def save_if_requested(hs, subdir):
if not hs.args.save_figures:
return
#print('[viz] Dumping Image')
fpath = hs.dirs.result_dir
if not subdir is None:
subdir = helpers.sanatize_fname2(subdir)
fpath = join(fpath, subdir)
helpers.ensurepath(fpath)
df2.save_figure(fpath=fpath, usetitle=True)
df2.reset()
def dump(hs, subdir=None, quality=False, overwrite=False):
if quality is True:
df2.FIGSIZE = df2.golden_wh2(12)
df2.DPI = 120
df2.FONTS.figtitle = df2.FONTS.small
if quality is False:
df2.FIGSIZE = df2.golden_wh2(8)
df2.DPI = 90
df2.FONTS.figtitle = df2.FONTS.smaller
#print('[viz] Dumping Image')
fpath = hs.dirs.result_dir
if subdir is not None:
fpath = join(fpath, subdir)
helpers.ensurepath(fpath)
df2.save_figure(fpath=fpath, usetitle=True, overwrite=overwrite)
df2.reset()
def test_realdata2():
from helpers import printWARN, printINFO
import warnings
import numpy.linalg as linalg
import numpy as np
import scipy.sparse as sparse
import scipy.sparse.linalg as sparse_linalg
import load_data2
import params
import draw_func2 as df2
import helpers
import spatial_verification
#params.reload_module()
#load_data2.reload_module()
#df2.reload_module()
db_dir = load_data2.MOTHERS
hs = load_data2.HotSpotter(db_dir)
assign_matches = hs.matcher.assign_matches
qcx = 0
cx = hs.get_other_cxs(qcx)[0]
fm, fs, score = hs.get_assigned_matches_to(qcx, cx)
# Get chips
rchip1 = hs.get_chip(qcx)
rchip2 = hs.get_chip(cx)
# Get keypoints
kpts1 = hs.get_kpts(qcx)
kpts2 = hs.get_kpts(cx)
# Get feature matches
kpts1_m = kpts1[fm[:, 0], :].T
kpts2_m = kpts2[fm[:, 1], :].T
title='(qx%r v cx%r)\n #match=%r' % (qcx, cx, len(fm))
df2.show_matches2(rchip1, rchip2, kpts1, kpts2, fm, fs, title=title)
np.random.seed(6)
subst = helpers.random_indexes(len(fm),len(fm))
kpts1_m = kpts1[fm[subst, 0], :].T
kpts2_m = kpts2[fm[subst, 1], :].T
df2.reload_module()
df2.SHOW_LINES = True
df2.ELL_LINEWIDTH = 2
df2.LINE_ALPHA = .5
df2.ELL_ALPHA = 1
df2.reset()
df2.show_keypoints(rchip1, kpts1_m.T, fignum=0, plotnum=121)
df2.show_keypoints(rchip2, kpts2_m.T, fignum=0, plotnum=122)
df2.show_matches2(rchip1, rchip2, kpts1_m.T, kpts2_m.T, title=title,
fignum=1, vert=True)
spatial_verification.reload_module()
with helpers.Timer():
aff_inliers1 = spatial_verification.aff_inliers_from_ellshape2(kpts1_m, kpts2_m, xy_thresh_sqrd)
with helpers.Timer():
aff_inliers2 = spatial_verification.aff_inliers_from_ellshape(kpts1_m, kpts2_m, xy_thresh_sqrd)
# Homogonize+Normalize
xy1_m = kpts1_m[0:2,:]
xy2_m = kpts2_m[0:2,:]
(xyz_norm1, T1) = spatial_verification.homogo_normalize_pts(xy1_m[:,aff_inliers1])
(xyz_norm2, T2) = spatial_verification.homogo_normalize_pts(xy2_m[:,aff_inliers1])
H_prime = spatial_verification.compute_homog(xyz_norm1, xyz_norm2)
H = linalg.solve(T2, H_prime).dot(T1) # Unnormalize
Hdet = linalg.det(H)
# Estimate final inliers
acd1_m = kpts1_m[2:5,:] # keypoint shape matrix [a 0; c d] matches
acd2_m = kpts2_m[2:5,:]
# Precompute the determinant of lower triangular matrix (a*d - b*c); b = 0
det1_m = acd1_m[0] * acd1_m[2]
