def _plot(data, px, title=''):
df2.figure(9003, docla=True, pnum=(2, 4, px))
df2.plot2(data.T[0], data.T[1], '.', title)
def _plotpts(data, px, color=df2.BLUE, label=''):
#df2.figure(9003, docla=True, pnum=(1, 1, px))
df2.plot2(data.T[0], data.T[1], '-', '', color=color, label=label)
df2.update()
def get_kp_border(rchip, kp):
np.set_printoptions(precision=8)
df2.reset()
df2.figure(9003, docla=True, doclf=True)
def _plotpts(data, px, color=df2.BLUE, label=''):
#df2.figure(9003, docla=True, pnum=(1, 1, px))
df2.plot2(data.T[0], data.T[1], '-', '', color=color, label=label)
df2.update()
def _plotarrow(x, y, dx, dy, color=df2.BLUE, label=''):
ax = df2.gca()
arrowargs = dict(head_width=.5, length_includes_head=True, label='')
arrow = df2.FancyArrow(x, y, dx, dy, **arrowargs)
arrow.set_edgecolor(color)
arrow.set_facecolor(color)
ax.add_patch(arrow)
df2.update()
def _2x2_eig(M2x2):
(evals, evecs) = np.linalg.eig(M2x2)
l1, l2 = evals
v1, v2 = evecs
return l1, l2, v1, v2
#-----------------------
# INPUT
#-----------------------
# We are given the keypoint in invA format
(x, y, ia11, ia21, ia22), ia12 = kp, 0
# invA2x2 is a transformation from points on a unit circle to the ellipse
invA2x2 = np.array([[ia11, ia12], [ia21, ia22]])
#-----------------------
# DRAWING
#-----------------------
# Lets start off by drawing the ellipse that we are goign to work with
# Create unit circle sample
tau = 2 * np.pi
theta_list = np.linspace(0, tau, 1000)
cicrle_pts = np.array([(np.cos(t), np.sin(t)) for t in theta_list])
ellipse_pts = invA2x2.dot(cicrle_pts.T).T
_plotpts(ellipse_pts, 0, df2.BLACK, label='invA2x2.dot(unit_circle)')
l1, l2, v1, v2 = _2x2_eig(invA2x2)
dx1, dy1 = (v1 * l1)
dx2, dy2 = (v2 * l2)
_plotarrow(0, 0, dx1, dy1, color=df2.ORANGE, label='invA2x2 e1')
_plotarrow(0, 0, dx2, dy2, color=df2.RED, label='invA2x2 e2')
#-----------------------
# REPRESENTATION
#-----------------------
# A2x2 is a transformation from points on the ellipse to a unit circle
A2x2 = np.linalg.inv(invA2x2)
# Points on a matrix satisfy (x).T.dot(E2x2).dot(x) = 1
E2x2 = A2x2.T.dot(A2x2)
#Lets check our assertion: (x).T.dot(E2x2).dot(x) = 1
checks = [pt.T.dot(E2x2).dot(pt) for pt in ellipse_pts]
assert all([abs(1 - check) < 1E-11 for check in checks])
#-----------------------
# CONIC SECTIONS
#-----------------------
# All of this was from the Perdoch paper, now lets move into conic sections
# We will use the notation from wikipedia
# http://en.wikipedia.org/wiki/Conic_section
# http://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections
# The matrix representation of a conic is:
((A, B, B_, C), (D, E, F)) = (E2x2.flatten(), (0, 0, 1))
assert B == B_, 'matrix should by symmetric'
# A_Q is our conic section (aka ellipse matrix)
A_Q = np.array(((A, B / 2, D / 2), (B / 2, C, E / 2), (D / 2, E / 2, F)))
assert np.linalg.det(A_Q) != 0, 'degenerate conic'
# As long as det(A_Q) is not 0 it is not degenerate and we can work with the
# minor 2x2 matrix
A_33 = np.array(((A, B / 2), (B / 2, C)))
# (det == 0)->parabola, (det < 0)->hyperbola, (det > 0)->ellipse
assert np.linalg.det(A_33) > 0, 'conic is not an ellipse'
