dModeldTheta = fluxdProfileInvSigma * dDistanceSqdTheta 

302 dModeldInvSigma = fluxdProfile * distanceSquared * 2 * invSigma 

303 

304 dModel = np.array([dModeldRho, dModeldTheta, dModeldInvSigma]) 

305 return model, dModel 

306 

307 def makeProfile(self, line, fitFlux=True): 

308 """Construct the line profile model 

309 

310 Parameters 

311 ---------- 

312 line : `Line` 

313 Parameters of the line profile to model 

314 fitFlux : bool (optional) 

315 Fit the amplitude of the line profile to the data 

316 

317 Returns 

318 ------- 

319 finalModel : np.ndarray 

320 Model for line profile 

321 """ 

322 model, _ = self._makeMaskedProfile(line, fitFlux=fitFlux) 

323 finalModel = np.zeros((self._ymax, self._xmax), dtype=self._dtype) 

324 finalModel[self.lineMask] = model 

325 return finalModel 

326 

327 def _lineChi2(self, line, grad=True): 

328 """Construct the chi2 between the data and the model 

329 

330 Parameters 

331 ---------- 

332 line : `Line` 

333 `Line` parameters for which to build model and calculate chi2 

334 grad : bool (optional) 

335 Whether or not to return the gradient and hessian 

336 

337 Returns 

338 ------- 

339 reducedChi : float 

340 Reduced chi2 of the model 

341 reducedDChi : np.ndarray 

342 Derivative of the chi2 with respect to rho, theta, invSigma 

343 reducedHessianChi : np.ndarray 

344 Hessian of the chi2 with respect to rho, theta, invSigma 

345 """ 

346 # Calculate chi2 

347 model, dModel = self._makeMaskedProfile(line) 

348 chi2 = (self._maskWeights * (self._maskData - model)**2).sum() 

349 if not grad: 

350 return chi2.sum() / self.lineMaskSize 

351 

352 # Calculate derivative and Hessian of chi2 

353 derivChi2 = ((-2 * self._maskWeights * (self._maskData - model))[None, :] * dModel).sum(axis=1) 

354 hessianChi2 = (2 * self._maskWeights * dModel[:, None, :] * dModel[None, :, :]).sum(axis=2) 

355 

356 reducedChi = chi2 / self.lineMaskSize 

357 reducedDChi = derivChi2 / self.lineMaskSize 

358 reducedHessianChi = hessianChi2 / self.lineMaskSize 

359 return reducedChi, reducedDChi, reducedHessianChi 

360 

361 def fit(self, dChi2Tol=0.1, maxIter=100): 

362 """Perform Newton-Raphson minimization to find line parameters 

363 

364 This method takes advantage of having known derivative and Hessian of 

365 the multivariate function to quickly and efficiently find the minimum. 

366 This is more efficient than the scipy implementation of the Newton- 

367 Raphson method, which doesn't take advantage of the Hessian matrix. The 

368 method here also performs a line search in the direction of the steepest 

369 derivative at each iteration, which reduces the number of iterations 

370 needed. 

371 

372 Parameters 

373 ---------- 

374 dChi2Tol : float (optional) 

375 Change in Chi2 tolerated for fit convergence 

376 maxIter : int (optional) 

377 Maximum number of fit iterations allowed. The fit should converge in 

378 ~10 iterations, depending on the value of dChi2Tol, but this 

379 maximum provides a backup. 

380 

381 Returns 

382 ------- 

383 outline : np.ndarray 

384 Coordinates and inverse width of fit line 

385 chi2 : float 

386 Reduced Chi2 of model fit to data 

387 fitFailure : bool 

388 Boolean where `False` corresponds to a successful fit 

389 """ 

390 # Do minimization on inverse of sigma to simplify derivatives: 

391 x = np.array([self._initLine.rho, self._initLine.theta, self._initLine.sigma**-1]) 

392 

393 dChi2 = 1 

394 iter = 0 

395 oldChi2 = 0 

396 fitFailure = False 

397 

398 def line_search(c, dx): 

399 testx = x - c * dx 

400 testLine = Line(testx[0], testx[1], testx[2]**-1) 

401 return self._lineChi2(testLine, grad=False) 

402 

403 while abs(dChi2) > dChi2Tol: 

404 line = Line(x[0], x[1], x[2]**-1) 

405 chi2, b, A = self._lineChi2(line) 

406 if chi2 == 0: 

407 break 

408 if not np.isfinite(A).all(): 

409 # TODO: DM-30797 Add warning here. 

