def findAstigmatism(fftarray, freq, defocus, resolution, ctfvalues, peakNum=1): """ find the astigmatism from a radial 1D estimate of the defocus """ #searchError = resolution/100. extrema = ctftools.getCtfExtrema(defocus, freq*1e10, ctfvalues['cs'], ctfvalues['volts'], ctfvalues['amplitude_contrast'], numzeros=peakNum*2+1, zerotype="all") if len(extrema) < 2*peakNum: return None minEdgeRadius = int(math.ceil(extrema[peakNum-1])) #first peak maxEdgeRadius = int(math.ceil(extrema[peakNum])) #second peak newshape = (maxEdgeRadius*2, maxEdgeRadius*2) print "newshape",newshape fftcenter = copy.deepcopy(imagefilter.frame_cut(fftarray, newshape)) showImage(fftcenter) shape = fftcenter.shape ## create a grid of distance from the center xhalfshape = shape[0]/2.0 x = numpy.arange(-xhalfshape, xhalfshape, 1) + 0.5 yhalfshape = shape[1]/2.0 y = numpy.arange(-yhalfshape, yhalfshape, 1) + 0.5 xx, yy = numpy.meshgrid(x, y) radialArray = xx**2 + yy**2 - 0.5 #radialArray = numpy.sqrt(radial) maxVal = fftcenter.max()*2 minVal = fftcenter.min() if debug is True: fftcenter = numpy.where(radialArray > maxEdgeRadius**2, maxVal, fftcenter) showImage(fftcenter) fftcenter = numpy.where(radialArray < minEdgeRadius**2, maxVal, fftcenter) showImage(fftcenter) angleArray = numpy.arctan2(-yy,xx) numSteps = 360 angleArray += math.pi angleArray /= 2*math.pi angleArray *= numSteps angleArray = numpy.asarray(angleArray, dtype=numpy.uint16) showImage(angleArray) dataIntegers = numpy.array(range(numSteps)) xyData = numpy.array( scipy.ndimage.measurements.minimum_position( fftcenter, angleArray, dataIntegers)) if debug is True: fftcenter[xyData[:,0], xyData[:,1]] = maxVal*3 showImage(fftcenter) ellipseParams = ellipse.totalLeastSquareEllipse(xyData, center=(xhalfshape, yhalfshape)) if ellipseParams is None: return None ellipse.printParamsDict(ellipseParams) if debug is True: numPoints = int(math.pi*(ellipseParams['a']+ellipseParams['b'])) ellPoints = ellipse.generate_ellipse(ellipseParams['a'], ellipseParams['b'], ellipseParams['alpha'], center=ellipseParams['center'], numpoints=numPoints, integers=True) fftcenter[ellPoints[:,0], ellPoints[:,1]] += maxVal showImage(fftcenter) return ellipseParams
def ellipseRANSAC(edgeMap, ellipseThresh=2, minPercentGoodPoints=0.001,
certainProb=0.9, maxiter=10000, maxRatio=4.0):
"""
takes 2D edge map from image and trys to find a good ellipse in the data
"""
shrinkEdgeMap = numpy.float64(trimZeroEdges(edgeMap))
#shrinkEdgeMap = numpy.float64(edgeMap)
shape = shrinkEdgeMap.shape
print "RANSAC shape", shape
## make a list of edges, with x, y radii
bottomEdgeMap = numpy.copy(shrinkEdgeMap)
bottomEdgeMap[:shape[0]/2,:] = 0
topEdgeMap = numpy.copy(shrinkEdgeMap)
topEdgeMap[shape[0]/2:,:] = 0
rightEdgeMap = numpy.copy(shrinkEdgeMap)
