def show_name(hs, nx, nx2_cxs=None, fnum=0, sel_cxs=[], subtitle='',
annote=False, **kwargs):
print('[viz] show_name nx=%r' % nx)
nx2_name = hs.tables.nx2_name
cx2_nx = hs.tables.cx2_nx
name = nx2_name[nx]
if not nx2_cxs is None:
cxs = nx2_cxs[nx]
else:
cxs = np.where(cx2_nx == nx)[0]
print('[viz] show_name %r' % hs.cidstr(cxs))
nRows, nCols = get_square_row_cols(len(cxs))
print('[viz*] r=%r, c=%r' % (nRows, nCols))
#gs2 = gridspec.GridSpec(nRows, nCols)
pnum = lambda px: (nRows, nCols, px + 1)
fig = df2.figure(fnum=fnum, pnum=pnum(0), **kwargs)
fig.clf()
# Trigger computation of all chips in parallel
hs.refresh_features(cxs)
for px, cx in enumerate(cxs):
show_chip(hs, cx=cx, pnum=pnum(px), draw_ell=annote, kpts_alpha=.2)
if cx in sel_cxs:
ax = df2.gca()
df2.draw_border(ax, df2.GREEN, 4)
#plot_cx3(hs, cx)
if isinstance(nx, np.ndarray):
nx = nx[0]
if isinstance(name, np.ndarray):
name = name[0]
figtitle = 'Name View nx=%r name=%r' % (nx, name)
df2.set_figtitle(figtitle)
def plot_time(unixtime_list):
import draw_func2 as df2
unixtime_list = np.array(unixtime_list)
fixed_time = unixtime_list[unixtime_list > 0]
df2.plot(sorted(unixtime_list))
ax = df2.gca()
ax.set_ylim(fixed_time.min(), fixed_time.max())
def _distplot(dists, color, label, distkey, plot_type=plot_type):
data = sorted(dists)
ax = df2.gca()
min_ = distkey2_min[distkey]
max_ = distkey2_max[distkey]
if plot_type == 'plot':
df2.plot(data, color=color, label=label)
#xticks = np.linspace(np.min(data), np.max(data), 3)
#yticks = np.linspace(0, len(data), 5)
#ax.set_xticks(xticks)
#ax.set_yticks(yticks)
ax.set_ylim(min_, max_)
ax.set_xlim(0, len(dists))
ax.set_ylabel('distance')
ax.set_xlabel('matches indexes (sorted by distance)')
df2.legend(loc='lower right')
if plot_type == 'pdf':
df2.plot_pdf(data, color=color, label=label)
ax.set_ylabel('pr')
ax.set_xlabel('distance')
ax.set_xlim(min_, max_)
df2.legend(loc='upper right')
df2.dark_background(ax)
df2.small_xticks(ax)
df2.small_yticks(ax)
def _distplot(dists, color, label, distkey, plot_type=plot_type):
data = sorted(dists)
ax = df2.gca()
min_ = distkey2_min[distkey]
max_ = distkey2_max[distkey]
if plot_type == 'plot':
df2.plot(data, color=color, label=label)
#xticks = np.linspace(np.min(data), np.max(data), 3)
#yticks = np.linspace(0, len(data), 5)
#ax.set_xticks(xticks)
#ax.set_yticks(yticks)
ax.set_ylim(min_, max_)
ax.set_xlim(0, len(dists))
ax.set_ylabel('distance')
ax.set_xlabel('matches indexes (sorted by distance)')
df2.legend(loc='lower right')
if plot_type == 'pdf':
df2.plot_pdf(data, color=color, label=label)
ax.set_ylabel('pr')
ax.set_xlabel('distance')
ax.set_xlim(min_, max_)
df2.legend(loc='upper right')
df2.dark_background(ax)
df2.small_xticks(ax)
df2.small_yticks(ax)
def show_keypoints(rchip, kpts, draw_ell=True, draw_pts=False, sel_fx=None, fnum=0,
pnum=None, color=None, rect=False, **kwargs):
df2.imshow(rchip, fnum=fnum, pnum=pnum, **kwargs)
_annotate_kpts(kpts, sel_fx, draw_ell, draw_pts, color=color, rect=rect)
ax = df2.gca()
