def gen_bias(lg, hg):
"""Helper function - creates and returns a bias object for use when creating Glyphs. Basically weights each line with the amount of ink on it, so when a writter uses every other line it strongly biases towards letters being assigned to the lines they wrote on."""
bias = defaultdict(float)
# Transform the line graph to line space...
ls_lg = LineGraph()
ls_lg.from_many(lg)
ihg = la.inv(hg)
ls_lg.transform(ihg, True)
# Add weight from all of the line segments...
for ei in xrange(ls_lg.edge_count):
edge = ls_lg.get_edge(ei)
vf = ls_lg.get_vertex(edge[0])
vt = ls_lg.get_vertex(edge[1])
dx = vt[0] - vf[0]
dy = vt[1] - vf[1]
mass = (vf[5] + vt[5]) * numpy.sqrt(dx * dx + dy * dy)
line = int(numpy.floor(0.5 * (vt[1] + vf[1])))
bias[line] += mass
# Normalise and return...
maximum = max(bias.values())
for key in bias.keys():
bias[key] /= maximum
return bias
def gen_bias(lg, hg):
"""Helper function - creates and returns a bias object for use when creating Glyphs. Basically weights each line with the amount of ink on it, so when a writter uses every other line it strongly biases towards letters being assigned to the lines they wrote on."""
bias = defaultdict(float)
# Transform the line graph to line space...
ls_lg = LineGraph()
ls_lg.from_many(lg)
ihg = la.inv(hg)
ls_lg.transform(ihg, True)
# Add weight from all of the line segments...
for ei in xrange(ls_lg.edge_count):
edge = ls_lg.get_edge(ei)
vf = ls_lg.get_vertex(edge[0])
vt = ls_lg.get_vertex(edge[1])
dx = vt[0] - vf[0]
dy = vt[1] - vf[1]
mass = (vf[5] + vt[5]) * numpy.sqrt(dx*dx + dy*dy)
line = int(numpy.floor(0.5 * (vt[1] + vf[1])))
bias[line] += mass
# Normalise and return...
maximum = max(bias.values())
for key in bias.keys():
bias[key] /= maximum
return bias
class Glyph:
"""Represents a glyph, that has been transformed into a suitable coordinate system; includes connectivity information."""
def __init__(self, lg, seg, hg, extra=0.4, bias=None):
"""Given a segmented LineGraph and segment number this extracts it, transforms it into the standard coordinate system and stores the homography used to get there. (hg transforms from line space, where there is a line for each y=integer, to the space of the original pixels.) Also records its position on its assigned line and line number so it can be ordered suitably. Does not store connectivity information - that is done later. extra is used for infering the line position, and is extra falloff to have either side of a line voting for it - a smoothing term basically. bias is an optional dictionary indexed by line number that gives a weight to assign to being assigned to that line - used to utilise the fact that data collection asks the writter to use every-other line, which helps avoid misassigned dropped j's for instance."""
if lg == None: return
# Extract the line graph...
self.lg = LineGraph()
self.adjacent = self.lg.from_segment(lg, seg)
self.seg = seg
# Tranform it to line space...
ihg = la.inv(hg)
self.lg.transform(ihg, True)
# Check if which line its on is tagged - exists as an override for annoying glyphs...
line = None
for tag in self.lg.get_tags():
if tag[0] == 'line':
# We have a tag of line - its position specifies the line the glyph is on...
point = self.lg.get_point(tag[1], tag[2])
line = int(numpy.floor(point[1]))
break
# Record which line it is on and its position along the line...
# (Works by assuming that the line is the one below the space where most of the mass of the glyph is. Takes it range to be that within the space, so crazy tails are cut off.)
min_x, max_x, min_y, max_y = self.lg.get_bounds()
self.source = (0.5 * (min_x + max_x), 0.5 * (min_y + max_y))
if line == None:
best_mass = 0.0
self.left_x = min_x
self.right_x = max_x
line = 0
start = int(numpy.trunc(min_y))
for pl in xrange(start, int(numpy.ceil(max_y))):
mass = 0.0
low_y = float(pl) - extra
high_y = float(pl + 1) + extra
left_x = None
right_x = None
for es in self.lg.within(min_x, max_x, low_y, high_y):
for ei in xrange(*es.indices(self.lg.edge_count)):
edge = self.lg.get_edge(ei)
vf = self.lg.get_vertex(edge[0])
vt = self.lg.get_vertex(edge[1])
if vf[1] > low_y and vf[1] < high_y and vt[
1] > low_y and vt[1] < high_y:
dx = vt[0] - vf[0]
dy = vt[1] - vf[1]
mass += (vf[5] + vt[5]) * numpy.sqrt(dx * dx +
dy * dy)
if left_x == None: left_x = min(vf[0], vt[0])
else: left_x = min(vf[0], vt[0], left_x)
if right_x == None: right_x = max(vf[0], vt[0])
else: right_x = max(vf[0], vt[0], right_x)
mass *= 1.0 / (1.0 + pl - start
) # Bias to choosing higher, for tails.
