def kpts_matrices(kpts):
# We are given the keypoint in invA format
# invV = perdoch.invA
# V = perdoch.A
# Z = perdoch.E
# invert into V
#invV = kpts_to_invV(kpts)
invV = ktool.get_invV_mats3x3(kpts)
V = ktool.invert_invV_mats(invV)
Z = ktool.get_Z_mats(V)
return invV, V, Z
def kpts_matrices(kpts):
# We are given the keypoint in invA format
# invV = perdoch.invA
# V = perdoch.A
# Z = perdoch.E
# invert into V
#invV = kpts_to_invV(kpts)
invV = ktool.get_invV_mats3x3(kpts)
V = ktool.invert_invV_mats(invV)
Z = ktool.get_Z_mats(V)
return invV, V, Z
def check_kpts_in_bounds(kpts_, width, height):
# Test to make sure the extents of the keypoints are in bounds
unit_bbox = np.array([(-1, -1, 1), (-1, 1, 1), (1, -1, 1), (1, 1, 1)]).T
#invV = kpts_to_invV(kpts_)
invV = ktool.get_invV_mats3x3(kpts_)
bbox_pts = [v.dot(unit_bbox)[0:2] for v in invV]
maxx = np.array([pts[0].max() for pts in bbox_pts]) < width
minx = np.array([pts[0].min() for pts in bbox_pts]) > 0
maxy = np.array([pts[1].max() for pts in bbox_pts]) < height
miny = np.array([pts[1].min() for pts in bbox_pts]) > 0
isvalid = np.array(maxx * minx * maxy * miny, dtype=np.bool)
return isvalid
def check_kpts_in_bounds(kpts_, width, height):
# Test to make sure the extents of the keypoints are in bounds
unit_bbox = np.array([(-1, -1, 1),
(-1, 1, 1),
( 1, -1, 1),
( 1, 1, 1)]).T
#invV = kpts_to_invV(kpts_)
invV = ktool.get_invV_mats3x3(kpts_)
bbox_pts = [v.dot(unit_bbox)[0:2] for v in invV]
maxx = np.array([pts[0].max() for pts in bbox_pts]) < width
minx = np.array([pts[0].min() for pts in bbox_pts]) > 0
maxy = np.array([pts[1].max() for pts in bbox_pts]) < height
miny = np.array([pts[1].min() for pts in bbox_pts]) > 0
isvalid = np.array(maxx * minx * maxy * miny, dtype=np.bool)
return isvalid
def sample_uniform(kpts, nSamples=128):
"""
SeeAlso:
python -m pyhesaff.tests.test_ellipse --test-in_depth_ellipse --show
"""
nKp = len(kpts)
# Get keypoint matrix forms
invV_mats3x3 = ktool.get_invV_mats3x3(kpts)
V_mats3x3 = ktool.invert_invV_mats(invV_mats3x3)
#-------------------------------
# Get uniform points on a circle
circle_pts = homogenous_circle_pts(nSamples + 1)[0:-1]
assert circle_pts.shape == (nSamples, 3)
#-------------------------------
# Get uneven points sample (get_uneven_point_sample)
polygon1_list = matrix_multiply(invV_mats3x3,
circle_pts.T).transpose(0, 2, 1)
assert polygon1_list.shape == (nKp, nSamples, 3)
# -------------------------------
# The transformed points are not sampled uniformly... Bummer
# We will sample points evenly across the sampled polygon
# then we will project them onto the ellipse
dists = np.array([circular_distance(arr) for arr in polygon1_list])
assert dists.shape == (nKp, nSamples)
# perimeter of the polygon
perimeter = dists.sum(1)
assert perimeter.shape == (nKp, )
# Take a perfect multiple of steps along the perimeter
multiplier = 1
step_size = perimeter / (nSamples * multiplier)
assert step_size.shape == (nKp, )
# Walk along edge
num_steps_list = []
offset_list = []
total_dist = np.zeros(step_size.shape) # step_size.copy()
dist_walked = np.zeros(step_size.shape)
assert dist_walked.shape == (nKp, )
assert total_dist.shape == (nKp, )
distsT = dists.T
assert distsT.shape == (nSamples, nKp)
# This loops over the pt samples and performs the operation for every keypoint
for count in range(nSamples):
segment_len = distsT[count]
# Find where your starting location is
offset_list.append(total_dist - dist_walked)
