def get_observation_chunk():
'''Make Nframes observations, and return them all, even the out-of-view ones'''
# I compute the full random block in one shot. This is useful for
# simulations that want to see identical poses when asking for N-1
# random poses and when asking for the first N-1 of a set of N random
# poses
# shape (Nframes,6)
randomblock = np.random.uniform(low=-1.0, high=1.0, size=(Nframes, 6))
# shape(Nframes,4,3)
Rt_ref_boardref = \
mrcal.Rt_from_rt( rt_ref_boardcenter + randomblock * rt_ref_boardcenter__noiseradius )
# shape = (Nframes, Nh,Nw,3)
boards_ref = mrcal.transform_point_Rt( # shape (Nframes, 1,1,4,3)
nps.mv(Rt_ref_boardref, 0, -5),
# shape ( Nh,Nw,3)
board_reference)
# I project full_board. Shape: (Nframes,Ncameras,Nh,Nw,2)
q = \
nps.mv( \
nps.cat( \
*[ mrcal.project( mrcal.transform_point_Rt(models[i].extrinsics_Rt_fromref(), boards_ref),
*models[i].intrinsics()) \
for i in range(Ncameras) ]),
0,1 )
return q, Rt_ref_boardref
def grad(f, x, step=1e-6):
r'''Computes df/dx at x
f is a function of one argument. If the input has shape Si and the output
has shape So, the returned gradient has shape So+Si. This applies central
differences
'''
d = np.zeros(x.shape, dtype=float)
dflat = d.ravel()
def df_dxi(i, d, dflat):
dflat[i] = step
fplus = f(x + d)
fminus = f(x - d)
j = (fplus - fminus) / (2. * step)
dflat[i] = 0
return j
# grad variable is in first dim
Jflat = nps.cat(*[df_dxi(i, d, dflat) for i in range(len(dflat))])
# grad variable is in last dim
Jflat = nps.mv(Jflat, 0, -1)
return Jflat.reshape(Jflat.shape[:-1] + d.shape)
def _splined_stereographic_domain(lensmodel):
r'''Return the stereographic domain for splined-stereographic lens models
SYNOPSIS
model = mrcal.cameramodel(model_filename)
lensmodel = model.intrinsics()[0]
domain_contour = mrcal._splined_stereographic_domain(lensmodel)
Splined stereographic models are defined by a splined surface. This surface is
indexed by normalized stereographic-projected points. This surface is defined in
some finite area, and this function reports a piecewise linear contour reporting
this region.
This function only makes sense for splined stereographic models.
RETURNED VALUE
An array of shape (N,2) containing a contour representing the projection domain.
'''
if not re.match('LENSMODEL_SPLINED_STEREOGRAPHIC', lensmodel):
raise Exception(f"This only makes sense with splined models. Input uses {lensmodel}")
ux,uy = mrcal.knots_for_splined_models(lensmodel)
# shape (Ny,Nx,2)
u = np.ascontiguousarray(nps.mv(nps.cat(*np.meshgrid(ux,uy)), 0, -1))
meta = mrcal.lensmodel_metadata(lensmodel)
if meta['order'] == 2:
# spline order is 3. The valid region is 1/2 segments inwards from the
# outer contour
return \
nps.glue( (u[0,1:-2] + u[1,1:-2]) / 2.,
(u[0,-2] + u[1,-2] + u[0,-1] + u[1,-1]) / 4.,
(u[1:-2, -2] + u[1:-2, -1]) / 2.,
(u[-2,-2] + u[-1,-2] + u[-2,-1] + u[-1,-1]) / 4.,
(u[-2, -2:1:-1] + u[-1, -2:1:-1]) / 2.,
(u[-2, 1] + u[-1, 1] + u[-2, 0] + u[-1, 0]) / 4.,
(u[-2:0:-1, 0] +u[-2:0:-1, 1]) / 2.,
(u[0, 0] +u[0, 1] + u[1, 0] +u[1, 1]) / 4.,
(u[0,1] + u[1,1]) / 2.,
axis = -2 )
elif meta['order'] == 3:
# spline order is 3. The valid region is the outer contour, leaving one
# knot out
return \
nps.glue( u[1,1:-2], u[1:-2, -2], u[-2, -2:1:-1], u[-2:0:-1, 1],
axis=-2 )
else:
raise Exception("I only support cubic (order==3) and quadratic (order==2) models")
def sample_imager(gridn_width, gridn_height, imager_width, imager_height):
r'''Returns regularly-sampled, gridded pixels coordinates across the imager
SYNOPSIS
q = sample_imager( 60, 40, *model.imagersize() )
print(q.shape)
===>
(40,60,2)
Note that the arguments are given in width,height order, as is customary when
generally talking about images and indexing. However, the output is in
height,width order, as is customary when talking about matrices and numpy
arrays.
If we ask for gridding dimensions (gridn_width, gridn_height), the output has
shape (gridn_height,gridn_width,2) where each row is an (x,y) pixel coordinate.
The top-left corner is at [0,0,:]:
sample_imager(...)[0,0] = [0,0]
The the bottom-right corner is at [-1,-1,:]:
sample_imager(...)[ -1, -1,:] =
sample_imager(...)[gridn_height-1,gridn_width-1,:] =
(imager_width-1,imager_height-1)
When making plots you probably want to call mrcal.imagergrid_using(). See the
that docstring for details.
ARGUMENTS
- gridn_width: how many points along the horizontal gridding dimension
- gridn_height: how many points along the vertical gridding dimension. If None,
we compute an integer gridn_height to maintain a square-ish grid:
gridn_height/gridn_width ~ imager_height/imager_width
- imager_width,imager_height: the width, height of the imager. With a
mrcal.cameramodel object this is *model.imagersize()
RETURNED VALUES
We return an array of shape (gridn_height,gridn_width,2). Each row is an (x,y)
pixel coordinate.