rightEdgeMap[:,:shape[1]/2] = 0
leftEdgeMap = numpy.copy(shrinkEdgeMap)
leftEdgeMap[:,shape[1]/2:] = 0
#sort edges into quadrants and choose that way
center = numpy.array(shape, dtype=numpy.float64)/2.0 - 0.5
edgeList = numpy.array(numpy.where(shrinkEdgeMap), dtype=numpy.float64).transpose() - center
bottomEdgeList = numpy.array(numpy.where(bottomEdgeMap), dtype=numpy.float64).transpose() - center
topEdgeList = numpy.array(numpy.where(topEdgeMap), dtype=numpy.float64).transpose() - center
rightEdgeList = numpy.array(numpy.where(rightEdgeMap), dtype=numpy.float64).transpose() - center
leftEdgeList = numpy.array(numpy.where(leftEdgeMap), dtype=numpy.float64).transpose() - center
numEdges = shrinkEdgeMap.sum()
if numEdges != len(edgeList):
print "something weird in array sizes"
return None
numSamples = 4
## count rejects
areaReject = 0
distReject = 0
ratioReject = 0
sizeReject = 0
validEllipse = 0
## reject criteria
maxDistFromCenter = math.hypot(shape[0], shape[1])/10.0
squareArea = max(edgeMap.shape)**2/4 #quarter of the image, little less than indcribed circle
maxShrinkRadius = int(max(shape)*0.7) #to the corner of shrink image
maxNormRadius = max(edgeMap.shape)/2 #to the side of full image
maxRadius = min(maxShrinkRadius, maxNormRadius)
minGoodPoints = minPercentGoodPoints*numEdges
finalMinEdges = numEdges*(1.0 - math.exp( math.log(1.0-certainProb)/maxiter ) )**(1.0/numSamples)
mostGoodPoints = 0
bestEllipseParams = None # {'center':(x,y), 'a':a, 'b':b, 'alpha':radians}
iternum = 0
t0 = time.time()
while iternum <= maxiter:
iternum += 1
currentProb = 1.0 - math.exp( math.log(1.0-certainProb)/iternum )
currentProb = currentProb**(1.0/numSamples)
if iternum % 500 == 0:
print ("RANSAC iter=%d/%d, points=%d, need=%d->%d, bestProb=%.1f, timePer=%.4f"
%(iternum, maxiter, mostGoodPoints, currentProb*numEdges,
finalMinEdges, mostGoodPoints/float(numEdges)*100,
(time.time()-t0)/float(iternum)))
## check to see if we can stop
if mostGoodPoints > currentProb*numEdges:
#currentProb = mostGoodPoints/float(numEdges)
#print "currentProb", currentProb
#successProb = 1.0 - math.exp( iternum * math.log(1.0 - currentProb**numSamples) )
print "\nRANSAC SUCCESS"
break
if currentProb < minPercentGoodPoints:
print "\nRANSAC FAILURE"
break
if iternum >= maxiter:
print "\nRANSAC GAVE UP"
break
#choose random edges
#might be better to sort edges into quadrants and choose that way
currentEdges = []
if len(bottomEdgeList) > 0:
currentEdges.append(random.choice(bottomEdgeList))
if len(topEdgeList) > 0:
currentEdges.append(random.choice(topEdgeList))
if len(leftEdgeList) > 0:
currentEdges.append(random.choice(leftEdgeList))
if len(rightEdgeList) > 0:
currentEdges.append(random.choice(rightEdgeList))
##NEIL IDEA: could select a random edge instead of an edge point???