if bias != None:
mass *= bias[pl]
if mass > best_mass:
best_mass = mass
self.left_x = left_x
self.right_x = right_x
line = pl
# Transform it so it is positioned to be sitting on line 1 of y, store the total homography that we have applied...
self.offset_x = -min_x
self.offset_y = -line
hg = numpy.eye(3, dtype=numpy.float32)
hg[0, 2] = self.offset_x
hg[1, 2] = self.offset_y
self.left_x += self.offset_x
self.right_x += self.offset_x
self.lg.transform(hg)
self.transform = numpy.dot(hg, ihg)
# Set as empty its before and after glyphs - None if there is no adjacency, or a tuple if there is: (glyph, list of connecting (link glyph, shared vertex in this, shared vertex in glyph, vertex in link glyph on this side, vertex in link glyph on glyph side), empty if none.)...
self.left = None
self.right = None
# Extract the character this glyph represents...
tags = self.lg.get_tags()
codes = [
t[0] for t in tags if len(filter(lambda c: c != '_', t[0])) == 1
]
self.key = codes[0] if len(codes) != 0 else None
self.code = -id(self)
# Cache stuff...
self.mass = None
self.center = None
self.feat = None
self.v_offset = None
def clone(self):
"""Returns a clone of this Glyph."""
ret = Glyph(None, None, None)
ret.lg = self.lg
ret.adjacent = self.adjacent
ret.seg = self.seg
ret.source = self.source
ret.left_x = self.left_x
ret.right_x = self.right_x
ret.offset_x = self.offset_x
ret.offset_y = self.offset_y
ret.transform = self.transform
ret.left = self.left
ret.right = self.right
ret.key = self.key
ret.code = self.code
ret.mass = None if self.mass == None else self.mass.copy()
ret.center = None if self.center == None else self.center.copy()
ret.feat = None if self.feat == None else map(lambda a: a.copy(),
self.feat)
ret.v_offset = self.v_offset
return ret
def get_linegraph(self):
return self.lg
def orig_left_x(self):
return self.left_x - self.offset_x
def orig_right_x(self):
return self.right_x - self.offset_x
def get_mass(self):
"""Returns a vector of [average density, average radius] - used for matching adjacent glyphs."""
if self.mass == None:
self.mass = numpy.zeros(2, dtype=numpy.float32)
weight = 0.0
for i in xrange(self.lg.vertex_count):
info = self.lg.get_vertex(i)
weight += 1.0
self.mass += (numpy.array([info[6], info[5]]) -
self.mass) / weight
return self.mass
def get_center(self):
"""Returns the 'center' of the glyph - its density weighted in an attempt to make it robust to crazy tails."""
if self.center == None:
self.center = numpy.zeros(2, dtype=numpy.float32)
weight = 0.0
for i in xrange(self.lg.vertex_count):
info = self.lg.get_vertex(i)
w = info[5] * info[5] * info[
6] # Radius squared * density - proportional to quantity of ink, assuming (correctly as rest of system currently works) even sampling.
if w > 1e-6:
weight += w
mult = w / weight
self.center[0] += (info[0] - self.center[0]) * mult
self.center[1] += (info[1] - self.center[1]) * mult
return self.center
def get_voffset(self):
"""Calculates and returns the vertical offset to apply to the glyph that corrects for any systematic bias in its flow calculation."""
if self.v_offset == None:
self.v_offset = 0.0
weight = 0.0
truth = self.get_center()[1]
# Calculate the estimated offsets from the left side and update the estimate, correctly factoring in the variance of the offset...
if self.left != None:
diff, sd = costs.glyph_pair_offset(self.left[0], self, 0.2,
True)
estimate = self.left[0].get_center()[1] + diff
offset = truth - estimate
est_weight = 1.0 / (sd**2.0)
weight += est_weight
self.v_offset += (offset - self.v_offset) * est_weight / weight
# Again from the right side...
if self.right != None:
diff, sd = costs.glyph_pair_offset(self, self.right[0], 0.2,
True)
estimate = self.right[0].get_center()[1] - diff
offset = truth - estimate
est_weight = 1.0 / (sd**2.0)
weight += est_weight
self.v_offset += (offset - self.v_offset) * est_weight / weight
return self.v_offset
def most_left(self):
"""Returns the coordinate of the furthest left vertex in the glyph."""