'''
if gridn_height is None:
gridn_height = int(round(imager_height/imager_width*gridn_width))
w = np.linspace(0,imager_width -1,gridn_width)
h = np.linspace(0,imager_height-1,gridn_height)
return np.ascontiguousarray(nps.mv(nps.cat(*np.meshgrid(w,h)),
0,-1))
def sample_dqref(observations, pixel_uncertainty_stdev, make_outliers=False):
# Outliers have weight < 0. The code will adjust the outlier observations
# also. But that shouldn't matter: they're outliers so those observations
# should be ignored
weight = observations[..., -1]
q_noise = np.random.randn(*observations.shape[:-1],
2) * pixel_uncertainty_stdev / nps.mv(
nps.cat(weight, weight), 0, -1)
if make_outliers:
if not hasattr(sample_dqref, 'idx_outliers_ref_flat'):
NobservedPoints = observations.size // 3
sample_dqref.idx_outliers_ref_flat = \
np.random.choice( NobservedPoints,
(NobservedPoints//100,), # 1% outliers
replace = False )
nps.clump(q_noise, n=3)[sample_dqref.idx_outliers_ref_flat, :] *= 20
observations_perturbed = observations.copy()
observations_perturbed[..., :2] += q_noise
return q_noise, observations_perturbed
lensmodel, intrinsics_data = m.intrinsics()
ref_p = np.array(
((10., 20., 100.), (25., 30., 90.), (5., 10., 94.), (-45., -20., 95.),
(-35., 14., 77.), (5., -0., 110.), (1., 50., 50.)))
# The points are all somewhere at +z. So the Camera poses are all ~ identity
ref_extrinsics_rt_fromref = np.array(
((-0.1, -0.07, 0.01, 10.0, 4.0, -7.0), (-0.01, 0.05, -0.02, 30.0, -8.0,
-8.0), (-0.1, 0.03, -0.03, 10.0,
-9.0, 20.0),
(0.04, -0.04, 0.03, -20.0, 2.0, -11.0), (0.01, 0.05, -0.05, -10.0, 3.0,
9.0)))
# shape (Ncamposes, Npoints, 3)
ref_p_cam = mrcal.transform_point_rt(nps.mv(ref_extrinsics_rt_fromref, -2, -3),
ref_p)
# shape (Ncamposes, Npoints, 2)
ref_q_cam = mrcal.project(ref_p_cam, lensmodel, intrinsics_data)
# Observations are incomplete. Not all points are observed from everywhere
indices_point_camintrinsics_camextrinsics = \
np.array(((0, 0, 1),
(0, 0, 2),
(0, 0, 4),
(1, 0, 0),
(1, 0, 1),
(1, 0, 4),
(2, 0, 0),
(2, 0, 1),
def hypothesis_board_corner_positions(icam_intrinsics=None,
idx_inliers=None,
**optimization_inputs):
r'''Reports the 3D chessboard points observed by a camera at calibration time
SYNOPSIS
model = mrcal.cameramodel("xxx.cameramodel")
optimization_inputs = model.optimization_inputs()
# shape (Nobservations, Nheight, Nwidth, 3)
pcam = mrcal.hypothesis_board_corner_positions(**optimization_inputs)[0]
i_intrinsics = \
optimization_inputs['indices_frame_camintrinsics_camextrinsics'][:,1]
# shape (Nobservations,1,1,Nintrinsics)
intrinsics = nps.mv(optimization_inputs['intrinsics'][i_intrinsics],-2,-4)
optimization_inputs['observations_board'][...,:2] = \
mrcal.project( pcam,
optimization_inputs['lensmodel'],
intrinsics )
# optimization_inputs now contains perfect, noiseless board observations
x = mrcal.optimizer_callback(**optimization_inputs)[1]
print(nps.norm2(x[:mrcal.num_measurements_boards(**optimization_inputs)]))
==>
0
The optimization routine generates hypothetical observations from a set of
parameters being evaluated, trying to match these hypothetical observations to
real observations. To facilitate analysis, this routine returns these
hypothetical coordinates of the chessboard corners being observed. This routine
reports the 3D points in the coordinate system of the observing camera.
The hypothetical points are constructed from
- The calibration object geometry
- The calibration object-reference transformation in
optimization_inputs['frames_rt_toref']
- The camera extrinsics (reference-camera transformation) in
optimization_inputs['extrinsics_rt_fromref']
- The table selecting the camera and calibration object frame for each
observation in
optimization_inputs['indices_frame_camintrinsics_camextrinsics']
ARGUMENTS
- icam_intrinsics: optional integer specifying which intrinsic camera in the
optimization_inputs we're looking at. If omitted (or None), we report
camera-coordinate points for all the cameras
- idx_inliers: optional numpy array of booleans of shape
(Nobservations,object_height,object_width) to select the outliers manually. If
omitted (or None), the outliers are selected automatically: idx_inliers =
observations_board[...,2] > 0. This argument is available to pick common
inliers from two separate solves.