if len(currentEdges) < 3:
print "error not enough edges"
break
currentEdges = numpy.array(currentEdges, dtype=numpy.int16)
## convert rows, columns into x, y by swapping columns
convertEdges = currentEdges.copy()
convertEdges[:,[0, 1]] = currentEdges[:,[1, 0]]
convertEdges = numpy.vstack( (currentEdges[:,1], currentEdges[:,0]) ).T
# solve centered ellipse, fixed center
centeredParams = ellipse.solveEllipseOLS(convertEdges)
#print centeredParams
if centeredParams is None:
#sys.stderr.write("c")
continue
## check to see if ellipse has a area smaller than circle inscribed in image
area = centeredParams['a'] * centeredParams['b']
if area > squareArea:
areaReject += 1
#sys.stderr.write("A%d "%(areaReject))
continue
radius = max(centeredParams['a'],centeredParams['b'])
if radius > maxRadius:
sizeReject += 1
#sys.stderr.write("S%d "%(sizeReject))
continue
ratio = centeredParams['a']/float(centeredParams['b'])
if ratio > maxRatio or ratio < 1.0/maxRatio:
ratioReject += 1
#sys.stderr.write("R%d "%(ratioReject))
continue
## check to see if ellipse has a circumference smaller than something
# solve general ellipse, floating center
## only a few points, can use solveEllipseGander fit
#generalParams = ellipse.solveEllipseB2AC(convertEdges)
generalParams = ellipse.solveEllipseGander(convertEdges)
if generalParams is not None:
## check center to see if its reasonably close to center
distFromCenter = math.hypot(generalParams['center'][0], generalParams['center'][1])
if distFromCenter > maxDistFromCenter:
distReject += 1
#sys.stderr.write("D%d "%(distReject))
continue
## check to see if ellipse has a area smaller than circle inscribed in image
area = math.pi * centeredParams['a'] * centeredParams['b']
if area > squareArea:
areaReject += 1
#sys.stderr.write("a%d "%(areaReject))
continue
radius = max(centeredParams['a'],centeredParams['b'])
if radius > maxRadius:
sizeReject += 1
#sys.stderr.write("s%d "%(sizeReject))
continue
ratio = centeredParams['a']/float(centeredParams['b'])
if ratio > maxRatio or ratio < 1.0/maxRatio:
## should be a > b
ratioReject += 1
#sys.stderr.write("r%d "%(ratioReject))
continue
## create an outline of the ellipse
ellipseMap = generateEllipseRangeMap2(centeredParams, ellipseThresh, shape)
if ellipseMap is None:
continue
## take overlap of edges and fit area to determine number of good points
goodPoints = (shrinkEdgeMap*ellipseMap).sum()
#if goodPoints > mostGoodPoints or iternum%100 == 0:
# print ("\ngood points=%d (best=%d; need=%d->%d, bestProb=%.1f, iter=%d/%d, timePer=%.4f)"
# %(goodPoints, mostGoodPoints, currentProb*numEdges, finalMinEdges,
# mostGoodPoints/float(numEdges)*100, iternum, maxiter,
# (time.time()-t0)/float(iternum)))
validEllipse += 1
if goodPoints < minGoodPoints or goodPoints < mostGoodPoints:
#sys.stderr.write(".")
continue
if goodPoints > mostGoodPoints:
### refine the ellipse parameters to see if we can do better
centeredEllipseMap1 = generateEllipseRangeMap2(centeredParams, ellipseThresh, shape)
centeredEllipseList1 = numpy.array(numpy.where(centeredEllipseMap1), dtype=numpy.float64).transpose() - center
betterEllipseParams1 = ellipse.totalLeastSquareEllipse(centeredEllipseList1)
betterEllipseMap1 = generateEllipseRangeMap2(betterEllipseParams1, ellipseThresh, shape)
betterGoodPoints1 = (shrinkEdgeMap*betterEllipseMap1).sum()
centeredEllipseMap2 = generateEllipseRangeMap2(centeredParams, ellipseThresh*8, shape)
centeredEllipseList2 = numpy.array(numpy.where(centeredEllipseMap2), dtype=numpy.float64).transpose() - center
betterEllipseParams2 = ellipse.totalLeastSquareEllipse(centeredEllipseList2)
