def printStatus(self,q):
"""Prints a status printout summarizing all tasks' errors."""
priorities = set()
names = dict()
errors = dict()
totalerrors = dict()
for t in self.taskList:
if t.weight==0: continue
priorities.add(t.level)
s = t.name
if len(s) > 8:
s = s[0:8]
err = t.getSensedError(q)
names.setdefault(t.level,[]).append(s)
errors.setdefault(t.level,[]).append("%.3f"%(vectorops.norm(err)),)
werrsq = vectorops.normSquared(vectorops.mul(err,t.weight))
totalerrors[t.level] = totalerrors.get(t.level,0.0) + werrsq
cols = 5
colwidth = 10
for p in priorities:
print "Priority",p,"weighted error^2",totalerrors[p]
pnames = names[p]
perrs = errors[p]
start = 0
while start < len(pnames):
last = min(start+cols,len(pnames))
print " Name: ",
for i in range(start,last):
print pnames[i],' '*(colwidth-len(pnames[i])),
print
print " Error: ",
for i in range(start,last):
print perrs[i],' '*(colwidth-len(perrs[i])),
print
start=last
def printStatus(self,q):
"""Prints a status printout summarizing all tasks' errors."""
priorities = set()
names = dict()
errors = dict()
totalerrors = dict()
for t in self.taskList:
if t.weight==0: continue
priorities.add(t.level)
s = t.name
if len(s) > 8:
s = s[0:8]
err = t.getSensedError(q)
names.setdefault(t.level,[]).append(s)
errors.setdefault(t.level,[]).append("%.3f"%(vectorops.norm(err)),)
werrsq = vectorops.normSquared(vectorops.mul(err,t.weight))
totalerrors[t.level] = totalerrors.get(t.level,0.0) + werrsq
cols = 5
colwidth = 10
for p in priorities:
print "Priority",p,"weighted error^2",totalerrors[p]
pnames = names[p]
perrs = errors[p]
start = 0
while start < len(pnames):
last = min(start+cols,len(pnames))
print " Name: ",
for i in range(start,last):
print pnames[i],' '*(colwidth-len(pnames[i])),
print
print " Error: ",
for i in range(start,last):
print perrs[i],' '*(colwidth-len(perrs[i])),
print
start=last
def extendTrace(self, trace, T):
if len(trace) < 2:
trace.append(T)
else:
pprev = trace[-2]
prev = trace[-1]
#check linearity
eold = se3.error(trace[-1], trace[-2])
enew = se3.error(T, trace[-1])
if angle(eold,
enew) > 0.1 or vectorops.normSquared(eold) > 0.02 * 0.02:
trace.append(T)
else:
#near-linear
trace[-1] = T
def calibrate_xform_camera(camera_link_transforms,
marker_link_transforms,
marker_observations,
marker_ids,
observation_relative_errors=None,
camera_initial_guess=None,
marker_initial_guess=None,
regularizationFactor=0,
maxIters=100,
tolerance=1e-7):
"""Single camera calibration function for a camera and markers on some
set of rigid bodies.
Given body transforms and a list of estimated calibration marker observations
in the camera frame, estimates both the camera transform relative to the
camera link as well as the marker transforms relative to their links.
M: is the set of m markers. By default there is at most one marker per link.
Markers can either be point markers (e.g., a mocap ball), or transform
markers (e.g., an AR tag or checkerboard pattern).
O: is the set of n observations, consisting of a reading (Tc_i,Tm_i,o_i,l_i)
where Tc_i is the camera link's transform, Tm_i is the marker link's
transform, o_i is the reading which consists of either a point or transform
estimate in the camera frame, and l_i is the ID of the marker (by default,
just its link)
Output: a tuple (err,Tc,marker_dict) where err is the norm of the
reconstruction residual, Tc is the estimated camera transform relative to the
camera's link, and marker_dict is a dict mapping each marker id to its
estimated position or transform on the marker's link.
Arguments:
- camera_link: an integer index or a RobotModelLink instance on which
the camera lies.
- calibration_configs: a list of the RobotModel configurations q_1,...,q_n
that generated the marker_observations list.