- **optimization_inputs: a dict() of arguments passable to mrcal.optimize() and
mrcal.optimizer_callback(). We use the geometric data. This dict is obtainable
from a cameramodel object by calling cameramodel.optimization_inputs()
RETURNED VALUE
- An array of shape (Nobservations, Nheight, Nwidth, 3) containing the
coordinates (in the coordinate system of each camera) of the chessboard
corners, for ALL the cameras. These correspond to the observations in
optimization_inputs['observations_board'], which also have shape
(Nobservations, Nheight, Nwidth, 3)
- An array of shape (Nobservations_thiscamera, Nheight, Nwidth, 3) containing
the coordinates (in the camera coordinate system) of the chessboard corners,
for the particular camera requested in icam_intrinsics. If icam_intrinsics is
None: this is the same array as the previous returned value
- an (N,3) array containing camera-frame 3D points observed at calibration time,
and accepted by the solver as inliers. This is a subset of the 2nd returned
array.
- an (N,3) array containing camera-frame 3D points observed at calibration time,
but rejected by the solver as outliers. This is a subset of the 2nd returned
array.
'''
observations_board = optimization_inputs.get('observations_board')
if observations_board is None:
return Exception("No board observations available")
indices_frame_camintrinsics_camextrinsics = \
optimization_inputs['indices_frame_camintrinsics_camextrinsics']
object_width_n = observations_board.shape[-2]
object_height_n = observations_board.shape[-3]
object_spacing = optimization_inputs['calibration_object_spacing']
calobject_warp = optimization_inputs.get('calobject_warp')
# shape (Nh,Nw,3)
full_object = mrcal.ref_calibration_object(object_width_n, object_height_n,
object_spacing, calobject_warp)
frames_Rt_toref = \
mrcal.Rt_from_rt( optimization_inputs['frames_rt_toref'] )\
[ indices_frame_camintrinsics_camextrinsics[:,0] ]
extrinsics_Rt_fromref = \
nps.glue( mrcal.identity_Rt(),
mrcal.Rt_from_rt(optimization_inputs['extrinsics_rt_fromref']),
axis = -3 ) \
[ indices_frame_camintrinsics_camextrinsics[:,2]+1 ]
Rt_cam_frame = mrcal.compose_Rt(extrinsics_Rt_fromref, frames_Rt_toref)
p_cam_calobjects = \
mrcal.transform_point_Rt(nps.mv(Rt_cam_frame,-3,-5), full_object)
# shape (Nobservations,Nheight,Nwidth)
if idx_inliers is None:
idx_inliers = observations_board[..., 2] > 0
idx_outliers = ~idx_inliers
if icam_intrinsics is None:
return \
p_cam_calobjects, \
p_cam_calobjects, \
p_cam_calobjects[idx_inliers, ...], \
p_cam_calobjects[idx_outliers, ...]
# The user asked for a specific camera. Separate out its data
# shape (Nobservations,)
idx_observations = indices_frame_camintrinsics_camextrinsics[:,
1] == icam_intrinsics
idx_inliers[~idx_observations] = False
idx_outliers[~idx_observations] = False
return \
p_cam_calobjects, \
p_cam_calobjects[idx_observations, ...], \
p_cam_calobjects[idx_inliers, ...], \
p_cam_calobjects[idx_outliers, ...]
noise_for_gradients = 1e-3
dqref, observations_perturbed = sample_dqref(baseline['observations_board'],
noise_for_gradients)
optimization_inputs = copy.deepcopy(baseline)
optimization_inputs['observations_board'] = observations_perturbed
mrcal.optimize(**optimization_inputs, do_apply_outlier_rejection=False)
p1, x1, J1 = mrcal.optimizer_callback(no_factorization=True,
**optimization_inputs)[:3]
J1 = J1.toarray()
dx_observed = x1 - x0
dp_observed = p1 - p0
w = observations_perturbed[..., 2]
w[w < 0] = 0 # outliers have weight=0
w = np.ravel(nps.mv(nps.cat(w, w), 0, -1)) # each weight controls x,y
xtJ1 = nps.inner(nps.transpose(J1), x1)
mrcal.pack_state(xtJ0, **optimization_inputs)
testutils.confirm_equal(xtJ1,
0,
eps=1e-2,
worstcase=True,
msg="dE/dp = 0 at the optimum: perturbed")
# I added noise reoptimized, did dx do the expected thing?
# I should have
# x(p+dp, qref+dqref) = x + J dp + dx/dqref dqref
# -> x1-x0 ~ J dp + dx/dqref dqref
# x[measurements] = (q - qref) * weight
# -> dx/dqref = -diag(weight)
def ref_calibration_object(W, H, object_spacing, calobject_warp=None):
r'''Return the geometry of the calibration object
SYNOPSIS
import gnuplotlib as gp
import numpysane as nps
obj = mrcal.ref_calibration_object( 10,6, 0.1 )
print(obj.shape)
===> (6, 10, 3)
gp.plot( nps.clump( obj[...,:2], n=2),
tuplesize = -2,
_with = 'points',
_xrange = (-0.1,1.0),
_yrange = (-0.1,0.6),
unset = 'grid',
square = True,
terminal = 'dumb 74,45')
0.6 +---------------------------------------------------------------+
| + + + + + |
| |
0.5 |-+ A A A A A A A A A A +-|
| |
| |
0.4 |-+ A A A A A A A A A A +-|
| |
| |
0.3 |-+ A A A A A A A A A A +-|
| |
| |
0.2 |-+ A A A A A A A A A A +-|
| |
| |
0.1 |-+ A A A A A A A A A A +-|
| |
| |
0 |-+ A A A A A A A A A A +-|
| |
| + + + + + |
-0.1 +---------------------------------------------------------------+
0 0.2 0.4 0.6 0.8 1
Returns the geometry of a calibration object in its own reference coordinate
system in a (H,W,3) array. Only a grid-of-points calibration object is
supported, possibly with some bowing (i.e. what the internal mrcal solver
supports). Each row of the output is an (x,y,z) point. The origin is at the
corner of the grid, so ref_calibration_object(...)[0,0,:] is
np.array((0,0,0)). The grid spans x and y, with z representing the depth: z=0
for a flat calibration object.