# How far can you possibly go?
total_dist += segment_len
# How many steps can you take?
num_steps = (total_dist - dist_walked) // step_size
num_steps_list.append(num_steps)
# Log how much further youve gotten
dist_walked += (num_steps * step_size)
# Check for floating point errors
# take an extra step if you need to
num_steps_list[-1] += np.round((perimeter - dist_walked) / step_size)
assert np.all(np.array(num_steps_list).sum(0) == nSamples)
"""
#offset_iter1 = zip(num_steps_list, distsT, offset_list)
#offset_list = [((step_size - offset) / dist, ((num * step_size) - offset) / dist, num)
#for num, dist, offset in zip(num_steps_list, distsT, offset_list)]
#offset_iter2 = offset_list
#cut_locs = [[
#np.linspace(off1, off2, n, endpoint=True) for (off1, off2, n) in zip(offset1, offset2, num)]
#for (offset1, offset2, num) in offset_iter2
#]
# store the percent location at each line segment where
# the cut will be made
"""
# HERE IS NEXT
cut_list = []
# This loops over the pt samples and performs the operation for every keypoint
for num, dist, offset in zip(num_steps_list, distsT, offset_list):
#if num == 0
#cut_list.append([])
#continue
# This was a bitch to keep track of
offset1 = (step_size - offset) / dist
offset2 = ((num * step_size) - offset) / dist
cut_locs = [
np.linspace(off1, off2, n, endpoint=True)
for (off1, off2, n) in zip(offset1, offset2, num)
]
# post check for divide by 0
cut_locs = [
np.array([0 if np.isinf(c) else c for c in cut])
for cut in cut_locs
]
cut_list.append(cut_locs)
cut_list = np.array(cut_list).T
assert cut_list.shape == (nKp, nSamples)
# =================
# METHOD 1
# =================
# Linearly interpolate between points on the polygons at the places we cut
def interpolate(pt1, pt2, percent):
# interpolate between point1 and point2
return ((1 - percent) * pt1) + ((percent) * pt2)
def polygon_points(polygon_pts, dist_list):
return np.array([
interpolate(polygon_pts[count],
polygon_pts[(count + 1) % nSamples], loc)
for count, locs in enumerate(dist_list) for loc in iter(locs)
])
new_locations = np.array([
polygon_points(polygon_pts, cuts)
for polygon_pts, cuts in zip(polygon1_list, cut_list)
])
# =================
# =================
# METHOD 2
"""
#from itertools import cycle as icycle
#from itertools import islice
#def icycle_shift1(iterable):
#return islice(icycle(poly_pts), 1, len(poly_pts) + 1)
#cutptsIter_list = [zip(iter(poly_pts), icycle_shift1(poly_pts), cuts)
#for poly_pts, cuts in zip(polygon1_list, cut_list)]
#new_locations = [[[((1 - cut) * pt1) + ((cut) * pt2) for cut in cuts]
#for (pt1, pt2, cuts) in cutPtsIter]
#for cutPtsIter in cutptsIter_list]
"""
# =================
# assert new_locations.shape == (nKp, nSamples, 3)
# Warp new_locations to the unit circle
#new_unit = V.dot(new_locations.T).T
new_unit = np.array(
[v.dot(newloc.T).T for v, newloc in zip(V_mats3x3, new_locations)])
# normalize new_unit
new_mag = np.sqrt((new_unit**2).sum(-1))
new_unorm_unit = new_unit / np.dstack([new_mag] * 3)
new_norm_unit = new_unorm_unit / np.dstack([new_unorm_unit[:, :, 2]] * 3)
# Get angle (might not be necessary)
#x_axis = np.array([1, 0, 0])
#arccos_list = x_axis.dot(new_norm_unit.T)
#uniform_theta_list = np.arccos(arccos_list)