info = self.lg.get_vertex(0)
best_x = info[0]
best_y = info[1]
for i in xrange(1, self.lg.vertex_count):
info = self.lg.get_vertex(0)
if info[0] < best_x:
best_x = info[0]
best_y = info[1]
return (best_x, best_y)
def most_right(self):
"""Returns the coordinate of the furthest right vertex in the glyph."""
info = self.lg.get_vertex(0)
best_x = info[0]
best_y = info[1]
for i in xrange(1, self.lg.vertex_count):
info = self.lg.get_vertex(0)
if info[0] > best_x:
best_x = info[0]
best_y = info[1]
return (best_x, best_y)
def get_feat(self):
"""Calculates and returns a feature for the glyph, or, more accuratly two features, representing (left, right), so some tricks can be done to make their use side dependent (For learning a function for matching to adjacent glyphs.)."""
if self.feat == None:
# First build a culumative distribution over the x axis range of the glyph...
min_x, max_x, min_y, max_y = self.lg.get_bounds()
culm = numpy.ones(32, dtype=numpy.float32)
culm *= 1e-2
min_x -= 1e-3
max_x += 1e-3
for i in xrange(self.lg.vertex_count):
info = self.lg.get_vertex(i)
w = info[5] * info[5] * info[6]
t = (info[0] - min_x) / (max_x - min_x)
t *= (culm.shape[0] - 1)
low = int(t)
high = low + 1
t -= low
culm[low] += (1.0 - t) * w
culm[high] += t * w
culm /= culm.sum()
culm = numpy.cumsum(culm)
# Now extract all the per sample features...
feat_param = {
'dir_travel': 0.1,
'travel_max': 1.0,
'travel_bins': 6,
'travel_ratio': 0.8,
'pos_bins': 3,
'pos_ratio': 0.9,
'radius_bins': 1,
'density_bins': 3
}
fv = self.lg.features(**feat_param)
# Combine them into the two halves, by weighting by the culumative; include density and radius as well...
left = numpy.zeros(fv.shape[1] + 2, dtype=numpy.float32)
right = numpy.zeros(fv.shape[1] + 2, dtype=numpy.float32)
left_total = 0.0
right_total = 0.0
for i in xrange(self.lg.vertex_count):
info = self.lg.get_vertex(i)
w = info[5] * info[5] * info[6]
t = (info[0] - min_x) / (max_x - min_x)
t *= (culm.shape[0] - 1)
low = int(t)
high = low + 1
t -= low
right_w = (1.0 - t) * culm[low] + t * culm[high]
left_w = 1.0 - right_w
left[0] += left_w * info[5]
right[0] += right_w * info[5]
left[1] += left_w * info[6]
right[1] += right_w * info[6]
left[2:] += w * left_w * fv[i, :]
right[2:] += w * right_w * fv[i, :]
left_total += left_w
right_total += right_w
left[:2] /= left_total
right[:2] /= right_total
left[2:] /= max(left[2:].sum(), 1e-6)
right[2:] /= max(right[2:].sum(), 1e-6)
self.feat = (left, right)
return self.feat
def __str__(self):
l = self.left[0].key if self.left != None else 'None'
r = self.right[0].key if self.right != None else 'None'
return 'Glyph %i: key = %s (%s|%s)' % (self.code, self.key, l, r)
class Glyph:
"""Represents a glyph, that has been transformed into a suitable coordinate system; includes connectivity information."""
def __init__(self, lg, seg, hg, extra = 0.4, bias = None):
"""Given a segmented LineGraph and segment number this extracts it, transforms it into the standard coordinate system and stores the homography used to get there. (hg transforms from line space, where there is a line for each y=integer, to the space of the original pixels.) Also records its position on its assigned line and line number so it can be ordered suitably. Does not store connectivity information - that is done later. extra is used for infering the line position, and is extra falloff to have either side of a line voting for it - a smoothing term basically. bias is an optional dictionary indexed by line number that gives a weight to assign to being assigned to that line - used to utilise the fact that data collection asks the writter to use every-other line, which helps avoid misassigned dropped j's for instance."""
if lg==None: return
# Extract the line graph...
self.lg = LineGraph()
self.adjacent = self.lg.from_segment(lg, seg)
self.seg = seg
# Tranform it to line space...
ihg = la.inv(hg)
self.lg.transform(ihg, True)
# Check if which line its on is tagged - exists as an override for annoying glyphs...
line = None
for tag in self.lg.get_tags():
if tag[0]=='line':
# We have a tag of line - its position specifies the line the glyph is on...
point = self.lg.get_point(tag[1], tag[2])
line = int(numpy.floor(point[1]))
break
# Record which line it is on and its position along the line...
# (Works by assuming that the line is the one below the space where most of the mass of the glyph is. Takes it range to be that within the space, so crazy tails are cut off.)