A simple parabolic board warping model is supported by passing a (2,) array in
calobject_warp. These 2 values describe additive flex along the x axis and along
the y axis, in that order. In each direction the flex is a parabola, with the
parameter k describing the max deflection at the center. If the edges were at
+-1 we'd have
z = k*(1 - x^2)
The edges we DO have are at (0,N-1), so the equivalent expression is
xr = x / (N-1)
z = k*( 1 - 4*xr^2 + 4*xr - 1 ) =
4*k*(xr - xr^2) =
ARGUMENTS
- W: how many points we have in the horizontal direction
- H: how many points we have in the vertical direction
- object_spacing: the distance between adjacent points in the calibration
object. If a scalar is given, a square object is assumed, and the vertical and
horizontal distances are assumed to be identical. An array of shape (..., 2)
can be given: the last dimension is (spacing_h, spacing_w), and the preceding
dimensions are used for broadcasting
- calobject_warp: optional array of shape (2,) defaults to None. Describes the
warping of the calibration object. If None, the object is flat. If an array is
given, the values describe the maximum additive deflection along the x and y
axes. Extended array can be given for broadcasting
This function supports broadcasting across object_spacing and calobject_warp
RETURNED VALUES
The calibration object geometry in a (..., H,W,3) array, with the leading
dimensions set by the broadcasting rules
'''
# shape (H,W)
xx, yy = np.meshgrid(np.arange(W, dtype=float), np.arange(H, dtype=float))
# shape (H,W,3)
full_object = nps.glue(nps.mv(nps.cat(xx, yy), 0, -1),
np.zeros((H, W, 1)),
axis=-1)
# object_spacing has shape (..., 2)
object_spacing = np.array(object_spacing)
if object_spacing.ndim == 0:
object_spacing = np.array((1, 1)) * object_spacing
object_spacing = nps.dummy(object_spacing, -2, -2)
# object_spacing now has shape (..., 1,1,2)
if object_spacing.ndim > 3:
# extend full_object to the output shape I want
full_object = full_object * np.ones(object_spacing.shape[:-3] +
(1, 1, 1))
full_object[..., :2] *= object_spacing
if calobject_warp is not None:
xr = xx / (W - 1)
yr = yy / (H - 1)
dx = 4. * xr * (1. - xr)
dy = 4. * yr * (1. - yr)
# To allow broadcasting over calobject_warp
if calobject_warp.ndim > 1:
# shape (..., 1,1,2)
calobject_warp = nps.dummy(calobject_warp, -2, -2)
# extend full_object to the output shape I want
full_object = full_object * np.ones(calobject_warp.shape[:-3] +
(1, 1, 1))
full_object[..., 2] += calobject_warp[..., 0] * dx
full_object[..., 2] += calobject_warp[..., 1] * dy
return full_object
def reproject_perturbed__fit_boards_ref(
q,
distance,
# shape (Ncameras, Nintrinsics)
baseline_intrinsics,
# shape (Ncameras, 6)
baseline_rt_cam_ref,
# shape (Nframes, 6)
baseline_rt_ref_frame,
# shape (2)
baseline_calobject_warp,
# shape (..., Ncameras, Nintrinsics)
query_intrinsics,
# shape (..., Ncameras, 6)
query_rt_cam_ref,
# shape (..., Nframes, 6)
query_rt_ref_frame,
# shape (..., 2)
query_calobject_warp):
r'''Reproject by explicitly computing a procrustes fit to align the reference
coordinate systems of the two solves. We match up the two sets of chessboard
points
'''
calobject_height, calobject_width = optimization_inputs_baseline[
'observations_board'].shape[1:3]
# shape (Nsamples, Nh, Nw, 3)
if query_calobject_warp.ndim > 1:
calibration_object_query = \
nps.cat(*[ mrcal.ref_calibration_object(calobject_width, calobject_height,
optimization_inputs_baseline['calibration_object_spacing'],
calobject_warp=calobject_warp) \
for calobject_warp in query_calobject_warp] )
else:
calibration_object_query = \
mrcal.ref_calibration_object(calobject_width, calobject_height,
optimization_inputs_baseline['calibration_object_spacing'],
calobject_warp=query_calobject_warp)
# shape (Nsamples, Nframes, Nh, Nw, 3)
pcorners_ref_query = \
mrcal.transform_point_rt( nps.dummy(query_rt_ref_frame, -2, -2),
nps.dummy(calibration_object_query, -4))
# shape (Nh, Nw, 3)
calibration_object_baseline = \
mrcal.ref_calibration_object(calobject_width, calobject_height,
optimization_inputs_baseline['calibration_object_spacing'],
calobject_warp=baseline_calobject_warp)
# frames_ref.shape is (Nframes, 6)
# shape (Nframes, Nh, Nw, 3)
pcorners_ref_baseline = \
mrcal.transform_point_rt( nps.dummy(baseline_rt_ref_frame, -2, -2),
calibration_object_baseline)
# shape (Nsamples,4,3)
Rt_refq_refb = \
mrcal.align_procrustes_points_Rt01( \
# shape (Nsamples,N,3)
nps.mv(nps.clump(nps.mv(pcorners_ref_query, -1,0),n=-3),0,-1),
# shape (N,3)
nps.clump(pcorners_ref_baseline, n=3))
# shape (Ncameras, 3)
p_cam_baseline = mrcal.unproject(
q, lensmodel, baseline_intrinsics, normalize=True) * distance
# shape (Ncameras, 3). In the ref coord system
p_ref_baseline = \