betterEllipseMap2 = generateEllipseRangeMap2(betterEllipseParams2, ellipseThresh, shape)
betterGoodPoints2 = (shrinkEdgeMap*betterEllipseMap2).sum()
#print goodPoints, betterGoodPoints1, betterGoodPoints2
if betterGoodPoints1 > goodPoints and betterGoodPoints1 > betterGoodPoints2:
bestEllipseParams = betterEllipseParams1
mostGoodPoints = betterGoodPoints1
elif betterGoodPoints2 > goodPoints:
bestEllipseParams = betterEllipseParams2
mostGoodPoints = betterGoodPoints2
else:
bestEllipseParams = centeredParams
mostGoodPoints = goodPoints
printParams(bestEllipseParams)
#if iternum > 100:
# imagefile.arrayToJpeg(centeredEllipseMap1, "map%05d.jpg"%(iternum))
### end loop and do stuff
#bestEllipseMap = generateEllipseRangeMap2(bestEllipseParams, ellipseThresh*1.5, edgeMap.shape)
#bestEllipseList = numpy.array(numpy.where(bestEllipseMap), dtype=numpy.float64).transpose() - center
#betterEllipseParams = ellipse.solveEllipseOLS(bestEllipseList)
print "total iterations", iternum
print "\tpercent good points %.1f"%(mostGoodPoints/float(numEdges)*100)
print "\ttime per iter %.2f ms"%(1000.*(time.time()-t0)/float(iternum))
print "\tvalid ellipses", validEllipse
print "\toff-center rejects", distReject
print "\tlarge area rejects", areaReject
print "\tlarge radius rejects", sizeReject
print "\toblong ratio rejects", ratioReject
if bestEllipseParams is not None:
printParams(bestEllipseParams)
else:
print "Fit failed"
return None
return bestEllipseParams
def findAstigmatism(fftarray, freq, defocus, resolution, ctfvalues, peakNum=1):
"""
find the astigmatism from a radial 1D estimate of the defocus
"""
#searchError = resolution/100.
extrema = ctftools.getCtfExtrema(defocus, freq*1e10,
ctfvalues['cs'], ctfvalues['volts'], ctfvalues['amplitude_contrast'],
numzeros=peakNum*2+1, zerotype="all")
if len(extrema) < 2*peakNum:
return None
minEdgeRadius = int(math.ceil(extrema[peakNum-1])) #first peak
maxEdgeRadius = int(math.ceil(extrema[peakNum])) #second peak
newshape = (maxEdgeRadius*2, maxEdgeRadius*2)
print "newshape",newshape
fftcenter = copy.deepcopy(imagefilter.frame_cut(fftarray, newshape))
showImage(fftcenter)
shape = fftcenter.shape
## create a grid of distance from the center
xhalfshape = shape[0]/2.0
x = numpy.arange(-xhalfshape, xhalfshape, 1) + 0.5
yhalfshape = shape[1]/2.0
y = numpy.arange(-yhalfshape, yhalfshape, 1) + 0.5
xx, yy = numpy.meshgrid(x, y)
radialArray = xx**2 + yy**2 - 0.5
#radialArray = numpy.sqrt(radial)
maxVal = fftcenter.max()*2
minVal = fftcenter.min()
if debug is True:
fftcenter = numpy.where(radialArray > maxEdgeRadius**2, maxVal, fftcenter)
showImage(fftcenter)
fftcenter = numpy.where(radialArray < minEdgeRadius**2, maxVal, fftcenter)
showImage(fftcenter)
angleArray = numpy.arctan2(-yy,xx)
numSteps = 360
angleArray += math.pi
angleArray /= 2*math.pi
angleArray *= numSteps
angleArray = numpy.asarray(angleArray, dtype=numpy.uint16)
showImage(angleArray)
dataIntegers = numpy.array(range(numSteps))
xyData = numpy.array(
scipy.ndimage.measurements.minimum_position(
fftcenter, angleArray, dataIntegers))
if debug is True:
fftcenter[xyData[:,0], xyData[:,1]] = maxVal*3
showImage(fftcenter)
ellipseParams = ellipse.totalLeastSquareEllipse(xyData, center=(xhalfshape, yhalfshape))
if ellipseParams is None:
return None
ellipse.printParamsDict(ellipseParams)
if debug is True:
numPoints = int(math.pi*(ellipseParams['a']+ellipseParams['b']))
ellPoints = ellipse.generate_ellipse(ellipseParams['a'], ellipseParams['b'],
ellipseParams['alpha'], center=ellipseParams['center'], numpoints=numPoints, integers=True)
fftcenter[ellPoints[:,0], ellPoints[:,1]] += maxVal
showImage(fftcenter)
return ellipseParams