410 fitFailure = True 

411 break 

412 dChi2 = oldChi2 - chi2 

413 cholesky = scipy.linalg.cho_factor(A) 

414 dx = scipy.linalg.cho_solve(cholesky, b) 

415 

416 factor, fmin, _, _ = scipy.optimize.brent(line_search, args=(dx,), full_output=True, tol=0.05) 

417 x -= factor * dx 

418 if (abs(x[0]) > 1.5 * self._rhoMax) or (iter > maxIter): 

419 fitFailure = True 

420 break 

421 oldChi2 = chi2 

422 iter += 1 

423 

424 outline = Line(x[0], x[1], abs(x[2])**-1) 

425 

426 return outline, chi2, fitFailure 

427 

428 

429class MaskStreaksConfig(pexConfig.Config): 

430 """Configuration parameters for `MaskStreaksTask` 

431 """ 

432 minimumKernelHeight = pexConfig.Field( 

433 doc="Minimum height of the streak-finding kernel relative to the tallest kernel", 

434 dtype=float, 

435 default=0.0, 

436 ) 

437 absMinimumKernelHeight = pexConfig.Field( 

438 doc="Minimum absolute height of the streak-finding kernel", 

439 dtype=float, 

440 default=5, 

441 ) 

442 clusterMinimumSize = pexConfig.Field( 

443 doc="Minimum size in pixels of detected clusters", 

444 dtype=int, 

445 default=50, 

446 ) 

447 clusterMinimumDeviation = pexConfig.Field( 

448 doc="Allowed deviation (in pixels) from a straight line for a detected " 

449 "line", 

450 dtype=int, 

451 default=2, 

452 ) 

453 delta = pexConfig.Field( 

454 doc="Stepsize in angle-radius parameter space", 

455 dtype=float, 

456 default=0.2, 

457 ) 

458 nSigma = pexConfig.Field( 

459 doc="Number of sigmas from center of kernel to include in voting " 

460 "procedure", 

461 dtype=float, 

462 default=2, 

463 ) 

464 rhoBinSize = pexConfig.Field( 

465 doc="Binsize in pixels for position parameter rho when finding " 

466 "clusters of detected lines", 

467 dtype=float, 

468 default=30, 

469 ) 

470 thetaBinSize = pexConfig.Field( 

471 doc="Binsize in degrees for angle parameter theta when finding " 

472 "clusters of detected lines", 

473 dtype=float, 

474 default=2, 

475 ) 

476 invSigma = pexConfig.Field( 

477 doc="Inverse of the Moffat sigma parameter (in units of pixels)" 

478 "describing the profile of the streak", 

479 dtype=float, 

480 default=10.**-1, 

481 ) 

482 footprintThreshold = pexConfig.Field( 

483 doc="Threshold at which to determine edge of line, in units of the line" 

484 "profile maximum", 

485 dtype=float, 

486 default=0.01 

487 ) 

488 dChi2Tolerance = pexConfig.Field( 

489 doc="Absolute difference in Chi2 between iterations of line profile" 

490 "fitting that is acceptable for convergence", 

491 dtype=float, 

492 default=0.1 

493 ) 

494 detectedMaskPlane = pexConfig.Field( 

495 doc="Name of mask with pixels above detection threshold, used for first" 

496 "estimate of streak locations", 

497 dtype=str, 

498 default="DETECTED" 

499 ) 

500 streaksMaskPlane = pexConfig.Field( 

501 doc="Name of mask plane holding detected streaks", 

502 dtype=str, 

503 default="STREAK" 

504 ) 

505 

506 

507class MaskStreaksTask(pipeBase.Task): 

508 """Find streaks or other straight lines in image data. 

509 

510 Nearby objects passing through the field of view of the telescope leave a 

511 bright trail in images. This class uses the Kernel Hough Transform (KHT) 

512 (Fernandes and Oliveira, 2007), implemented in `lsst.houghtransform`. The 

513 procedure works by taking a binary image, either provided as put or produced 

514 from the input data image, using a Canny filter to make an image of the 

515 edges in the original image, then running the KHT on the edge image. The KHT 

516 identifies clusters of non-zero points, breaks those clusters of points into 

517 straight lines, keeps clusters with a size greater than the user-set 

518 threshold, then performs a voting procedure to find the best-fit coordinates 

519 of any straight lines. Given the results of the KHT algorithm, clusters of 

520 lines are identified and grouped (generally these correspond to the two 

521 edges of a strea) and a profile is fit to the streak in the original 

522 (non-binary) image. 