mrcal.transform_point_rt( mrcal.invert_rt(baseline_rt_cam_ref),
p_cam_baseline )
# shape (Nsamples,Ncameras,3)
p_ref_query = \
mrcal.transform_point_Rt(nps.mv(Rt_refq_refb,-3,-4),
p_ref_baseline)
# shape (..., Ncameras, 3)
p_cam_query = \
mrcal.transform_point_rt(query_rt_cam_ref, p_ref_query)
# shape (..., Ncameras, 2)
q1 = mrcal.project(p_cam_query, lensmodel, query_intrinsics)
if q1.shape[-3] == 1: q1 = q1[0, :, :]
return q1
def reproject_perturbed__mean_frames(
q,
distance,
# shape (Ncameras, Nintrinsics)
baseline_intrinsics,
# shape (Ncameras, 6)
baseline_rt_cam_ref,
# shape (Nframes, 6)
baseline_rt_ref_frame,
# shape (2)
baseline_calobject_warp,
# shape (..., Ncameras, Nintrinsics)
query_intrinsics,
# shape (..., Ncameras, 6)
query_rt_cam_ref,
# shape (..., Nframes, 6)
query_rt_ref_frame,
# shape (..., 2)
query_calobject_warp):
r'''Reproject by computing the mean in the space of frames
This is what the uncertainty computation does (as of 2020/10/26). The implied
rotation here is aphysical (it is a mean of multiple rotation matrices)
'''
# shape (Ncameras, 3)
p_cam_baseline = mrcal.unproject(
q, lensmodel, baseline_intrinsics, normalize=True) * distance
# shape (Ncameras, 3)
p_ref_baseline = \
mrcal.transform_point_rt( mrcal.invert_rt(baseline_rt_cam_ref),
p_cam_baseline )
if fixedframes:
p_ref_query = p_ref_baseline
else:
# shape (Nframes, Ncameras, 3)
# The point in the coord system of all the frames
p_frames = mrcal.transform_point_rt( \
nps.dummy(mrcal.invert_rt(baseline_rt_ref_frame),-2),
p_ref_baseline)
# shape (..., Nframes, Ncameras, 3)
p_ref_query_allframes = \
mrcal.transform_point_rt( nps.dummy(query_rt_ref_frame, -2),
p_frames )
if args.reproject_perturbed == 'mean-frames':
# "Normal" path: I take the mean of all the frame-coord-system
# representations of my point
if not fixedframes:
# shape (..., Ncameras, 3)
p_ref_query = np.mean(p_ref_query_allframes, axis=-3)
# shape (..., Ncameras, 3)
p_cam_query = \
mrcal.transform_point_rt(query_rt_cam_ref, p_ref_query)
# shape (..., Ncameras, 2)
return mrcal.project(p_cam_query, lensmodel, query_intrinsics)
else:
# Experimental path: I take the mean of the projections, not the points
# in the reference frame
# guaranteed that not fixedframes: I asserted this above
# shape (..., Nframes, Ncameras, 3)
p_cam_query_allframes = \
mrcal.transform_point_rt(nps.dummy(query_rt_cam_ref, -3),
p_ref_query_allframes)
# shape (..., Nframes, Ncameras, 2)
q_reprojected = mrcal.project(p_cam_query_allframes, lensmodel,
nps.dummy(query_intrinsics, -3))
if args.reproject_perturbed != 'mean-frames-using-meanq-penalize-big-shifts':
return np.mean(q_reprojected, axis=-3)
else:
# Experiment. Weighted mean to de-emphasize points with huge shifts
w = 1. / nps.mag(q_reprojected - q)
w = nps.mv(nps.cat(w, w), 0, -1)
return \
np.sum(q_reprojected*w, axis=-3) / \
np.sum(w, axis=-3)
def image_transformation_map(model_from,
model_to,
intrinsics_only=False,
distance=None,
plane_n=None,
plane_d=None,
mask_valid_intrinsics_region_from=False):
r'''Compute a reprojection map between two models
SYNOPSIS
model_orig = mrcal.cameramodel("xxx.cameramodel")
image_orig = cv2.imread("image.jpg")
model_pinhole = mrcal.pinhole_model_for_reprojection(model_orig,
fit = "corners")
mapxy = mrcal.image_transformation_map(model_orig, model_pinhole,
intrinsics_only = True)
image_undistorted = mrcal.transform_image(image_orig, mapxy)
# image_undistorted is now a pinhole-reprojected version of image_orig
Returns the transformation that describes a mapping
- from pixel coordinates of an image of a scene observed by model_to
- to pixel coordinates of an image of the same scene observed by model_from
This transformation can then be applied to a whole image by calling
mrcal.transform_image().
This function returns a transformation map in an (Nheight,Nwidth,2) array. The
image made by model_to will have shape (Nheight,Nwidth). Each pixel (x,y) in
this image corresponds to a pixel mapxy[y,x,:] in the image made by model_from.
One application of this function is to validate the models in a stereo pair. For
instance, reprojecting one camera's image at distance=infinity should produce
exactly the same image that is observed by the other camera when looking at very
far objects, IF the intrinsics and rotation are correct. If the images don't
line up well, we know that some part of the models is off. Similarly, we can use
big planes (such as observations of the ground) and plane_n, plane_d to validate.
This function has several modes of operation:
- intrinsics, extrinsics
Used if not intrinsics_only and \
plane_n is None and \
plane_d is None
This is the default. For each pixel in the output, we use the full model to
unproject a given distance out, and then use the full model to project back
into the other camera.