det2_m = acd2_m[0] * acd2_m[2]
# Matrix Multiply xyacd matrix by H
# [[A, B, X],
# [C, D, Y],
# [E, F, Z]]
# dot
# [(a, 0, x),
# (c, d, y),
# (0, 0, 1)]
# =
# [(a*A + c*B + 0*E, 0*A + d*B + 0*X, x*A + y*B + 1*X),
# (a*C + c*D + 0*Y, 0*C + d*D + 0*Y, x*C + y*D + 1*Y),
# (a*E + c*F + 0*Z, 0*E + d*F + 0*Z, x*E + y*F + 1*Z)]
# =
# [(a*A + c*B, d*B, x*A + y*B + X),
# (a*C + c*D, d*D, x*C + y*D + Y),
# (a*E + c*F, d*F, x*E + y*F + Z)]
# # IF x=0 and y=0
# =
# [(a*A + c*B, d*B, 0*A + 0*B + X),
# (a*C + c*D, d*D, 0*C + 0*D + Y),
# (a*E + c*F, d*F, 0*E + 0*F + Z)]
# =
# [(a*A + c*B, d*B, X),
# (a*C + c*D, d*D, Y),
# (a*E + c*F, d*F, Z)]
# ---
# A11 = a*A + c*B
# A21 = a*C + c*D
# A31 = a*E + c*F
# A12 = d*B
# A22 = d*D
# A32 = d*F
# A31 = X
# A32 = Y
# A33 = Z
#
# det(A) = A11*(A22*A33 - A23*A32) - A12*(A21*A33 - A23*A31) + A13*(A21*A32 - A22*A31)
det1_mAt = det1_m * Hdet
# Check Error in position and scale
xy_sqrd_err = (x1_mAt - x2_m)**2 + (y1_mAt - y2_m)**2
scale_sqrd_err = det1_mAt / det2_m
# Check to see if outliers are within bounds
xy_inliers = xy_sqrd_err < xy_thresh_sqrd
s1_inliers = scale_sqrd_err > scale_thresh_low
s2_inliers = scale_sqrd_err < scale_thresh_high
_inliers, = np.where(np.logical_and(np.logical_and(xy_inliers, s1_inliers), s2_inliers))
xy1_mHt = transform_xy(H, xy1_m) # Transform Kpts1 to Kpts2-space
sqrd_dist_error = np.sum( (xy1_mHt - xy2_m)**2, axis=0) # Final Inlier Errors
inliers = sqrd_dist_error < xy_thresh_sqrd
df2.show_matches2(rchip1, rchip2, kpts1_m.T[best_inliers1], kpts2_m.T[aff_inliers1], title=title, fignum=2, vert=False)
df2.show_matches2(rchip1, rchip2, kpts1_m.T[best_inliers2], kpts2_m.T[aff_inliers2], title=title, fignum=3, vert=False)
df2.present(wh=(600,400))
data_ = pca.transform(data)
nn2_data_ = pca.transform(nn2_data)
qx2_nn_ = pca.transform(qx2_nn)
krx2_query_ = pca.transform(krx2_query)
krx2_nn_ = pca.transform(krx2_nn)
else:
print('Plotting full dimensionality')
query_ = (query)
data_ = (data)
qx2_nn_ = (qx2_nn)
krx2_query_ = (krx2_query)
krx2_nn_ = (krx2_nn)
# Figure and Axis
plt = df2.plt
df2.reset()
fig = plt.figure(1)
if tdim == 2:
ax = fig.add_subplot(111)
elif tdim > 2:
from mpl_toolkits.mplot3d import Axes3D
ax = fig.add_subplot(111, projection='3d')
def plot_points(data, color, marker):
dataT = data.T
if len(dataT) == 2:
ax.plot(dataT[0],
dataT[1],
color=color,
marker=marker,
data_ = pca.transform(data)
nn2_data_ = pca.transform(nn2_data)
qx2_nn_ = pca.transform(qx2_nn)
krx2_query_ = pca.transform(krx2_query)
krx2_nn_ = pca.transform(krx2_nn)
else:
print('Plotting full dimensionality')
query_ = (query)
data_ = (data)
qx2_nn_ = (qx2_nn)
krx2_query_ = (krx2_query)
krx2_nn_ = (krx2_nn)
# Figure and Axis
plt = df2.plt
df2.reset()
fig = plt.figure(1)
if tdim == 2:
ax = fig.add_subplot(111)
elif tdim > 2:
from mpl_toolkits.mplot3d import Axes3D
ax = fig.add_subplot(111, projection='3d')
def plot_points(data, color, marker):
dataT = data.T