ax._hs_viewtype = 'keypoints'
ax._hs_kpts = kpts
def _on_chip_click(event):
print_('[inter] clicked chip')
ax, x, y = event.inaxes, event.xdata, event.ydata
if ax is None or x is None:
# The click is not in any axis
print('... out of axis')
annote_ptr[0] = (annote_ptr[0] + 1) % 3
mode = annote_ptr[0]
draw_ell = mode == 1
draw_pts = mode == 2
print('... default kpts view mode=%r' % mode)
_chip_view(draw_ell=draw_ell, draw_pts=draw_pts)
else:
hs_viewtype = ax.__dict__.get('_hs_viewtype', '')
print_(' hs_viewtype=%r' % hs_viewtype)
if hs_viewtype == 'chip' and event.key == 'shift':
print('... masking')
# TODO: Do better integration of masking
_chip_view()
df2.disconnect_callback(fig, 'button_press_event')
mc = mask_creator.MaskCreator(df2.gca()) # NOQA
elif hs_viewtype == 'chip':
kpts = hs.get_kpts(cx)
if len(kpts) > 0:
fx = nearest_point(x, y, kpts)[0]
print('... clicked fx=%r' % fx)
_select_ith_kpt(fx)
else:
print('... len(kpts) == 0')
else:
print('...Unknown viewtype')
viz.draw()
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 _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 show_keypoints(rchip,
kpts,
draw_ell=True,
draw_pts=False,
sel_fx=None,
fnum=0,
pnum=None,
color=None,
rect=False,
**kwargs):
df2.imshow(rchip, fnum=fnum, pnum=pnum, **kwargs)
_annotate_kpts(kpts, sel_fx, draw_ell, draw_pts, color=color, rect=rect)
ax = df2.gca()
ax._hs_viewtype = 'keypoints'
ax._hs_kpts = kpts
def show_name(hs,
nx,
nx2_cxs=None,
fnum=0,
sel_cxs=[],
subtitle='',
annote=False,
**kwargs):
print('[viz] show_name nx=%r' % nx)
nx2_name = hs.tables.nx2_name
cx2_nx = hs.tables.cx2_nx
name = nx2_name[nx]
if not nx2_cxs is None:
cxs = nx2_cxs[nx]
else:
cxs = np.where(cx2_nx == nx)[0]
print('[viz] show_name %r' % hs.cidstr(cxs))
nRows, nCols = get_square_row_cols(len(cxs))
print('[viz*] r=%r, c=%r' % (nRows, nCols))
#gs2 = gridspec.GridSpec(nRows, nCols)
pnum = lambda px: (nRows, nCols, px + 1)
fig = df2.figure(fnum=fnum, pnum=pnum(0), **kwargs)
fig.clf()
# Trigger computation of all chips in parallel
hs.refresh_features(cxs)
for px, cx in enumerate(cxs):
show_chip(hs, cx=cx, pnum=pnum(px), draw_ell=annote, kpts_alpha=.2)
if cx in sel_cxs:
ax = df2.gca()
df2.draw_border(ax, df2.GREEN, 4)
#plot_cx3(hs, cx)
if isinstance(nx, np.ndarray):
nx = nx[0]
if isinstance(name, np.ndarray):
name = name[0]
figtitle = 'Name View nx=%r name=%r' % (nx, name)
df2.set_figtitle(figtitle)
def annotate_chipres(hs,
res,
cx,
showTF=True,
showScore=True,
title_pref='',
title_suff='',
show_2nd_gname=True,
show_2nd_name=True,
show_1st=True,
time_appart=True,
in_image=False,
offset1=(0, 0),
offset2=(0, 0),
show_query=True,
xywh2=None,
**kwargs):
printDBG('[viz] annotate_chipres()')
#print('Did not expect args: %r' % (kwargs.keys(),))
qcx = res.qcx
score = res.cx2_score[cx]
matched_kpts = np.float32(len(res.cx2_fs[cx]))
# print('matched_kpts= %r'%str(matched_kpts))
# TODO Use this function when you clean show_chipres
(truestr, falsestr, nonamestr) = ('TRUE', 'FALSE', '???')