- marker_observations: a list of estimated positions or transformations
of calibration markers o_1,...,o_n, given in the camera's reference
frame (z forward, x right, y down).
If o_i is a 3-vector, the marker is considered to be a point marker.
If a se3 element (R,t) is given, the marker is considered to be
a transform marker. You may not mix point and transform observations
for a single marker ID.
- marker_ids: a list of marker ID #'s l_1,...,l_n corresponding to
each observation, e.g., the link index on which each marker lies.
- observation_relative_errors: if you have an idea of the magnitude of
each observation error, it can be placed into this list. Must be
a list of n floats, 3-lists (point markers), or 6-lists (transform
markers). By default, errors will be set proportionally to the
observed distance between the camera and marker.
- camera_initial_guess: if not None, an initial guess for the camera transform
- marker_initial_guess: if not None, a dictionary containing initial guesses
for the marker transforms
- regularizationFactor: if nonzero, the optimization penalizes deviation
of the estimated camera transform and marker transforms from zero
proportionally to this factor.
- maxIters: maximum number of iterations for optimization.
- tolerance: optimization convergence tolerance. Stops when the change of
estimates falls below this threshold
"""
if len(camera_link_transforms) != len(marker_ids):
raise ValueError("Must provide the same number of marker IDs as camera transforms")
if len(marker_link_transforms) != len(marker_ids):
raise ValueError("Must provide the same number of marker IDs as marker transforms")
if len(marker_observations) != len(marker_ids):
raise ValueError("Must provide the same number of marker observations as marker transforms")
#get all unique marker ids
marker_id_list = list(set(marker_ids))
#detect marker types
marker_types = dict((v,None) for v in marker_id_list)
for i,(obs,id) in enumerate(zip(marker_observations,marker_ids)):
if len(obs)==3:
if marker_types[id] == 't':
raise ValueError("Provided both point and transform observations for observation #%d, id %s\n"%(i,str(id)))
marker_types[id] = 'p'
elif len(obs)==2 and len(obs[0])==9 and len(obs[1])==3:
if marker_types[id] == 'p':
raise ValueError("Provided both point and transform observations for observation #%d, id %s\n"%(i,str(id)))
marker_types[id] = 't'
else:
raise ValueError("Invalid observation for observation #%d, id %s\n"%(i,str(id)))
n = len(marker_observations)
m = len(marker_id_list)
#get all the observation weights
observation_weights = []
if observation_relative_errors is None:
#default weights: proportional to distance
for obs in marker_observations:
if len(obs) == 3:
observation_weights.append(1.0/vectorops.norm(obs))
else:
observation_weights.append(1.0/vectorops.norm(obs[1]))
observation_weights = [1.0]*len(observation_weights)
else:
if len(observation_relative_errors) != n:
raise ValueError("Invalid length of observation errors")
for err in observation_relative_errors:
if hasattr(err,'__iter__'):
observation_weights.append([1.0/v for v in err])
else:
observation_weights.append(1.0/err)
#initial guesses
if camera_initial_guess == None:
camera_initial_guess = se3.identity()
if any(v == 't' for v in marker_types.itervalues()):
#estimate camera rotation from point estimates because rotations are more prone to initialization failures
point_observations = []
marker_point_rel = []
for i,obs in enumerate(marker_observations):
if len(obs)==2:
point_observations.append(obs[1])
else:
point_observations.append(obs)
marker_point_rel.append(se3.mul(se3.inv(camera_link_transforms[i]),marker_link_transforms[i])[1])
camera_initial_guess = (point_fit_rotation_3d(point_observations,marker_point_rel),[0.0]*3)
print "Estimated camera rotation from points:",camera_initial_guess
if marker_initial_guess == None:
