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aligning.py
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aligning.py
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'''
Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation
RANSAC for Similarity Transformation Estimation
Written by Srinath Sridhar
'''
import numpy as np
import cv2
import itertools
def estimateSimilarityTransform(source: np.array, target: np.array, verbose=False):
SourceHom = np.transpose(np.hstack([source, np.ones([source.shape[0], 1])]))
TargetHom = np.transpose(np.hstack([target, np.ones([source.shape[0], 1])]))
# Auto-parameter selection based on source-target heuristics
TargetNorm = np.mean(np.linalg.norm(target, axis=1))
SourceNorm = np.mean(np.linalg.norm(source, axis=1))
RatioTS = (TargetNorm / SourceNorm)
RatioST = (SourceNorm / TargetNorm)
PassT = RatioST if(RatioST>RatioTS) else RatioTS
StopT = PassT / 100
nIter = 100
if verbose:
print('Pass threshold: ', PassT)
print('Stop threshold: ', StopT)
print('Number of iterations: ', nIter)
SourceInliersHom, TargetInliersHom, BestInlierRatio = getRANSACInliers(SourceHom, TargetHom, MaxIterations=nIter, PassThreshold=PassT, StopThreshold=StopT)
if(BestInlierRatio < 0.1):
print('[ WARN ] - Something is wrong. Small BestInlierRatio: ', BestInlierRatio)
return None, None, None, None
Scales, Rotation, Translation, OutTransform = estimateSimilarityUmeyama(SourceInliersHom, TargetInliersHom)
if verbose:
print('BestInlierRatio:', BestInlierRatio)
print('Rotation:\n', Rotation)
print('Translation:\n', Translation)
print('Scales:', Scales)
return Scales, Rotation, Translation, OutTransform
def estimateRestrictedAffineTransform(source: np.array, target: np.array, verbose=False):
SourceHom = np.transpose(np.hstack([source, np.ones([source.shape[0], 1])]))
TargetHom = np.transpose(np.hstack([target, np.ones([source.shape[0], 1])]))
RetVal, AffineTrans, Inliers = cv2.estimateAffine3D(source, target)
# We assume no shear in the affine matrix and decompose into rotation, non-uniform scales, and translation
Translation = AffineTrans[:3, 3]
NUScaleRotMat = AffineTrans[:3, :3]
# NUScaleRotMat should be the matrix SR, where S is a diagonal scale matrix and R is the rotation matrix (equivalently RS)
# Let us do the SVD of NUScaleRotMat to obtain R1*S*R2 and then R = R1 * R2
R1, ScalesSorted, R2 = np.linalg.svd(NUScaleRotMat, full_matrices=True)
if verbose:
print('-----------------------------------------------------------------------')
# Now, the scales are sort in ascending order which is painful because we don't know the x, y, z scales
# Let's figure that out by evaluating all 6 possible permutations of the scales
ScalePermutations = list(itertools.permutations(ScalesSorted))
MinResidual = 1e8
Scales = ScalePermutations[0]
OutTransform = np.identity(4)
Rotation = np.identity(3)
for ScaleCand in ScalePermutations:
CurrScale = np.asarray(ScaleCand)
CurrTransform = np.identity(4)
CurrRotation = (np.diag(1 / CurrScale) @ NUScaleRotMat).transpose()
CurrTransform[:3, :3] = np.diag(CurrScale) @ CurrRotation
CurrTransform[:3, 3] = Translation
# Residual = evaluateModel(CurrTransform, SourceHom, TargetHom)
Residual = evaluateModelNonHom(source, target, CurrScale,CurrRotation, Translation)
if verbose:
# print('CurrTransform:\n', CurrTransform)
print('CurrScale:', CurrScale)
print('Residual:', Residual)
print('AltRes:', evaluateModelNoThresh(CurrTransform, SourceHom, TargetHom))
if Residual < MinResidual:
MinResidual = Residual
Scales = CurrScale
Rotation = CurrRotation
OutTransform = CurrTransform
if verbose:
print('Best Scale:', Scales)
if verbose:
print('Affine Scales:', Scales)
print('Affine Translation:', Translation)
print('Affine Rotation:\n', Rotation)
print('-----------------------------------------------------------------------')
return Scales, Rotation, Translation, OutTransform