min_x, max_x, min_y, max_y = self.lg.get_bounds()
self.source = (0.5 * (min_x + max_x), 0.5 * (min_y + max_y))
if line==None:
best_mass = 0.0
self.left_x = min_x
self.right_x = max_x
line = 0
start = int(numpy.trunc(min_y))
for pl in xrange(start, int(numpy.ceil(max_y))):
mass = 0.0
low_y = float(pl) - extra
high_y = float(pl+1) + extra
left_x = None
right_x = None
for es in self.lg.within(min_x, max_x, low_y, high_y):
for ei in xrange(*es.indices(self.lg.edge_count)):
edge = self.lg.get_edge(ei)
vf = self.lg.get_vertex(edge[0])
vt = self.lg.get_vertex(edge[1])
if vf[1]>low_y and vf[1]<high_y and vt[1]>low_y and vt[1]<high_y:
dx = vt[0] - vf[0]
dy = vt[1] - vf[1]
mass += (vf[5] + vt[5]) * numpy.sqrt(dx*dx + dy*dy)
if left_x==None: left_x = min(vf[0], vt[0])
else: left_x = min(vf[0], vt[0], left_x)
if right_x==None: right_x = max(vf[0], vt[0])
else: right_x = max(vf[0], vt[0], right_x)
mass *= 1.0/(1.0+pl - start) # Bias to choosing higher, for tails.
if bias!=None:
mass *= bias[pl]
if mass>best_mass:
best_mass = mass
self.left_x = left_x
self.right_x = right_x
line = pl
# Transform it so it is positioned to be sitting on line 1 of y, store the total homography that we have applied...
self.offset_x = -min_x
self.offset_y = -line
hg = numpy.eye(3, dtype=numpy.float32)
hg[0,2] = self.offset_x
hg[1,2] = self.offset_y
self.left_x += self.offset_x
self.right_x += self.offset_x
self.lg.transform(hg)
self.transform = numpy.dot(hg, ihg)
# Set as empty its before and after glyphs - None if there is no adjacency, or a tuple if there is: (glyph, list of connecting (link glyph, shared vertex in this, shared vertex in glyph, vertex in link glyph on this side, vertex in link glyph on glyph side), empty if none.)...
self.left = None
self.right = None
# Extract the character this glyph represents...
tags = self.lg.get_tags()
codes = [t[0] for t in tags if len(filter(lambda c: c!='_', t[0]))==1]
self.key = codes[0] if len(codes)!=0 else None
self.code = -id(self)
# Cache stuff...
self.mass = None
self.center = None
self.feat = None
self.v_offset = None
def clone(self):
"""Returns a clone of this Glyph."""
ret = Glyph(None, None, None)
ret.lg = self.lg
ret.adjacent = self.adjacent
ret.seg = self.seg
ret.source = self.source
ret.left_x = self.left_x
ret.right_x = self.right_x
ret.offset_x = self.offset_x
ret.offset_y = self.offset_y
ret.transform = self.transform
ret.left = self.left
ret.right = self.right
ret.key = self.key
ret.code = self.code
ret.mass = None if self.mass==None else self.mass.copy()
ret.center = None if self.center==None else self.center.copy()
ret.feat = None if self.feat==None else map(lambda a: a.copy(), self.feat)
ret.v_offset = self.v_offset
return ret
def get_linegraph(self):
return self.lg
def orig_left_x(self):
return self.left_x - self.offset_x
def orig_right_x(self):
return self.right_x - self.offset_x
def get_mass(self):
"""Returns a vector of [average density, average radius] - used for matching adjacent glyphs."""
if self.mass==None:
self.mass = numpy.zeros(2, dtype=numpy.float32)
weight = 0.0
for i in xrange(self.lg.vertex_count):
info = self.lg.get_vertex(i)
weight += 1.0
self.mass += (numpy.array([info[6], info[5]]) - self.mass) / weight
return self.mass
def get_center(self):
"""Returns the 'center' of the glyph - its density weighted in an attempt to make it robust to crazy tails."""
if self.center==None:
self.center = numpy.zeros(2, dtype=numpy.float32)
weight = 0.0
for i in xrange(self.lg.vertex_count):
info = self.lg.get_vertex(i)
w = info[5] * info[5] * info[6] # Radius squared * density - proportional to quantity of ink, assuming (correctly as rest of system currently works) even sampling.