marker_initial_guess = dict((l,(se3.identity() if marker_types[l]=='t' else [0.0]*3)) for l in marker_id_list)
else:
marker_initial_guess = marker_initial_guess.copy()
for l in marker_id_list:
if l not in marker_initial_guess:
marker_initial_guess[l] = (se3.identity() if marker_types[l]=='t' else [0.0]*3)
camera_transform = camera_initial_guess
marker_transforms = marker_initial_guess.copy()
if DO_VISUALIZATION:
rgroup = coordinates.addGroup("calibration")
rgroup.addFrame("camera link",worldCoordinates=camera_link_transforms[-1])
rgroup.addFrame("marker link",worldCoordinates=marker_link_transforms[-1])
rgroup.addFrame("camera estimate",parent="camera link",relativeCoordinates=camera_transform)
rgroup.addFrame("marker estimate",parent="marker link",relativeCoordinates=marker_transforms.values()[0])
for i,obs in enumerate(marker_observations):
rgroup.addFrame("obs"+str(i)+" estimate",parent="camera estimate",relativeCoordinates=obs)
vis.add("coordinates",rgroup)
vis.dialog()
point_observations_only = all(marker_types[marker] == 'p' for marker in marker_id_list)
xform_observations_only = all(marker_types[marker] == 't' for marker in marker_id_list)
if not point_observations_only and not xform_observations_only:
raise NotImplementedError("Can't calibrate camera from mixed point/transform markers yet")
for iters in range(maxIters):
#attempt to minimize the error on the following over all observations i
#camera_link_transform(q_i)*camera_transform*observation_i = marker_link_transform(l_i,q_i)*marker_transform(l_i)
#first, we'll assume the camera transform is fixed and then optimize the marker transforms.
#then, we'll assume the marker transforms are fixed and then optimize the camera transform.
#finally we'll check the error to detect convergence
#1. Estimate marker transforms from current camera transform
new_marker_transforms = dict((l,(TransformStats(zero=marker_initial_guess[l],prior=regularizationFactor) if marker_types[l]=='t' else VectorStats(value,zero=[0.0]*3,prior=RegularizationFactor))) for l in marker_id_list)
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
Trel = se3.mul(se3.inv(Tmlink),se3.mul(Tclink,camera_transform))
if marker_types[marker] == 't':
estimate = se3.mul(Trel,obs)
else:
estimate = se3.apply(Trel,obs)
new_marker_transforms[marker].add(estimate,observation_weights[i])
print "ITERATION",iters
#print " ESTIMATED MARKER TRANSFORMS:",dict((k,v.average) for (k,v) in new_marker_transforms.iteritems())
#2. Estimate camera transform from current marker transforms
new_camera_transform = TransformStats(zero=camera_initial_guess,prior=regularizationFactor)
if point_observations_only:
#TODO: weighted point fitting
relative_points = []
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
pRel = se3.apply(se3.inv(Tclink),se3.apply(Tmlink,new_marker_transforms[marker].average))
relative_points.append(pRel)
new_camera_transform.add(point_fit_xform_3d(marker_observations,relative_points),sum(observation_weights))
else:
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
Trel = se3.mul(se3.inv(Tclink),se3.mul(Tmlink,new_marker_transforms[marker].average))
estimate = se3.mul(Trel,se3.inv(obs))
new_camera_transform.add(estimate,observation_weights[i])
#print " ESTIMATED CAMERA TRANSFORMS:",new_camera_transform.average
#3. compute difference between last and current estimates
diff = 0.0
diff += vectorops.normSquared(se3.error(camera_transform,new_camera_transform.average))
for marker in marker_id_list:
if marker_types[marker]=='t':
diff += vectorops.normSquared(se3.error(marker_transforms[marker],new_marker_transforms[marker].average))
else:
diff += vectorops.distanceSquared(marker_transforms[marker],new_marker_transforms[marker].average)
camera_transform = new_camera_transform.average
for marker in marker_id_list:
marker_transforms[marker] = new_marker_transforms[marker].average
if math.sqrt(diff) < tolerance:
#converged!