is_true, is_unknown = hs.is_true_match(qcx, cx)
isgt_str = nonamestr if is_unknown else (truestr if is_true else falsestr)
match_color = {
nonamestr: df2.UNKNOWN_PURP,
truestr: df2.TRUE_GREEN,
falsestr: df2.FALSE_RED
}[isgt_str]
# Build title
title = '*%s*' % isgt_str if showTF else ''
if showScore:
score_str = (' score=' + helpers.num_fmt(score)) % (score)
score_str += (' matched_kpts=' +
helpers.num_fmt(matched_kpts)) % (matched_kpts)
title += score_str
title = title_pref + str(title) + title_suff
# Build xlabel
xlabel_ = []
if 'show_1st':
xlabel_.append('top_gname=%r' % hs.cx2_gname(qcx))
xlabel_.append('top_name=%r' % hs.cx2_name(qcx))
if 'show_2nd_gname':
xlabel_.append('\n below_gname=%r' % hs.cx2_gname(cx))
if 'show_2nd_name':
xlabel_.append('below_name=%r' % hs.cx2_name(cx))
if 'time_appart':
xlabel_.append('\n' + hs.get_timedelta_str(qcx, cx))
xlabel = ', '.join(xlabel_)
ax = df2.gca()
ax._hs_viewtype = 'chipres'
ax._hs_qcx = qcx
ax._hs_cx = cx
if NO_LABEL_OVERRIDE:
title = ''
xlabel = ''
df2.set_title(title, ax)
df2.set_xlabel(xlabel, ax)
if in_image:
roi1 = hs.cx2_roi(qcx) + np.array(list(offset1) + [0, 0])
roi2 = hs.cx2_roi(cx) + np.array(list(offset2) + [0, 0])
theta1 = hs.cx2_theta(qcx)
theta2 = hs.cx2_theta(cx)
# HACK!
lbl1 = 'q' + hs.cidstr(qcx)
lbl2 = hs.cidstr(cx)
if show_query:
df2.draw_roi(roi1, bbox_color=df2.ORANGE, label=lbl1, theta=theta1)
df2.draw_roi(roi2, bbox_color=match_color, label=lbl2, theta=theta2)
# No matches draw a red box
if len(res.cx2_fm[cx]) == 0:
df2.draw_boxedX(roi2, theta=theta2)
else:
if xywh2 is None:
xy, w, h = df2._axis_xy_width_height(ax)
xywh2 = (xy[0], xy[1], w, h)
df2.draw_border(ax, match_color, 4, offset=offset2)
# No matches draw a red box
if len(res.cx2_fm[cx]) == 0:
df2.draw_boxedX(xywh2)
def annotate_chipres(hs, res, cx, showTF=True, showScore=True, title_pref='',
title_suff='', show_gname=False, show_name=True,
time_appart=True, in_image=False, offset1=(0, 0),
offset2=(0, 0), show_query=True, xywh2=None, **kwargs):
printDBG('[viz] annotate_chipres()')
#print('Did not expect args: %r' % (kwargs.keys(),))
qcx = res.qcx
score = res.cx2_score[cx]
# TODO Use this function when you clean show_chipres
(truestr, falsestr, nonamestr) = ('TRUE', 'FALSE', '???')
is_true, is_unknown = hs.is_true_match(qcx, cx)
isgt_str = nonamestr if is_unknown else (truestr if is_true else falsestr)
match_color = {nonamestr: df2.UNKNOWN_PURP,
truestr: df2.TRUE_GREEN,
falsestr: df2.FALSE_RED}[isgt_str]
# Build title
title = '*%s*' % isgt_str if showTF else ''
if showScore:
score_str = (' score=' + helpers.num_fmt(score)) % (score)
title += score_str
title = title_pref + str(title) + title_suff
# Build xlabel
xlabel_ = []
if 'show_gname':
xlabel_.append('gname=%r' % hs.cx2_gname(cx))
if 'show_name':
xlabel_.append('name=%r' % hs.cx2_name(cx))
if 'time_appart':
xlabel_.append('\n' + hs.get_timedelta_str(qcx, cx))
xlabel = ', '.join(xlabel_)
ax = df2.gca()
ax._hs_viewtype = 'chipres'
ax._hs_qcx = qcx
ax._hs_cx = cx
if NO_LABEL_OVERRIDE:
title = ''
xlabel = ''
df2.set_title(title, ax)
df2.set_xlabel(xlabel, ax)
if in_image:
roi1 = hs.cx2_roi(qcx) + np.array(list(offset1) + [0, 0])
roi2 = hs.cx2_roi(cx) + np.array(list(offset2) + [0, 0])
theta1 = hs.cx2_theta(qcx)
theta2 = hs.cx2_theta(cx)