def getRANSACInliers(SourceHom, TargetHom, MaxIterations=100, PassThreshold=200, StopThreshold=1):
BestResidual = 1e10
BestInlierRatio = 0
BestInlierIdx = np.arange(SourceHom.shape[1])
for i in range(0, MaxIterations):
# Pick 5 random (but corresponding) points from source and target
RandIdx = np.random.randint(SourceHom.shape[1], size=5)
_, _, _, OutTransform = estimateSimilarityUmeyama(SourceHom[:, RandIdx], TargetHom[:, RandIdx])
Residual, InlierRatio, InlierIdx = evaluateModel(OutTransform, SourceHom, TargetHom, PassThreshold)
if Residual < BestResidual:
BestResidual = Residual
BestInlierRatio = InlierRatio
BestInlierIdx = InlierIdx
if BestResidual < StopThreshold:
break
# print('Iteration: ', i)
# print('Residual: ', Residual)
# print('Inlier ratio: ', InlierRatio)
return SourceHom[:, BestInlierIdx], TargetHom[:, BestInlierIdx], BestInlierRatio
def evaluateModel(OutTransform, SourceHom, TargetHom, PassThreshold):
Diff = TargetHom - np.matmul(OutTransform, SourceHom)
ResidualVec = np.linalg.norm(Diff[:3, :], axis=0)
Residual = np.linalg.norm(ResidualVec)
InlierIdx = np.where(ResidualVec < PassThreshold)
nInliers = np.count_nonzero(InlierIdx)
InlierRatio = nInliers / SourceHom.shape[1]
return Residual, InlierRatio, InlierIdx[0]
def evaluateModelNoThresh(OutTransform, SourceHom, TargetHom):
Diff = TargetHom - np.matmul(OutTransform, SourceHom)
ResidualVec = np.linalg.norm(Diff[:3, :], axis=0)
Residual = np.linalg.norm(ResidualVec)
return Residual
def evaluateModelNonHom(source, target, Scales, Rotation, Translation):
RepTrans = np.tile(Translation, (source.shape[0], 1))
TransSource = (np.diag(Scales) @ Rotation @ source.transpose() + RepTrans.transpose()).transpose()
Diff = target - TransSource
ResidualVec = np.linalg.norm(Diff, axis=0)
Residual = np.linalg.norm(ResidualVec)
return Residual
def testNonUniformScale(SourceHom, TargetHom):
OutTransform = np.matmul(TargetHom, np.linalg.pinv(SourceHom))
ScaledRotation = OutTransform[:3, :3]
Translation = OutTransform[:3, 3]
Sx = np.linalg.norm(ScaledRotation[0, :])
Sy = np.linalg.norm(ScaledRotation[1, :])
Sz = np.linalg.norm(ScaledRotation[2, :])
Rotation = np.vstack([ScaledRotation[0, :] / Sx, ScaledRotation[1, :] / Sy, ScaledRotation[2, :] / Sz])
print('Rotation matrix norm:', np.linalg.norm(Rotation))
Scales = np.array([Sx, Sy, Sz])
# # Check
# Diff = TargetHom - np.matmul(OutTransform, SourceHom)
# Residual = np.linalg.norm(Diff[:3, :], axis=0)
return Scales, Rotation, Translation, OutTransform
def estimateSimilarityUmeyama(SourceHom, TargetHom):
# Copy of original paper is at: http://web.stanford.edu/class/cs273/refs/umeyama.pdf
SourceCentroid = np.mean(SourceHom[:3, :], axis=1)
TargetCentroid = np.mean(TargetHom[:3, :], axis=1)
nPoints = SourceHom.shape[1]
CenteredSource = SourceHom[:3, :] - np.tile(SourceCentroid, (nPoints, 1)).transpose()
CenteredTarget = TargetHom[:3, :] - np.tile(TargetCentroid, (nPoints, 1)).transpose()
CovMatrix = np.matmul(CenteredTarget, np.transpose(CenteredSource)) / nPoints
if np.isnan(CovMatrix).any():
print('nPoints:', nPoints)
print(SourceHom.shape)
print(TargetHom.shape)
raise RuntimeError('There are NANs in the input.')
U, D, Vh = np.linalg.svd(CovMatrix, full_matrices=True)
d = (np.linalg.det(U) * np.linalg.det(Vh)) < 0.0
if d:
D[-1] = -D[-1]
U[:, -1] = -U[:, -1]
Rotation = np.matmul(U, Vh).T # Transpose is the one that works
varP = np.var(SourceHom[:3, :], axis=1).sum()
ScaleFact = 1/varP * np.sum(D) # scale factor
Scales = np.array([ScaleFact, ScaleFact, ScaleFact])
ScaleMatrix = np.diag(Scales)
Translation = TargetHom[:3, :].mean(axis=1) - SourceHom[:3, :].mean(axis=1).dot(ScaleFact*Rotation)
OutTransform = np.identity(4)
OutTransform[:3, :3] = ScaleMatrix @ Rotation
OutTransform[:3, 3] = Translation
# # Check
# Diff = TargetHom - np.matmul(OutTransform, SourceHom)
# Residual = np.linalg.norm(Diff[:3, :], axis=0)
return Scales, Rotation, Translation, OutTransform