print "Converged with diff %g on iteration %d"%(math.sqrt(diff),iters)
break
print " ESTIMATE CHANGE:",math.sqrt(diff)
error = 0.0
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
Tc = se3.mul(Tclink,camera_transform)
if marker_types[marker] == 't':
Tm = se3.mul(Tmlink,marker_transforms[marker])
error += vectorops.normSquared(se3.error(se3.mul(Tc,obs),Tm))
else:
Tm = se3.apply(Tmlink,marker_transforms[marker])
error += vectorops.distanceSquared(se3.apply(Tc,obs),Tm)
print " OBSERVATION ERROR:",math.sqrt(error)
#raw_input()
if DO_VISUALIZATION:
rgroup.setFrameCoordinates("camera estimate",camera_transform)
rgroup.setFrameCoordinates("marker estimate",marker_transforms.values()[0])
for i,obs in enumerate(marker_observations):
rgroup.setFrameCoordinates("obs"+str(i)+" estimate",obs)
vis.add("coordinates",rgroup)
vis.dialog()
if math.sqrt(diff) >= tolerance:
print "Max iters reached"
error = 0.0
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
Tc = se3.mul(Tclink,camera_transform)
if marker_types[marker] == 't':
Tm = se3.mul(Tmlink,marker_transforms[marker])
error += vectorops.normSquared(se3.error(se3.mul(Tc,obs),Tm))
else:
Tm = se3.apply(Tmlink,marker_transforms[marker])
error += vectorops.distanceSquared(se3.apply(Tc,obs),Tm)
return (math.sqrt(error),camera_transform,marker_transforms)
def calibrate_xform_camera(camera_link_transforms,
marker_link_transforms,
marker_observations,
marker_ids,
observation_relative_errors=None,
camera_initial_guess=None,
marker_initial_guess=None,
regularizationFactor=0,
maxIters=100,
tolerance=1e-7):
"""Single camera calibration function for a camera and markers on some
set of rigid bodies.
Given body transforms and a list of estimated calibration marker observations
in the camera frame, estimates both the camera transform relative to the
camera link as well as the marker transforms relative to their links.
M: is the set of m markers. By default there is at most one marker per link.
Markers can either be point markers (e.g., a mocap ball), or transform
markers (e.g., an AR tag or checkerboard pattern).
O: is the set of n observations, consisting of a reading (Tc_i,Tm_i,o_i,l_i)
where Tc_i is the camera link's transform, Tm_i is the marker link's
transform, o_i is the reading which consists of either a point or transform
estimate in the camera frame, and l_i is the ID of the marker (by default,
just its link)
Output: a tuple (err,Tc,marker_dict) where err is the norm of the
reconstruction residual, Tc is the estimated camera transform relative to the
camera's link, and marker_dict is a dict mapping each marker id to its
estimated position or transform on the marker's link.
Arguments:
- camera_link: an integer index or a RobotModelLink instance on which
the camera lies.
- calibration_configs: a list of the RobotModel configurations q_1,...,q_n
that generated the marker_observations list.
- marker_observations: a list of estimated positions or transformations
of calibration markers o_1,...,o_n, given in the camera's reference
frame (z forward, x right, y down).
If o_i is a 3-vector, the marker is considered to be a point marker.
If a se3 element (R,t) is given, the marker is considered to be
a transform marker. You may not mix point and transform observations
for a single marker ID.
- marker_ids: a list of marker ID #'s l_1,...,l_n corresponding to
each observation, e.g., the link index on which each marker lies.
- observation_relative_errors: if you have an idea of the magnitude of
each observation error, it can be placed into this list. Must be
a list of n floats, 3-lists (point markers), or 6-lists (transform
markers). By default, errors will be set proportionally to the
observed distance between the camera and marker.
- camera_initial_guess: if not None, an initial guess for the camera transform
- marker_initial_guess: if not None, a dictionary containing initial guesses
for the marker transforms
- regularizationFactor: if nonzero, the optimization penalizes deviation
of the estimated camera transform and marker transforms from zero
proportionally to this factor.
- maxIters: maximum number of iterations for optimization.