if len(dataT) == 2:
ax.plot(dataT[0], dataT[1], color=color, marker=marker, linestyle='None')
elif len(dataT) == 3:
ax.scatter(dataT[0], dataT[1], dataT[2], color=color, marker=marker)
def plot_lines(point_pairs, color):
def in_depth_ellipse2x2(rchip, kp):
#-----------------------
# SETUP
#-----------------------
from hotspotter import draw_func2 as df2
np.set_printoptions(precision=8)
tau = 2 * np.pi
df2.reset()
df2.figure(9003, docla=True, doclf=True)
ax = df2.gca()
ax.invert_yaxis()
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=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 will call perdoch's invA = invV
print('--------------------------------')
print('Let V = Perdoch.A')
print('Let Z = Perdoch.E')
print('--------------------------------')
print('Input from Perdoch\'s detector: ')
# We are given the keypoint in invA format
(x, y, ia11, ia21, ia22), ia12 = kp, 0
invV = np.array([[ia11, ia12], [ia21, ia22]])
V = np.linalg.inv(invV)
# <HACK>
#invV = V / np.linalg.det(V)
#V = np.linalg.inv(V)
# </HACK>
Z = (V.T).dot(V)
print('invV is a transform from points on a unit-circle to the ellipse')
helpers.horiz_print('invV = ', invV)
print('--------------------------------')
print('V is a transformation from points on the ellipse to a unit circle')
helpers.horiz_print('V = ', V)
print('--------------------------------')
print('Points on a matrix satisfy (x).T.dot(Z).dot(x) = 1')
print('where Z = (V.T).dot(V)')
helpers.horiz_print('Z = ', Z)
# Define points on a unit circle
theta_list = np.linspace(0, tau, 50)
cicrle_pts = np.array([(np.cos(t), np.sin(t)) for t in theta_list])
# Transform those points to the ellipse using invV
ellipse_pts1 = invV.dot(cicrle_pts.T).T
# Transform those points to the ellipse using V
ellipse_pts2 = V.dot(cicrle_pts.T).T
#Lets check our assertion: (x_).T.dot(Z).dot(x_) = 1
checks1 = [x_.T.dot(Z).dot(x_) for x_ in ellipse_pts1]
checks2 = [x_.T.dot(Z).dot(x_) for x_ in ellipse_pts2]
assert all([abs(1 - check) < 1E-11 for check in checks1])
#assert all([abs(1 - check) < 1E-11 for check in checks2])
print('... all of our plotted points satisfy this')
#=======================
# THE CONIC SECTION
#=======================
# 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
#-----------------------
# MATRIX REPRESENTATION
#-----------------------
# The matrix representation of a conic is:
(A, B2, B2_, C) = Z.flatten()
(D, E, F) = (0, 0, 1)
B = B2 * 2
assert B2 == B2_, 'matrix should by symmetric'
print('--------------------------------')
print('Now, using wikipedia\' matrix representation of a conic.')
con = np.array(((' A', 'B / 2', 'D / 2'), ('B / 2', ' C', 'E / 2'),
('D / 2', 'E / 2', ' F')))
helpers.horiz_print('A matrix A_Q = ', con)
# 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)))
helpers.horiz_print('A_Q = ', A_Q)
#-----------------------
# DEGENERATE CONICS
#-----------------------
print('----------------------------------')
print('As long as det(A_Q) != it is not degenerate.')