# Centers are obtained by solving for where the gradient of the quadratic
# becomes 0. Without going through the derivation the calculation is...
# These should be 0, 0 if we are at the origin, or our original x, y
# coordinate specified by the keypoints. I'm doing the calculation just for
# shits and giggles
x_center = (B * E - (2 * C * D)) / (4 * A * C - B**2)
y_center = (D * B - (2 * A * E)) / (4 * A * C - B**2)
#=================
# DRAWING
#=================
# Now we are going to determine the major and minor axis
# of this beast. It just the center augmented by the eigenvecs
l1, l2, v1, v2 = _2x2_eig(A_33)
dx1, dy1 = 0 - (v1 / np.sqrt(l1))
dx2, dy2 = 0 - (v2 / np.sqrt(l2))
_plotarrow(0, 0, dx1, dy1, color=df2.BLUE)
_plotarrow(0, 0, dx2, dy2, color=df2.BLUE)
# The angle between the major axis and our x axis is:
x_axis = np.array([1, 0])
theta = np.arccos(x_axis.dot(evec1))
# The eccentricity is determined by:
nu = 1
numer = 2 * np.sqrt((A - C)**2 + B**2)
denom = nu * (A + C) + np.sqrt((A - C)**2 + B**2)
eccentricity = np.sqrt(numer / denom)
from scipy.special import ellipeinc
# Algebraic form of connic
#assert (a * (x ** 2)) + (b * (x * y)) + (c * (y ** 2)) + (d * x) + (e * y) + (f) == 0
#---------------------
invA = np.array([[a, 0], [c, d]])
Ashape = np.linalg.inv(np.array([[a, 0], [c, d]]))
Ashape /= np.sqrt(np.linalg.det(Ashape))
tau = 2 * np.pi
nSamples = 100
theta_list = np.linspace(0, tau, nSamples)
# Create unit circle sample
cicrle_pts = np.array([(np.cos(t), np.sin(t)) for t in theta_list])
circle_hpts = np.hstack([cicrle_pts, np.ones((len(cicrle_pts), 1))])
# Transform as if the unit cirle was the warped patch
ashape_pts = Ashape.dot(cicrle_pts.T).T
inv = np.linalg.inv
svd = np.linalg.svd
U, S_, V = svd(Ashape)
S = np.diag(S_)
pxl_list3 = invA.dot(cicrle_pts[:, 0:2].T).T
pxl_list4 = invA.dot(ashape_pts[:, 0:2].T).T
pxl_list5 = invA.T.dot(cicrle_pts[:, 0:2].T).T
pxl_list6 = invA.T.dot(ashape_pts[:, 0:2].T).T
pxl_list7 = inv(V).dot(ashape_pts[:, 0:2].T).T
pxl_list8 = inv(U).dot(ashape_pts[:, 0:2].T).T
df2.draw()
def _plot(data, px, title=''):
df2.figure(9003, docla=True, pnum=(2, 4, px))
df2.plot2(data.T[0], data.T[1], '.', title)
df2.figure(9003, doclf=True)
_plot(cicrle_pts, 1, 'unit circle')
_plot(ashape_pts, 2, 'A => circle shape')
_plot(pxl_list3, 3)
_plot(pxl_list4, 4)
_plot(pxl_list5, 5)
_plot(pxl_list6, 6)
_plot(pxl_list7, 7)
_plot(pxl_list8, 8)
df2.draw()
invA = np.array([[a, 0, x], [c, d, y], [0, 0, 1]])
pxl_list = invA.dot(circle_hpts.T).T[:, 0:2]
df2.figure(9002, doclf=True)
df2.imshow(rchip)
df2.plot2(pxl_list.T[0], pxl_list.T[1], '.')