# HACK!
lbl1 = 'q' + hs.cidstr(qcx)
lbl2 = hs.cidstr(cx)
if show_query:
df2.draw_roi(roi1, bbox_color=df2.ORANGE, label=lbl1, theta=theta1)
df2.draw_roi(roi2, bbox_color=match_color, label=lbl2, theta=theta2)
# No matches draw a red box
if len(res.cx2_fm[cx]) == 0:
df2.draw_boxedX(roi2, theta=theta2)
else:
if xywh2 is None:
xy, w, h = df2._axis_xy_width_height(ax)
xywh2 = (xy[0], xy[1], w, h)
df2.draw_border(ax, match_color, 4, offset=offset2)
# No matches draw a red box
if len(res.cx2_fm[cx]) == 0:
df2.draw_boxedX(xywh2)
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 begin_interaction(type_, fnum):
print('[inter] starting %s interaction' % type_)
fig = df2.figure(fnum=fnum, docla=True, doclf=True)
ax = df2.gca()
df2.disconnect_callback(fig, 'button_press_event', axes=[ax])
return fig
def query_last_feature():
viz.show_nearest_descriptors(hs, qcx, last_state.last_fx, df2.next_fnum())
fig3 = df2.gca()
df2.connect_callback(fig3, 'button_press_event', _click_chipres_click)
df2.update()
def show_descriptors_match_distances(orgres2_distance,
fnum=1,
db_name='',
**kwargs):
disttype_list = orgres2_distance.itervalues().next().keys()
orgtype_list = orgres2_distance.keys()
(nRow, nCol) = len(orgtype_list), len(disttype_list)
nColors = nRow * nCol
color_list = df2.distinct_colors(nColors)
df2.figure(fnum=fnum, docla=True, doclf=True)
pnum_ = lambda px: (nRow, nCol, px + 1)
plot_type = helpers.get_arg('--plot-type', default='plot')
# Remember min and max val for each distance type (l1, emd...)
distkey2_min = {distkey: np.uint64(-1) for distkey in disttype_list}
distkey2_max = {distkey: 0 for distkey in disttype_list}
def _distplot(dists, color, label, distkey, plot_type=plot_type):
data = sorted(dists)
ax = df2.gca()
min_ = distkey2_min[distkey]
max_ = distkey2_max[distkey]
if plot_type == 'plot':
df2.plot(data, color=color, label=label, yscale='linear')
#xticks = np.linspace(np.min(data), np.max(data), 3)
#yticks = np.linspace(0, len(data), 5)
#ax.set_xticks(xticks)
#ax.set_yticks(yticks)
ax.set_ylim(min_, max_)
ax.set_xlim(0, len(dists))
ax.set_ylabel('distance')
ax.set_xlabel('matches indexes (sorted by distance)')
df2.legend(loc='lower right')
if plot_type == 'pdf':
df2.plot_pdf(data, color=color, label=label)
ax.set_ylabel('pr')
ax.set_xlabel('distance')
ax.set_xlim(min_, max_)
df2.legend(loc='upper left')
df2.dark_background(ax)
df2.small_xticks(ax)
df2.small_yticks(ax)
px = 0
for orgkey in orgtype_list:
for distkey in disttype_list:
dists = orgres2_distance[orgkey][distkey]
if len(dists) == 0:
continue
min_ = dists.min()
max_ = dists.max()
distkey2_min[distkey] = min(distkey2_min[distkey], min_)
distkey2_max[distkey] = max(distkey2_max[distkey], max_)
for count, orgkey in enumerate(orgtype_list):
for distkey in disttype_list:
printDBG('[allres-viz] plotting: %r' % ((orgkey, distkey), ))
dists = orgres2_distance[orgkey][distkey]
df2.figure(fnum=fnum, pnum=pnum_(px))
color = color_list[px]
title = distkey + ' ' + orgkey
label = 'P(%s | %s)' % (distkey, orgkey)
_distplot(dists, color, label, distkey, **kwargs)
if count == 0:
ax = df2.gca()
ax.set_title(distkey)
px += 1
subtitle = 'the matching distances between sift descriptors'
title = '(sift) matching distances'
if db_name != '':
title = db_name + ' ' + title
df2.set_figtitle(title, subtitle)
df2.adjust_subplots_safe()
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()