if w>1e-6:
weight += w
mult = w / weight
self.center[0] += (info[0] - self.center[0]) * mult
self.center[1] += (info[1] - self.center[1]) * mult
return self.center
def get_voffset(self):
"""Calculates and returns the vertical offset to apply to the glyph that corrects for any systematic bias in its flow calculation."""
if self.v_offset==None:
self.v_offset = 0.0
weight = 0.0
truth = self.get_center()[1]
# Calculate the estimated offsets from the left side and update the estimate, correctly factoring in the variance of the offset...
if self.left!=None:
diff, sd = costs.glyph_pair_offset(self.left[0], self, 0.2, True)
estimate = self.left[0].get_center()[1] + diff
offset = truth - estimate
est_weight = 1.0 / (sd**2.0)
weight += est_weight
self.v_offset += (offset - self.v_offset) * est_weight / weight
# Again from the right side...
if self.right!=None:
diff, sd = costs.glyph_pair_offset(self, self.right[0], 0.2, True)
estimate = self.right[0].get_center()[1] - diff
offset = truth - estimate
est_weight = 1.0 / (sd**2.0)
weight += est_weight
self.v_offset += (offset - self.v_offset) * est_weight / weight
return self.v_offset
def most_left(self):
"""Returns the coordinate of the furthest left vertex in the glyph."""
info = self.lg.get_vertex(0)
best_x = info[0]
best_y = info[1]
for i in xrange(1,self.lg.vertex_count):
info = self.lg.get_vertex(0)
if info[0]<best_x:
best_x = info[0]
best_y = info[1]
return (best_x, best_y)
def most_right(self):
"""Returns the coordinate of the furthest right vertex in the glyph."""
info = self.lg.get_vertex(0)
best_x = info[0]
best_y = info[1]
for i in xrange(1,self.lg.vertex_count):
info = self.lg.get_vertex(0)
if info[0]>best_x:
best_x = info[0]
best_y = info[1]
return (best_x, best_y)
def get_feat(self):
"""Calculates and returns a feature for the glyph, or, more accuratly two features, representing (left, right), so some tricks can be done to make their use side dependent (For learning a function for matching to adjacent glyphs.)."""
if self.feat==None:
# First build a culumative distribution over the x axis range of the glyph...
min_x, max_x, min_y, max_y = self.lg.get_bounds()
culm = numpy.ones(32, dtype=numpy.float32)
culm *= 1e-2
min_x -= 1e-3
max_x += 1e-3
for i in xrange(self.lg.vertex_count):
info = self.lg.get_vertex(i)
w = info[5] * info[5] * info[6]
t = (info[0] - min_x) / (max_x - min_x)
t *= (culm.shape[0]-1)
low = int(t)
high = low + 1
t -= low
culm[low] += (1.0 - t) * w
culm[high] += t * w
culm /= culm.sum()
culm = numpy.cumsum(culm)
# Now extract all the per sample features...
feat_param = {'dir_travel':0.1, 'travel_max':1.0, 'travel_bins':6, 'travel_ratio':0.8, 'pos_bins':3, 'pos_ratio':0.9, 'radius_bins':1, 'density_bins':3}
fv = self.lg.features(**feat_param)
# Combine them into the two halves, by weighting by the culumative; include density and radius as well...
left = numpy.zeros(fv.shape[1]+2, dtype=numpy.float32)
right = numpy.zeros(fv.shape[1]+2, dtype=numpy.float32)
left_total = 0.0
right_total = 0.0
for i in xrange(self.lg.vertex_count):
info = self.lg.get_vertex(i)
w = info[5] * info[5] * info[6]
t = (info[0] - min_x) / (max_x - min_x)
t *= (culm.shape[0]-1)
low = int(t)
high = low + 1
t -= low
right_w = (1.0-t) * culm[low] + t * culm[high]
left_w = 1.0 - right_w
left[0] += left_w * info[5]
right[0] += right_w * info[5]
left[1] += left_w * info[6]
right[1] += right_w * info[6]
left[2:] += w * left_w * fv[i,:]
right[2:] += w * right_w * fv[i,:]
left_total += left_w
right_total += right_w
left[:2] /= left_total
right[:2] /= right_total
left[2:] /= max(left[2:].sum(), 1e-6)
right[2:] /= max(right[2:].sum(), 1e-6)
self.feat = (left, right)
return self.feat
def __str__(self):
l = self.left[0].key if self.left!=None else 'None'
r = self.right[0].key if self.right!=None else 'None'
return 'Glyph %i: key = %s (%s|%s)' % (self.code, self.key, l, r)