df2.draw()
vals = [cv2.getRectSubPix(rchip, (1, 1), tuple(pxl)) for pxl in pxl_list]
return vals
def _plot(data, px, title=''):
df2.figure(9003, docla=True, pnum=(2, 4, px))
df2.plot2(data.T[0], data.T[1], '.', title)
def _plotpts(data, px, color=df2.BLUE, label=''):
#df2.figure(9003, docla=True, pnum=(1, 1, px))
df2.plot2(data.T[0], data.T[1], '-', '', color=color, label=label)
df2.update()
def get_kp_border(rchip, kp):
np.set_printoptions(precision=8)
df2.reset()
df2.figure(9003, docla=True, doclf=True)
def _plotpts(data, px, color=df2.BLUE, label=''):
#df2.figure(9003, docla=True, pnum=(1, 1, px))
df2.plot2(data.T[0], data.T[1], '-', '', color=color, label=label)
df2.update()
def _plotarrow(x, y, dx, dy, color=df2.BLUE, label=''):
ax = df2.gca()
arrowargs = dict(head_width=.5, length_includes_head=True, label='')
arrow = df2.FancyArrow(x, y, dx, dy, **arrowargs)
arrow.set_edgecolor(color)
arrow.set_facecolor(color)
ax.add_patch(arrow)
df2.update()
def _2x2_eig(M2x2):
(evals, evecs) = np.linalg.eig(M2x2)
l1, l2 = evals
v1, v2 = evecs
return l1, l2, v1, v2
#-----------------------
# INPUT
#-----------------------
# We are given the keypoint in invA format
(x, y, ia11, ia21, ia22), ia12 = kp, 0
# invA2x2 is a transformation from points on a unit circle to the ellipse
invA2x2 = np.array([[ia11, ia12],
[ia21, ia22]])
#-----------------------
# DRAWING
#-----------------------
# Lets start off by drawing the ellipse that we are goign to work with
# Create unit circle sample
tau = 2 * np.pi
theta_list = np.linspace(0, tau, 1000)
cicrle_pts = np.array([(np.cos(t), np.sin(t)) for t in theta_list])
ellipse_pts = invA2x2.dot(cicrle_pts.T).T
_plotpts(ellipse_pts, 0, df2.BLACK, label='invA2x2.dot(unit_circle)')
l1, l2, v1, v2 = _2x2_eig(invA2x2)
dx1, dy1 = (v1 * l1)
dx2, dy2 = (v2 * l2)
_plotarrow(0, 0, dx1, dy1, color=df2.ORANGE, label='invA2x2 e1')
_plotarrow(0, 0, dx2, dy2, color=df2.RED, label='invA2x2 e2')
#-----------------------
# REPRESENTATION
#-----------------------
# A2x2 is a transformation from points on the ellipse to a unit circle
A2x2 = np.linalg.inv(invA2x2)
# Points on a matrix satisfy (x).T.dot(E2x2).dot(x) = 1
E2x2 = A2x2.T.dot(A2x2)
#Lets check our assertion: (x).T.dot(E2x2).dot(x) = 1
checks = [pt.T.dot(E2x2).dot(pt) for pt in ellipse_pts]
assert all([abs(1 - check) < 1E-11 for check in checks])
#-----------------------
# CONIC SECTIONS
#-----------------------
# All of this was from the Perdoch paper, now lets move into conic sections
# We will use the notation from wikipedia
# http://en.wikipedia.org/wiki/Conic_section
# http://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections
# The matrix representation of a conic is:
((A, B, B_, C), (D, E, F)) = (E2x2.flatten(), (0, 0, 1))
assert B == B_, 'matrix should by symmetric'
# A_Q is our conic section (aka ellipse matrix)
A_Q = np.array((( A, B / 2, D / 2),
(B / 2, C, E / 2),
(D / 2, E / 2, F)))
assert np.linalg.det(A_Q) != 0, 'degenerate conic'
# As long as det(A_Q) is not 0 it is not degenerate and we can work with the
# minor 2x2 matrix
A_33 = np.array((( A, B / 2),
(B / 2, C)))
# (det == 0)->parabola, (det < 0)->hyperbola, (det > 0)->ellipse
assert np.linalg.det(A_33) > 0, 'conic is not an ellipse'