523 """ 

524 

525 ConfigClass = MaskStreaksConfig 

526 _DefaultName = "maskStreaks" 

527 

528 @pipeBase.timeMethod 

529 def find(self, maskedImage): 

530 """Find streaks in a masked image 

531 

532 Parameters 

533 ---------- 

534 maskedImage : `lsst.afw.image.maskedImage` 

535 The image in which to search for streaks. 

536 

537 Returns 

538 ------- 

539 result : `lsst.pipe.base.Struct` 

540 Result struct with components: 

541 

542 - ``originalLines``: lines identified by kernel hough transform 

543 - ``lineClusters``: lines grouped into clusters in rho-theta space 

544 - ``lines``: final result for lines after line-profile fit 

545 - ``mask``: 2-d boolean mask where detected lines are True 

546 """ 

547 mask = maskedImage.getMask() 

548 detectionMask = (mask.array & mask.getPlaneBitMask(self.config.detectedMaskPlane)) 

549 

550 self.edges = self._cannyFilter(detectionMask) 

551 self.lines = self._runKHT(self.edges) 

552 

553 if len(self.lines) == 0: 

554 lineMask = np.zeros(detectionMask.shape, dtype=bool) 

555 fitLines = LineCollection([], []) 

556 clusters = LineCollection([], []) 

557 else: 

558 clusters = self._findClusters(self.lines) 

559 fitLines, lineMask = self._fitProfile(clusters, maskedImage) 

560 

561 # The output mask is the intersection of the fit streaks and the image detections 

562 outputMask = lineMask & detectionMask.astype(bool) 

563 

564 return pipeBase.Struct( 

565 lines=fitLines, 

566 lineClusters=clusters, 

567 originalLines=self.lines, 

568 mask=outputMask, 

569 ) 

570 

571 @pipeBase.timeMethod 

572 def run(self, maskedImage): 

573 """Find and mask streaks in a masked image. 

574 

575 Finds streaks in the image and modifies maskedImage in place by adding a 

576 mask plane with any identified streaks. 

577 

578 Parameters 

579 ---------- 

580 maskedImage : `lsst.afw.image.maskedImage` 

581 The image in which to search for streaks. The mask detection plane 

582 corresponding to `config.detectedMaskPlane` must be set with the 

583 detected pixels. 

584 

585 Returns 

586 ------- 

587 result : `lsst.pipe.base.Struct` 

588 Result struct with components: 

589 

590 - ``originalLines``: lines identified by kernel hough transform 

591 - ``lineClusters``: lines grouped into clusters in rho-theta space 

592 - ``lines``: final result for lines after line-profile fit 

593 """ 

594 streaks = self.find(maskedImage) 

595 

596 maskedImage.mask.addMaskPlane(self.config.streaksMaskPlane) 

597 maskedImage.mask.array[streaks.mask] |= maskedImage.mask.getPlaneBitMask(self.config.streaksMaskPlane) 

598 

599 return pipeBase.Struct( 

600 lines=streaks.lines, 

601 lineClusters=streaks.lineClusters, 

602 originalLines=streaks.originalLines, 

603 ) 

604 

605 def _cannyFilter(self, image): 

606 """Apply a canny filter to the data in order to detect edges 

607 

608 Parameters 

609 ---------- 

610 image : `np.ndarray` 

611 2-d image data on which to run filter 

612 

613 Returns 

614 ------- 

615 cannyData : `np.ndarray` 

616 2-d image of edges found in input image 

617 """ 

618 filterData = image.astype(int) 

619 return canny(filterData, low_threshold=0, high_threshold=1, sigma=0.1) 

620 

621 def _runKHT(self, image): 

622 """Run Kernel Hough Transform on image. 

623 

624 Parameters 

625 ---------- 

626 image : `np.ndarray` 

627 2-d image data on which to detect lines 

628 

629 Returns 

630 ------- 

631 result : `LineCollection` 

632 Collection of detected lines, with their detected rho and theta 

633 coordinates. 

634 """ 

635 lines = lsst.kht.find_lines(image, self.config.clusterMinimumSize, 

636 self.config.clusterMinimumDeviation, self.config.delta, 

637 self.config.minimumKernelHeight, self.config.nSigma, 

638 self.config.absMinimumKernelHeight) 

639 

640 return LineCollection(lines.rho, lines.theta) 

641 

642 def _findClusters(self, lines): 

643 """Group lines that are close in parameter space and likely describe 

644 the same streak. 