print('If the conic is not degenerate, we can use the 2x2 minor: A_33')
print('det(A_Q) = %s' % str(np.linalg.det(A_Q)))
assert np.linalg.det(A_Q) != 0, 'degenerate conic'
A_33 = np.array(((A, B / 2), (B / 2, C)))
helpers.horiz_print('A_33 = ', A_33)
#-----------------------
# CONIC CLASSIFICATION
#-----------------------
print('----------------------------------')
print('The determinant of the minor classifies the type of conic it is')
print('(det == 0): parabola, (det < 0): hyperbola, (det > 0): ellipse')
print('det(A_33) = %s' % str(np.linalg.det(A_33)))
assert np.linalg.det(A_33) > 0, 'conic is not an ellipse'
print('... this is indeed an ellipse')
#-----------------------
# CONIC CENTER
#-----------------------
print('----------------------------------')
print('the centers of the ellipse are obtained by: ')
print('x_center = (B * E - (2 * C * D)) / (4 * A * C - B ** 2)')
print('y_center = (D * B - (2 * A * E)) / (4 * A * C - B ** 2)')
# 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)
helpers.horiz_print('x_center = ', x_center)
helpers.horiz_print('y_center = ', y_center)
#-----------------------
# MAJOR AND MINOR AXES
#-----------------------
# Now we are going to determine the major and minor axis
# of this beast. It just the center augmented by the eigenvecs
print('----------------------------------')
# The angle between the major axis and our x axis is:
l1, l2, v1, v2 = _2x2_eig(A_33)
x_axis = np.array([1, 0])
theta = np.arccos(x_axis.dot(v1))
# 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
#-----------------------
# DRAWING
#-----------------------
# Lets start off by drawing the ellipse that we are goign to work with
# Create unit circle sample
# Draw the keypoint using the tried and true df2
# Other things should subsiquently align
df2.draw_kpts2(np.array([(0, 0, ia11, ia21, ia22)]),
ell_linewidth=4,
ell_color=df2.DEEP_PINK,
ell_alpha=1,
arrow=True,
rect=True)
# Plot ellipse points
_plotpts(ellipse_pts1, 0, df2.YELLOW, label='invV.dot(cicrle_pts.T).T')
# Plot ellipse axis
# !HELP! I DO NOT KNOW WHY I HAVE TO DIVIDE, SQUARE ROOT, AND NEGATE!!!
l1, l2, v1, v2 = _2x2_eig(A_33)
dx1, dy1 = (v1 / np.sqrt(l1))
dx2, dy2 = (v2 / np.sqrt(l2))
_plotarrow(0, 0, dx1, -dy1, color=df2.ORANGE, label='ellipse axis')
_plotarrow(0, 0, dx2, -dy2, color=df2.ORANGE)
# Plot ellipse orientation
orient_axis = invV.dot(np.eye(2))
dx1, dx2, dy1, dy2 = orient_axis.flatten()
_plotarrow(0, 0, dx1, dy1, color=df2.BLUE, label='ellipse rotation')
_plotarrow(0, 0, dx2, dy2, color=df2.BLUE)
df2.legend()
df2.dark_background()
df2.gca().invert_yaxis()
return locals()
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 in_depth_ellipse2x2(rchip, kp):
#-----------------------
# SETUP
#-----------------------
from hotspotter import draw_func2 as df2
np.set_printoptions(precision=8)
tau = 2 * np.pi
df2.reset()
df2.figure(9003, docla=True, doclf=True)
ax = df2.gca()
ax.invert_yaxis()
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=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 will call perdoch's invA = invV
print('--------------------------------')
print('Let V = Perdoch.A')
print('Let Z = Perdoch.E')
print('--------------------------------')
print('Input from Perdoch\'s detector: ')
# We are given the keypoint in invA format
(x, y, ia11, ia21, ia22), ia12 = kp, 0
invV = np.array([[ia11, ia12],
[ia21, ia22]])
V = np.linalg.inv(invV)
# <HACK>
#invV = V / np.linalg.det(V)
#V = np.linalg.inv(V)
# </HACK>
Z = (V.T).dot(V)
print('invV is a transform from points on a unit-circle to the ellipse')
helpers.horiz_print('invV = ', invV)
print('--------------------------------')
print('V is a transformation from points on the ellipse to a unit circle')
helpers.horiz_print('V = ', V)
print('--------------------------------')
print('Points on a matrix satisfy (x).T.dot(Z).dot(x) = 1')
print('where Z = (V.T).dot(V)')
helpers.horiz_print('Z = ', Z)
# Define points on a unit circle
theta_list = np.linspace(0, tau, 50)
cicrle_pts = np.array([(np.cos(t), np.sin(t)) for t in theta_list])
# Transform those points to the ellipse using invV
ellipse_pts1 = invV.dot(cicrle_pts.T).T
# Transform those points to the ellipse using V
ellipse_pts2 = V.dot(cicrle_pts.T).T
#Lets check our assertion: (x_).T.dot(Z).dot(x_) = 1
checks1 = [x_.T.dot(Z).dot(x_) for x_ in ellipse_pts1]
checks2 = [x_.T.dot(Z).dot(x_) for x_ in ellipse_pts2]
assert all([abs(1 - check) < 1E-11 for check in checks1])
#assert all([abs(1 - check) < 1E-11 for check in checks2])
print('... all of our plotted points satisfy this')
#=======================
# THE CONIC SECTION
#=======================
# 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
#-----------------------
# MATRIX REPRESENTATION
#-----------------------
# The matrix representation of a conic is:
(A, B2, B2_, C) = Z.flatten()
(D, E, F) = (0, 0, 1)
B = B2 * 2
assert B2 == B2_, 'matrix should by symmetric'
print('--------------------------------')
print('Now, using wikipedia\' matrix representation of a conic.')