- intrinsics only
Used if intrinsics_only and \
plane_n is None and \
plane_d is None
Similar, but the extrinsics are ignored. We unproject the pixels in one model,
and project the into the other camera. The two camera coordinate systems are
assumed to line up perfectly
- plane
Used if plane_n is not None and
plane_d is not None
We map observations of a given plane in camera FROM coordinates coordinates to
where this plane would be observed by camera TO. We unproject each pixel in
one camera, compute the intersection point with the plane, and project that
intersection point back to the other camera. This uses ALL the intrinsics,
extrinsics and the plane representation. The plane is represented by a normal
vector plane_n, and the distance to the normal plane_d. The plane is all
points p such that inner(p,plane_n) = plane_d. plane_n does not need to be
normalized; any scaling is compensated in plane_d.
ARGUMENTS
- model_from: the mrcal.cameramodel object describing the camera used to capture
the input image. We always use the intrinsics. if not intrinsics_only: we use
the extrinsics also
- model_to: the mrcal.cameramodel object describing the camera that would have
captured the image we're producing. We always use the intrinsics. if not
intrinsics_only: we use the extrinsics also
- intrinsics_only: optional boolean, defaulting to False. If False: we respect
the relative transformation in the extrinsics of the camera models.
- distance: optional value, defaulting to None. Used only if not
intrinsics_only. We reproject points in space a given distance out. If
distance is None (the default), we look out to infinity. This is equivalent to
using only the rotation component of the extrinsics, ignoring the translation.
- plane_n: optional numpy array of shape (3,); None by default. If given, we
produce a transformation to map observations of a given plane to the same
pixels in the source and target images. This argument describes the normal
vector in the coordinate system of model_from. The plane is all points p such
that inner(p,plane_n) = plane_d. plane_n does not need to be normalized; any
scaling is compensated in plane_d. If given, plane_d should be given also, and
intrinsics_only should be False. if given, we use the full intrinsics and
extrinsics of both camera models
- plane_d: optional floating-point value; None by default. If given, we produce
a transformation to map observations of a given plane to the same pixels in
the source and target images. The plane is all points p such that
inner(p,plane_n) = plane_d. plane_n does not need to be normalized; any
scaling is compensated in plane_d. If given, plane_n should be given also, and
intrinsics_only should be False. if given, we use the full intrinsics and
extrinsics of both camera models
- mask_valid_intrinsics_region_from: optional boolean defaulting to False. If
True, points outside the valid-intrinsics region in the FROM image are set to
black, and thus do not appear in the output image
RETURNED VALUE
A numpy array of shape (Nheight,Nwidth,2) where Nheight and Nwidth represent the
imager dimensions of model_to. This array contains 32-bit floats, as required by
cv2.remap() (the function providing the internals of mrcal.transform_image()).
This array can be passed to mrcal.transform_image()
'''
if (plane_n is None and plane_d is not None) or \
(plane_n is not None and plane_d is None):
raise Exception(
"plane_n and plane_d should both be None or neither should be None"
)
if plane_n is not None and \
intrinsics_only:
raise Exception(
"We're looking at remapping a plane (plane_d, plane_n are not None), so intrinsics_only should be False"
)
if distance is not None and \
(plane_n is not None or intrinsics_only):
raise Exception(
"'distance' makes sense only without plane_n/plane_d and without intrinsics_only"
)
if intrinsics_only:
Rt_to_from = None
else:
Rt_to_from = mrcal.compose_Rt(model_to.extrinsics_Rt_fromref(),
model_from.extrinsics_Rt_toref())
lensmodel_from, intrinsics_data_from = model_from.intrinsics()
lensmodel_to, intrinsics_data_to = model_to.intrinsics()
if re.match("LENSMODEL_OPENCV",lensmodel_from) and \
lensmodel_to == "LENSMODEL_PINHOLE" and \
plane_n is None and \
not mask_valid_intrinsics_region_from and \
distance is None:
# This is a common special case. This branch works identically to the
# other path (the other side of this "if" can always be used instead),
# but the opencv-specific code is optimized and at one point ran faster
# than the code on the other side.
#
# The mask_valid_intrinsics_region_from isn't implemented in this path.
# It COULD be, then this faster path could be used
import cv2
fxy_from = intrinsics_data_from[0:2]
cxy_from = intrinsics_data_from[2:4]
cameraMatrix_from = np.array(
((fxy_from[0], 0, cxy_from[0]), (0, fxy_from[1], cxy_from[1]),
(0, 0, 1)))
fxy_to = intrinsics_data_to[0:2]
cxy_to = intrinsics_data_to[2:4]
cameraMatrix_to = np.array(
((fxy_to[0], 0, cxy_to[0]), (0, fxy_to[1], cxy_to[1]), (0, 0, 1)))
output_shape = model_to.imagersize()
distortion_coeffs = intrinsics_data_from[4:]
if Rt_to_from is not None:
R_to_from = Rt_to_from[:3, :]
if np.trace(R_to_from) > 3. - 1e-12:
R_to_from = None # identity, so I pass None
else:
R_to_from = None
return nps.glue( *[ nps.dummy(arr,-1) for arr in \
cv2.initUndistortRectifyMap(cameraMatrix_from, distortion_coeffs,
R_to_from,
cameraMatrix_to, tuple(output_shape),
cv2.CV_32FC1)],
axis = -1)
W_from, H_from = model_from.imagersize()
W_to, H_to = model_to.imagersize()
# shape: (Nheight,Nwidth,2). Contains (x,y) rows
grid = np.ascontiguousarray(nps.mv(
nps.cat(*np.meshgrid(np.arange(W_to), np.arange(H_to))), 0, -1),
dtype=float)
v = mrcal.unproject(grid, lensmodel_to, intrinsics_data_to)
if plane_n is not None:
R_to_from = Rt_to_from[:3, :]
t_to_from = Rt_to_from[3, :]