# Maybe this?
# Find the angle from the center of the circle
theta_list2 = np.arctan2(new_norm_unit[:, :, 1], new_norm_unit[:, :, 0])
# assert uniform_theta_list.shape = (nKp, nSample)
# Use this angle to unevenly sample the perimeter of the circle
uneven_cicrle_pts = np.dstack(
[np.cos(theta_list2),
np.sin(theta_list2),
np.ones(theta_list2.shape)])
# The uneven circle points were sampled in such a way that when they are
# transformeed they will be approximately uniform along the boundary of the
# ellipse.
uniform_ell_hpts = [
v.dot(pts.T).T for (v, pts) in zip(invV_mats3x3, uneven_cicrle_pts)
]
# Remove the homogenous coordinate and we're done
ell_border_pts_list = [pts[:, 0:2] for pts in uniform_ell_hpts]
return ell_border_pts_list
def sample_uniform(kpts, nSamples=128):
"""
SeeAlso:
python -m pyhesaff.tests.test_ellipse --test-in_depth_ellipse --show
"""
nKp = len(kpts)
# Get keypoint matrix forms
invV_mats3x3 = ktool.get_invV_mats3x3(kpts)
V_mats3x3 = ktool.invert_invV_mats(invV_mats3x3)
#-------------------------------
# Get uniform points on a circle
circle_pts = homogenous_circle_pts(nSamples + 1)[0:-1]
assert circle_pts.shape == (nSamples, 3)
#-------------------------------
# Get uneven points sample (get_uneven_point_sample)
polygon1_list = matrix_multiply(invV_mats3x3, circle_pts.T).transpose(0, 2, 1)
assert polygon1_list.shape == (nKp, nSamples, 3)
# -------------------------------
# The transformed points are not sampled uniformly... Bummer
# We will sample points evenly across the sampled polygon
# then we will project them onto the ellipse
dists = np.array([circular_distance(arr) for arr in polygon1_list])
assert dists.shape == (nKp, nSamples)
# perimeter of the polygon
perimeter = dists.sum(1)
assert perimeter.shape == (nKp,)
# Take a perfect multiple of steps along the perimeter
multiplier = 1
step_size = perimeter / (nSamples * multiplier)
assert step_size.shape == (nKp,)
# Walk along edge
num_steps_list = []
offset_list = []
total_dist = np.zeros(step_size.shape) # step_size.copy()
dist_walked = np.zeros(step_size.shape)
assert dist_walked.shape == (nKp,)
assert total_dist.shape == (nKp,)
distsT = dists.T
assert distsT.shape == (nSamples, nKp)
# This loops over the pt samples and performs the operation for every keypoint
for count in range(nSamples):
segment_len = distsT[count]
# Find where your starting location is
offset_list.append(total_dist - dist_walked)