con = np.array(((' A', 'B / 2', 'D / 2'),
('B / 2', ' C', 'E / 2'),
('D / 2', 'E / 2', ' F')))
helpers.horiz_print('A matrix A_Q = ', con)
# 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)))
helpers.horiz_print('A_Q = ', A_Q)
#-----------------------
# DEGENERATE CONICS
#-----------------------
print('----------------------------------')
print('As long as det(A_Q) != it is not degenerate.')
print('If the conic is not degenerate, we can use the 2x2 minor: A_33')
print('det(A_Q) = %s' % str(np.linalg.det(A_Q)))
assert np.linalg.det(A_Q) != 0, 'degenerate conic'
A_33 = np.array((( A, B / 2),
(B / 2, C)))
helpers.horiz_print('A_33 = ', A_33)
#-----------------------
# CONIC CLASSIFICATION
#-----------------------
print('----------------------------------')
print('The determinant of the minor classifies the type of conic it is')
print('(det == 0): parabola, (det < 0): hyperbola, (det > 0): ellipse')
print('det(A_33) = %s' % str(np.linalg.det(A_33)))
assert np.linalg.det(A_33) > 0, 'conic is not an ellipse'
print('... this is indeed an ellipse')
#-----------------------
# CONIC CENTER
#-----------------------
print('----------------------------------')
print('the centers of the ellipse are obtained by: ')
print('x_center = (B * E - (2 * C * D)) / (4 * A * C - B ** 2)')
print('y_center = (D * B - (2 * A * E)) / (4 * A * C - B ** 2)')
# 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)
helpers.horiz_print('x_center = ', x_center)
helpers.horiz_print('y_center = ', y_center)
#-----------------------
# MAJOR AND MINOR AXES
#-----------------------
# Now we are going to determine the major and minor axis
# of this beast. It just the center augmented by the eigenvecs
print('----------------------------------')
# The angle between the major axis and our x axis is:
l1, l2, v1, v2 = _2x2_eig(A_33)
x_axis = np.array([1, 0])
theta = np.arccos(x_axis.dot(v1))
# 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
#-----------------------
# DRAWING
#-----------------------
# Lets start off by drawing the ellipse that we are goign to work with
# Create unit circle sample
# Draw the keypoint using the tried and true df2
# Other things should subsiquently align
df2.draw_kpts2(np.array([(0, 0, ia11, ia21, ia22)]), ell_linewidth=4,
ell_color=df2.DEEP_PINK, ell_alpha=1, arrow=True, rect=True)
# Plot ellipse points
_plotpts(ellipse_pts1, 0, df2.YELLOW, label='invV.dot(cicrle_pts.T).T')
# Plot ellipse axis
# !HELP! I DO NOT KNOW WHY I HAVE TO DIVIDE, SQUARE ROOT, AND NEGATE!!!
l1, l2, v1, v2 = _2x2_eig(A_33)
dx1, dy1 = (v1 / np.sqrt(l1))
dx2, dy2 = (v2 / np.sqrt(l2))
_plotarrow(0, 0, dx1, -dy1, color=df2.ORANGE, label='ellipse axis')
_plotarrow(0, 0, dx2, -dy2, color=df2.ORANGE)
# Plot ellipse orientation
orient_axis = invV.dot(np.eye(2))
dx1, dx2, dy1, dy2 = orient_axis.flatten()
_plotarrow(0, 0, dx1, dy1, color=df2.BLUE, label='ellipse rotation')
_plotarrow(0, 0, dx2, dy2, color=df2.BLUE)
df2.legend()
df2.dark_background()
df2.gca().invert_yaxis()
return locals()
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