# The homography definition. Derived in many places. For instance in
# "Motion and structure from motion in a piecewise planar environment"
# by Olivier Faugeras, F. Lustman.
A_to_from = plane_d * R_to_from + nps.outer(t_to_from, plane_n)
A_from_to = np.linalg.inv(A_to_from)
v = nps.matmult(v, nps.transpose(A_from_to))
else:
if Rt_to_from is not None:
if distance is not None:
v = mrcal.transform_point_Rt(
mrcal.invert_Rt(Rt_to_from),
v / nps.dummy(nps.mag(v), -1) * distance)
else:
R_to_from = Rt_to_from[:3, :]
v = nps.matmult(v, R_to_from)
mapxy = mrcal.project(v, lensmodel_from, intrinsics_data_from)
if mask_valid_intrinsics_region_from:
# Using matplotlib to compute the out-of-bounds points. It doesn't
# support broadcasting, so I do that manually with a clump/reshape
from matplotlib.path import Path
region = Path(model_from.valid_intrinsics_region())
is_inside = region.contains_points(nps.clump(mapxy, n=2)).reshape(
mapxy.shape[:2])
mapxy[~is_inside, :] = -1
return mapxy.astype(np.float32)
def image_transformation_map(model_from, model_to,
use_rotation = False,
plane_n = None,
plane_d = None,
mask_valid_intrinsics_region_from = False):
r'''Compute a reprojection map between two models
SYNOPSIS
model_orig = mrcal.cameramodel("xxx.cameramodel")
image_orig = cv2.imread("image.jpg")
model_pinhole = mrcal.pinhole_model_for_reprojection(model_orig,
fit = "corners")
mapxy = mrcal.image_transformation_map(model_orig, model_pinhole)
image_undistorted = mrcal.transform_image(image_orig, mapxy)
# image_undistorted is now a pinhole-reprojected version of image_orig
Returns the transformation that describes a mapping
- from pixel coordinates of an image of a scene observed by model_to
- to pixel coordinates of an image of the same scene observed by model_from
This transformation can then be applied to a whole image by calling
mrcal.transform_image().
This function returns a transformation map in an (Nheight,Nwidth,2) array. The
image made by model_to will have shape (Nheight,Nwidth). Each pixel (x,y) in
this image corresponds to a pixel mapxy[y,x,:] in the image made by model_from.
This function has 3 modes of operation:
- intrinsics-only
This is the default. Selected if
- use_rotation = False
- plane_n = None
- plane_d = None
All of the extrinsics are ignored. If the two cameras have the same
orientation, then their observations of infinitely-far-away objects will line
up exactly
- rotation
This can be selected explicitly with
- use_rotation = True
- plane_n = None
- plane_d = None
Here we use the rotation component of the relative extrinsics. The relative
translation is impossible to use without knowing what we're looking at, so IT
IS ALWAYS IGNORED. If the relative orientation in the models matches reality,
then the two cameras' observations of infinitely-far-away objects will line up
exactly
- plane
This is selected if
- use_rotation = True
- plane_n is not None
- plane_d is not None
We map observations of a given plane in camera FROM coordinates
coordinates to where this plane would be observed by camera TO. This uses
ALL the intrinsics, extrinsics and the plane representation. If all of
these are correct, the observations of this plane would line up exactly in
the remapped-camera-fromimage and the camera-to image. The plane is
represented in camera-from coordinates by a normal vector plane_n, and the
distance to the normal plane_d. The plane is all points p such that
inner(p,plane_n) = plane_d. plane_n does not need to be normalized; any
scaling is compensated in plane_d.
ARGUMENTS
- model_from: the mrcal.cameramodel object describing the camera used to capture
the input image
- model_to: the mrcal.cameramodel object describing the camera that would have
captured the image we're producing
- use_rotation: optional boolean, defaulting to False. If True: we respect the
relative rotation in the extrinsics of the camera models.
- plane_n: optional numpy array of shape (3,); None by default. If given, we
produce a transformation to map observations of a given plane to the same
pixels in the source and target images. This argument describes the normal
vector in the coordinate system of model_from. The plane is all points p such
that inner(p,plane_n) = plane_d. plane_n does not need to be normalized; any
scaling is compensated in plane_d. If given, plane_d should be given also, and
use_rotation should be True. if given, we use the full intrinsics and
extrinsics of both camera models
- plane_d: optional floating-point value; None by default. If given, we produce
a transformation to map observations of a given plane to the same pixels in
the source and target images. The plane is all points p such that
inner(p,plane_n) = plane_d. plane_n does not need to be normalized; any
scaling is compensated in plane_d. If given, plane_n should be given also, and
use_rotation should be True. if given, we use the full intrinsics and
extrinsics of both camera models
- mask_valid_intrinsics_region_from: optional boolean defaulting to False. If
True, points outside the valid-intrinsics region in the FROM image are set to
black, and thus do not appear in the output image
RETURNED VALUE
A numpy array of shape (Nheight,Nwidth,2) where Nheight and Nwidth represent the
imager dimensions of model_to. This array contains 32-bit floats, as required by
cv2.remap() (the function providing the internals of mrcal.transform_image()).