- tolerance: optimization convergence tolerance. Stops when the change of
estimates falls below this threshold
"""
if len(camera_link_transforms) != len(marker_ids):
raise ValueError("Must provide the same number of marker IDs as camera transforms")
if len(marker_link_transforms) != len(marker_ids):
raise ValueError("Must provide the same number of marker IDs as marker transforms")
if len(marker_observations) != len(marker_ids):
raise ValueError("Must provide the same number of marker observations as marker transforms")
#get all unique marker ids
marker_id_list = list(set(marker_ids))
#detect marker types
marker_types = dict((v,None) for v in marker_id_list)
for i,(obs,id) in enumerate(zip(marker_observations,marker_ids)):
if len(obs)==3:
if marker_types[id] == 't':
raise ValueError("Provided both point and transform observations for observation #%d, id %s\n"%(i,str(id)))
marker_types[id] = 'p'
elif len(obs)==2 and len(obs[0])==9 and len(obs[1])==3:
if marker_types[id] == 'p':
raise ValueError("Provided both point and transform observations for observation #%d, id %s\n"%(i,str(id)))
marker_types[id] = 't'
else:
raise ValueError("Invalid observation for observation #%d, id %s\n"%(i,str(id)))
n = len(marker_observations)
m = len(marker_id_list)
#get all the observation weights
observation_weights = []
if observation_relative_errors is None:
#default weights: proportional to distance
for obs in marker_observations:
if len(obs) == 3:
observation_weights.append(1.0/vectorops.norm(obs))
else:
observation_weights.append(1.0/vectorops.norm(obs[1]))
observation_weights = [1.0]*len(observation_weights)
else:
if len(observation_relative_errors) != n:
raise ValueError("Invalid length of observation errors")
for err in observation_relative_errors:
if hasattr(err,'__iter__'):
observation_weights.append([1.0/v for v in err])
else:
observation_weights.append(1.0/err)
#initial guesses
if camera_initial_guess == None:
camera_initial_guess = se3.identity()
if any(v == 't' for v in marker_types.itervalues()):
#estimate camera rotation from point estimates because rotations are more prone to initialization failures
point_observations = []
marker_point_rel = []
for i,obs in enumerate(marker_observations):
if len(obs)==2:
point_observations.append(obs[1])
else:
point_observations.append(obs)
marker_point_rel.append(se3.mul(se3.inv(camera_link_transforms[i]),marker_link_transforms[i])[1])
camera_initial_guess = (point_fit_rotation_3d(point_observations,marker_point_rel),[0.0]*3)
print "Estimated camera rotation from points:",camera_initial_guess
if marker_initial_guess == None:
marker_initial_guess = dict((l,(se3.identity() if marker_types[l]=='t' else [0.0]*3)) for l in marker_id_list)
else:
marker_initial_guess = marker_initial_guess.copy()
for l in marker_id_list:
if l not in marker_initial_guess:
marker_initial_guess[l] = (se3.identity() if marker_types[l]=='t' else [0.0]*3)
camera_transform = camera_initial_guess
marker_transforms = marker_initial_guess.copy()
if DO_VISUALIZATION:
rgroup = coordinates.addGroup("calibration")
rgroup.addFrame("camera link",worldCoordinates=camera_link_transforms[-1])
rgroup.addFrame("marker link",worldCoordinates=marker_link_transforms[-1])
rgroup.addFrame("camera estimate",parent="camera link",relativeCoordinates=camera_transform)
rgroup.addFrame("marker estimate",parent="marker link",relativeCoordinates=marker_transforms.values()[0])
for i,obs in enumerate(marker_observations):
rgroup.addFrame("obs"+str(i)+" estimate",parent="camera estimate",relativeCoordinates=obs)
visualization.add("coordinates",rgroup)
visualization.dialog()
point_observations_only = all(marker_types[marker] == 'p' for marker in marker_id_list)
xform_observations_only = all(marker_types[marker] == 't' for marker in marker_id_list)
if not point_observations_only and not xform_observations_only:
raise NotImplementedError("Can't calibrate camera from mixed point/transform markers yet")
for iters in range(maxIters):
#attempt to minimize the error on the following over all observations i
#camera_link_transform(q_i)*camera_transform*observation_i = marker_link_transform(l_i,q_i)*marker_transform(l_i)
#first, we'll assume the camera transform is fixed and then optimize the marker transforms.