# Centers are obtained by solving for where the gradient of the quadratic
# becomes 0. Without going through the derivation the calculation is...
# These should be 0, 0 if we are at the origin, or our original x, y
# coordinate specified by the keypoints. I'm doing the calculation just for
# shits and giggles
x_center = (B * E - (2 * C * D)) / (4 * A * C - B ** 2)
y_center = (D * B - (2 * A * E)) / (4 * A * C - B ** 2)
#=================
# DRAWING
#=================
# Now we are going to determine the major and minor axis
# of this beast. It just the center augmented by the eigenvecs
l1, l2, v1, v2 = _2x2_eig(A_33)
dx1, dy1 = 0 - (v1 / np.sqrt(l1))
dx2, dy2 = 0 - (v2 / np.sqrt(l2))
_plotarrow(0, 0, dx1, dy1, color=df2.BLUE)
_plotarrow(0, 0, dx2, dy2, color=df2.BLUE)
# The angle between the major axis and our x axis is:
x_axis = np.array([1, 0])
theta = np.arccos(x_axis.dot(evec1))
# The eccentricity is determined by:
nu = 1
numer = 2 * np.sqrt((A - C) ** 2 + B ** 2)
denom = nu * (A + C) + np.sqrt((A - C) ** 2 + B ** 2)
eccentricity = np.sqrt(numer / denom)
from scipy.special import ellipeinc
# Algebraic form of connic
#assert (a * (x ** 2)) + (b * (x * y)) + (c * (y ** 2)) + (d * x) + (e * y) + (f) == 0
#---------------------
invA = np.array([[a, 0],
[c, d]])
Ashape = np.linalg.inv(np.array([[a, 0],
[c, d]]))
Ashape /= np.sqrt(np.linalg.det(Ashape))
tau = 2 * np.pi
nSamples = 100
theta_list = np.linspace(0, tau, nSamples)
# Create unit circle sample
cicrle_pts = np.array([(np.cos(t), np.sin(t)) for t in theta_list])
circle_hpts = np.hstack([cicrle_pts, np.ones((len(cicrle_pts), 1))])
# Transform as if the unit cirle was the warped patch
ashape_pts = Ashape.dot(cicrle_pts.T).T
inv = np.linalg.inv
svd = np.linalg.svd
U, S_, V = svd(Ashape)
S = np.diag(S_)
pxl_list3 = invA.dot(cicrle_pts[:, 0:2].T).T
pxl_list4 = invA.dot(ashape_pts[:, 0:2].T).T
pxl_list5 = invA.T.dot(cicrle_pts[:, 0:2].T).T
pxl_list6 = invA.T.dot(ashape_pts[:, 0:2].T).T
pxl_list7 = inv(V).dot(ashape_pts[:, 0:2].T).T
pxl_list8 = inv(U).dot(ashape_pts[:, 0:2].T).T
df2.draw()
def _plot(data, px, title=''):
df2.figure(9003, docla=True, pnum=(2, 4, px))
df2.plot2(data.T[0], data.T[1], '.', title)
df2.figure(9003, doclf=True)
_plot(cicrle_pts, 1, 'unit circle')
_plot(ashape_pts, 2, 'A => circle shape')
_plot(pxl_list3, 3)
_plot(pxl_list4, 4)
_plot(pxl_list5, 5)
_plot(pxl_list6, 6)
_plot(pxl_list7, 7)
_plot(pxl_list8, 8)
df2.draw()
invA = np.array([[a, 0, x],
[c, d, y],
[0, 0, 1]])
pxl_list = invA.dot(circle_hpts.T).T[:, 0:2]
df2.figure(9002, doclf=True)
df2.imshow(rchip)
df2.plot2(pxl_list.T[0], pxl_list.T[1], '.')
df2.draw()
vals = [cv2.getRectSubPix(rchip, (1, 1), tuple(pxl)) for pxl in pxl_list]
return vals