645 

646 Parameters 

647 ---------- 

648 lines : `LineCollection` 

649 Collection of lines to group into clusters 

650 

651 Returns 

652 ------- 

653 result : `LineCollection` 

654 Average `Line` for each cluster of `Line`s in the input 

655 `LineCollection` 

656 """ 

657 # Scale variables by threshold bin-size variable so that rho and theta 

658 # are on the same scale. Since the clustering algorithm below stops when 

659 # the standard deviation <= 1, after rescaling each cluster will have a 

660 # standard deviation at or below the bin-size. 

661 x = lines.rhos / self.config.rhoBinSize 

662 y = lines.thetas / self.config.thetaBinSize 

663 X = np.array([x, y]).T 

664 nClusters = 1 

665 

666 # Put line parameters in clusters by starting with all in one, then 

667 # subdividing until the parameters of each cluster have std dev=1. 

668 # If nClusters == len(lines), each line will have its own 'cluster', so 

669 # the standard deviations of each cluster must be zero and the loop 

670 # is guaranteed to stop. 

671 while True: 

672 kmeans = KMeans(n_clusters=nClusters).fit(X) 

673 clusterStandardDeviations = np.zeros((nClusters, 2)) 

674 for c in range(nClusters): 

675 inCluster = X[kmeans.labels_ == c] 

676 clusterStandardDeviations[c] = np.std(inCluster, axis=0) 

677 # Are the rhos and thetas in each cluster all below the threshold? 

678 if (clusterStandardDeviations <= 1).all(): 

679 break 

680 nClusters += 1 

681 

682 # The cluster centers are final line estimates 

683 finalClusters = kmeans.cluster_centers_.T 

684 

685 # Rescale variables: 

686 finalRhos = finalClusters[0] * self.config.rhoBinSize 

687 finalThetas = finalClusters[1] * self.config.thetaBinSize 

688 result = LineCollection(finalRhos, finalThetas) 

689 

690 return result 

691 

692 def _fitProfile(self, lines, maskedImage): 

693 """Fit the profile of the streak. 

694 

695 Given the initial parameters of detected lines, fit a model for the 

696 streak to the original (non-binary image). The assumed model is a 

697 straight line with a Moffat profile. 

698 

699 Parameters 

700 ---------- 

701 lines : `LineCollection` 

702 Collection of guesses for `Line`s detected in the image 

703 maskedImage : `lsst.afw.image.maskedImage` 

704 Original image to be used to fit profile of streak. 

705 

706 Returns 

707 ------- 

708 lineFits : `LineCollection` 

709 Collection of `Line` profiles fit to the data 

710 finalMask : `np.ndarray` 

711 2d mask array with detected streaks=1. 

712 """ 

713 data = maskedImage.image.array 

714 weights = maskedImage.variance.array**-1 

715 # Mask out any pixels with non-finite weights 

716 weights[~np.isfinite(weights) | ~np.isfinite(data)] = 0 

717 

718 lineFits = LineCollection([], []) 

719 finalLineMasks = [np.zeros(data.shape, dtype=bool)] 

720 for line in lines: 

721 line.sigma = self.config.invSigma**-1 

722 lineModel = LineProfile(data, weights, line=line) 

723 # Skip any lines that do not cover any data (sometimes happens because of chip gaps) 

724 if lineModel.lineMaskSize == 0: 

725 continue 

726 

727 fit, chi2, fitFailure = lineModel.fit(dChi2Tol=self.config.dChi2Tolerance) 

728 

729 # Initial estimate should be quite close: fit is deemed unsuccessful if rho or theta 

730 # change more than the allowed bin in rho or theta: 

731 if ((abs(fit.rho - line.rho) > 2 * self.config.rhoBinSize) 

732 or (abs(fit.theta - line.theta) > 2 * self.config.thetaBinSize)): 

733 fitFailure = True 

734 

735 if fitFailure: 

736 continue 

737 

738 # Make mask 

739 lineModel.setLineMask(fit) 

740 finalModel = lineModel.makeProfile(fit) 

741 # Take absolute value, as streaks are allowed to be negative 

742 finalModelMax = abs(finalModel).max() 

743 finalLineMask = abs(finalModel) > self.config.footprintThreshold 

744 # Drop this line if the model profile is below the footprint threshold 

745 if not finalLineMask.any(): 

746 continue 

747 fit.chi2 = chi2 

748 fit.finalModelMax = finalModelMax 

749 lineFits.append(fit) 

750 finalLineMasks.append(finalLineMask) 

751 

752 finalMask = np.array(finalLineMasks).any(axis=0) 

753 

754 return lineFits, finalMask