This array can be passed to mrcal.transform_image()
'''
if (plane_n is None and plane_d is not None) or \
(plane_n is not None and plane_d is None):
raise Exception("plane_n and plane_d should both be None or neither should be None")
if plane_n is not None and plane_d is not None and \
not use_rotation:
raise Exception("We're looking at remapping a plane (plane_d, plane_n are not None), so use_rotation should be True")
Rt_to_from = None
if use_rotation:
Rt_to_r = model_to. extrinsics_Rt_fromref()
Rt_r_from = model_from.extrinsics_Rt_toref()
Rt_to_from = mrcal.compose_Rt(Rt_to_r, Rt_r_from)
lensmodel_from,intrinsics_data_from = model_from.intrinsics()
lensmodel_to, intrinsics_data_to = model_to. intrinsics()
if re.match("LENSMODEL_OPENCV",lensmodel_from) and \
lensmodel_to == "LENSMODEL_PINHOLE" and \
plane_n is None and \
not mask_valid_intrinsics_region_from:
# This is a common special case. This branch works identically to the
# other path (the other side of this "if" can always be used instead),
# but the opencv-specific code is optimized and at one point ran faster
# than the code on the other side.
#
# The mask_valid_intrinsics_region_from isn't implemented in this path.
# It COULD be, then this faster path could be used
fxy_from = intrinsics_data_from[0:2]
cxy_from = intrinsics_data_from[2:4]
cameraMatrix_from = np.array(((fxy_from[0], 0, cxy_from[0]),
( 0, fxy_from[1], cxy_from[1]),
( 0, 0, 1)))
fxy_to = intrinsics_data_to[0:2]
cxy_to = intrinsics_data_to[2:4]
cameraMatrix_to = np.array(((fxy_to[0], 0, cxy_to[0]),
( 0, fxy_to[1], cxy_to[1]),
( 0, 0, 1)))
output_shape = model_to.imagersize()
distortion_coeffs = intrinsics_data_from[4: ]
if Rt_to_from is not None:
R_to_from = Rt_to_from[:3,:]
if np.trace(R_to_from) > 3. - 1e-12:
R_to_from = None # identity, so I pass None
else:
R_to_from = None
return nps.glue( *[ nps.dummy(arr,-1) for arr in \
cv2.initUndistortRectifyMap(cameraMatrix_from, distortion_coeffs,
R_to_from,
cameraMatrix_to, tuple(output_shape),
cv2.CV_32FC1)],
axis = -1)
W_from,H_from = model_from.imagersize()
W_to, H_to = model_to. imagersize()
# shape: (Nheight,Nwidth,2). Contains (x,y) rows
grid = np.ascontiguousarray(nps.mv(nps.cat(*np.meshgrid(np.arange(W_to),
np.arange(H_to))),
0,-1),
dtype = float)
if lensmodel_to == "LENSMODEL_PINHOLE":
# Faster path for the unproject. Nice, simple closed-form solution
fxy_to = intrinsics_data_to[0:2]
cxy_to = intrinsics_data_to[2:4]
v = np.zeros( (grid.shape[0], grid.shape[1], 3), dtype=float)
v[..., :2] = (grid-cxy_to)/fxy_to
v[..., 2] = 1
elif lensmodel_to == "LENSMODEL_STEREOGRAPHIC":
# Faster path for the unproject. Nice, simple closed-form solution
v = mrcal.unproject_stereographic(grid, *intrinsics_data_to[:4])
else:
v = mrcal.unproject(grid, lensmodel_to, intrinsics_data_to)
if plane_n is not None:
R_to_from = Rt_to_from[:3,:]
t_to_from = Rt_to_from[ 3,:]
# The homography definition. Derived in many places. For instance in
# "Motion and structure from motion in a piecewise planar environment"
# by Olivier Faugeras, F. Lustman.
A_to_from = plane_d * R_to_from + nps.outer(t_to_from, plane_n)
A_from_to = np.linalg.inv(A_to_from)
v = nps.matmult( v, nps.transpose(A_from_to) )
else:
if Rt_to_from is not None:
R_to_from = Rt_to_from[:3,:]
if np.trace(R_to_from) < 3. - 1e-12:
# rotation isn't identity. apply
v = nps.matmult(v, R_to_from)
mapxy = mrcal.project( v, lensmodel_from, intrinsics_data_from )
if mask_valid_intrinsics_region_from:
# Using matplotlib to compute the out-of-bounds points. It doesn't
# support broadcasting, so I do that manually with a clump/reshape
from matplotlib.path import Path
region = Path(model_from.valid_intrinsics_region())
is_inside = region.contains_points(nps.clump(mapxy,n=2)).reshape(mapxy.shape[:2])
mapxy[ ~is_inside, :] = -1
return mapxy.astype(np.float32)
1 + k[5] * r2 + k[6] * r4 + k[7] * r6))
try:
m = mrcal.cameramodel(args.model)
except:
print(f"Couldn't read '{args.model}' as a camera model", file=sys.stderr)
sys.exit(1)
W, H = m.imagersize()
Nw = 40
Nh = 30
# shape (Nh,Nw,2)
xy = \
nps.mv(nps.cat(*np.meshgrid( np.linspace(0,W-1,Nw),
np.linspace(0,H-1,Nh) )),
0,-1)
fxy = m.intrinsics()[1][0:2]
cxy = m.intrinsics()[1][2:4]
# shape (Nh,Nw,2)
v = mrcal.unproject(np.ascontiguousarray(xy), *m.intrinsics())
v0 = mrcal.unproject(cxy, *m.intrinsics())
# shape (Nh,Nw)
costh = nps.inner(v, v0) / (nps.mag(v) * nps.mag(v0))
th = np.arccos(costh)
# shape (Nh,Nw,2)
xy_rel = xy - cxy
# shape (Nh,Nw)