#then, we'll assume the marker transforms are fixed and then optimize the camera transform.
#finally we'll check the error to detect convergence
#1. Estimate marker transforms from current camera transform
new_marker_transforms = dict((l,(TransformStats(zero=marker_initial_guess[l],prior=regularizationFactor) if marker_types[l]=='t' else VectorStats(value,zero=[0.0]*3,prior=RegularizationFactor))) for l in marker_id_list)
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
Trel = se3.mul(se3.inv(Tmlink),se3.mul(Tclink,camera_transform))
if marker_types[marker] == 't':
estimate = se3.mul(Trel,obs)
else:
estimate = se3.apply(Trel,obs)
new_marker_transforms[marker].add(estimate,observation_weights[i])
print "ITERATION",iters
#print " ESTIMATED MARKER TRANSFORMS:",dict((k,v.average) for (k,v) in new_marker_transforms.iteritems())
#2. Estimate camera transform from current marker transforms
new_camera_transform = TransformStats(zero=camera_initial_guess,prior=regularizationFactor)
if point_observations_only:
#TODO: weighted point fitting
relative_points = []
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
pRel = se3.apply(se3.inv(Tclink),se3.apply(Tmlink,new_marker_transforms[marker].average))
relative_points.append(pRel)
new_camera_transform.add(point_fit_xform_3d(marker_observations,relative_points),sum(observation_weights))
else:
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
Trel = se3.mul(se3.inv(Tclink),se3.mul(Tmlink,new_marker_transforms[marker].average))
estimate = se3.mul(Trel,se3.inv(obs))
new_camera_transform.add(estimate,observation_weights[i])
#print " ESTIMATED CAMERA TRANSFORMS:",new_camera_transform.average
#3. compute difference between last and current estimates
diff = 0.0
diff += vectorops.normSquared(se3.error(camera_transform,new_camera_transform.average))
for marker in marker_id_list:
if marker_types[marker]=='t':
diff += vectorops.normSquared(se3.error(marker_transforms[marker],new_marker_transforms[marker].average))
else:
diff += vectorops.distanceSquared(marker_transforms[marker],new_marker_transforms[marker].average)
camera_transform = new_camera_transform.average
for marker in marker_id_list:
marker_transforms[marker] = new_marker_transforms[marker].average
if math.sqrt(diff) < tolerance:
#converged!
print "Converged with diff %g on iteration %d"%(math.sqrt(diff),iters)
break
print " ESTIMATE CHANGE:",math.sqrt(diff)
error = 0.0
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
Tc = se3.mul(Tclink,camera_transform)
if marker_types[marker] == 't':
Tm = se3.mul(Tmlink,marker_transforms[marker])
error += vectorops.normSquared(se3.error(se3.mul(Tc,obs),Tm))
else:
Tm = se3.apply(Tmlink,marker_transforms[marker])
error += vectorops.distanceSquared(se3.apply(Tc,obs),Tm)
print " OBSERVATION ERROR:",math.sqrt(error)
#raw_input()
if DO_VISUALIZATION:
rgroup.setFrameCoordinates("camera estimate",camera_transform)
rgroup.setFrameCoordinates("marker estimate",marker_transforms.values()[0])
for i,obs in enumerate(marker_observations):
rgroup.setFrameCoordinates("obs"+str(i)+" estimate",obs)
visualization.add("coordinates",rgroup)
visualization.dialog()
if math.sqrt(diff) >= tolerance:
print "Max iters reached"
error = 0.0
for i in xrange(n):
marker = marker_ids[i]
Tclink = camera_link_transforms[i]
Tmlink = marker_link_transforms[i]
obs = marker_observations[i]
Tc = se3.mul(Tclink,camera_transform)
if marker_types[marker] == 't':
Tm = se3.mul(Tmlink,marker_transforms[marker])
error += vectorops.normSquared(se3.error(se3.mul(Tc,obs),Tm))
else:
Tm = se3.apply(Tmlink,marker_transforms[marker])
error += vectorops.distanceSquared(se3.apply(Tc,obs),Tm)
return (math.sqrt(error),camera_transform,marker_transforms)