# How far can you possibly go?
total_dist += segment_len
# How many steps can you take?
num_steps = (total_dist - dist_walked) // step_size
num_steps_list.append(num_steps)
# Log how much further youve gotten
dist_walked += (num_steps * step_size)
# Check for floating point errors
# take an extra step if you need to
num_steps_list[-1] += np.round((perimeter - dist_walked) / step_size)
assert np.all(np.array(num_steps_list).sum(0) == nSamples)
"""
#offset_iter1 = zip(num_steps_list, distsT, offset_list)
#offset_list = [((step_size - offset) / dist, ((num * step_size) - offset) / dist, num)
#for num, dist, offset in zip(num_steps_list, distsT, offset_list)]
#offset_iter2 = offset_list
#cut_locs = [[
#np.linspace(off1, off2, n, endpoint=True) for (off1, off2, n) in zip(offset1, offset2, num)]
#for (offset1, offset2, num) in offset_iter2
#]
# store the percent location at each line segment where
# the cut will be made
"""
# HERE IS NEXT
cut_list = []
# This loops over the pt samples and performs the operation for every keypoint
for num, dist, offset in zip(num_steps_list, distsT, offset_list):
#if num == 0
#cut_list.append([])
#continue
# This was a bitch to keep track of
offset1 = (step_size - offset) / dist
offset2 = ((num * step_size) - offset) / dist
cut_locs = [np.linspace(off1, off2, n, endpoint=True) for (off1, off2, n) in zip(offset1, offset2, num)]
# post check for divide by 0
cut_locs = [np.array([0 if np.isinf(c) else c for c in cut]) for cut in cut_locs]
cut_list.append(cut_locs)
cut_list = np.array(cut_list).T
assert cut_list.shape == (nKp, nSamples)
# =================
# METHOD 1
# =================
# Linearly interpolate between points on the polygons at the places we cut
def interpolate(pt1, pt2, percent):
# interpolate between point1 and point2
return ((1 - percent) * pt1) + ((percent) * pt2)
def polygon_points(polygon_pts, dist_list):
return np.array([interpolate(polygon_pts[count], polygon_pts[(count + 1) % nSamples], loc)
for count, locs in enumerate(dist_list)
for loc in iter(locs)])
new_locations = np.array([polygon_points(polygon_pts, cuts) for polygon_pts,
cuts in zip(polygon1_list, cut_list)])
# =================
# =================
# METHOD 2
"""
#from itertools import cycle as icycle
#from itertools import islice
#def icycle_shift1(iterable):
#return islice(icycle(poly_pts), 1, len(poly_pts) + 1)
#cutptsIter_list = [zip(iter(poly_pts), icycle_shift1(poly_pts), cuts)
#for poly_pts, cuts in zip(polygon1_list, cut_list)]
#new_locations = [[[((1 - cut) * pt1) + ((cut) * pt2) for cut in cuts]
#for (pt1, pt2, cuts) in cutPtsIter]
#for cutPtsIter in cutptsIter_list]
"""
# =================
# assert new_locations.shape == (nKp, nSamples, 3)
# Warp new_locations to the unit circle
#new_unit = V.dot(new_locations.T).T
new_unit = np.array([v.dot(newloc.T).T for v, newloc in zip(V_mats3x3, new_locations)])
# normalize new_unit
new_mag = np.sqrt((new_unit ** 2).sum(-1))
new_unorm_unit = new_unit / np.dstack([new_mag] * 3)
new_norm_unit = new_unorm_unit / np.dstack([new_unorm_unit[:, :, 2]] * 3)
# Get angle (might not be necessary)
#x_axis = np.array([1, 0, 0])
#arccos_list = x_axis.dot(new_norm_unit.T)
#uniform_theta_list = np.arccos(arccos_list)
# Maybe this?
# Find the angle from the center of the circle
theta_list2 = np.arctan2(new_norm_unit[:, :, 1], new_norm_unit[:, :, 0])
# assert uniform_theta_list.shape = (nKp, nSample)
# Use this angle to unevenly sample the perimeter of the circle
uneven_cicrle_pts = np.dstack([np.cos(theta_list2), np.sin(theta_list2), np.ones(theta_list2.shape)])
# The uneven circle points were sampled in such a way that when they are
# transformeed they will be approximately uniform along the boundary of the
# ellipse.
uniform_ell_hpts = [v.dot(pts.T).T for (v, pts) in zip(invV_mats3x3, uneven_cicrle_pts)]
# Remove the homogenous coordinate and we're done
ell_border_pts_list = [pts[:, 0:2] for pts in uniform_ell_hpts]
return ell_border_pts_list
