def catMap(delaunayMap,
rectified = True,
includeTerminalPositions = False):
"""catMap(delaunayMap,
rectified = True,
includeTerminalPositions = False)
Extract a CAT (chordal axis transform) from a GeoMap object
containing a Delaunay Triangulation. Implements the rectified
version (from L.Prasad's DGCI'05 article), which also works for
GeoMaps with non-triangular Faces.
Expects outer faces of the delaunayMap to be marked with the
OUTER_FACE flag (in order to skip these faces and work only on the
inner parts of the shapes), and edges which belong to the
constrained segments of the CDT to be marked with the
CONTOUR_SEGMENT flag (i.e. an edge is a chord iff
'not edge.flag(CONTOUR_SEGMENT)')
Usually, you will do sth. along:
>>> del1 = delaunay.faceCDTMap(map1.face(173), map1.imageSize())
>>> cat1 = delaunay.catMap(del1, rectified = False)
The optional parameter `rectified` has been set to False here to
use the original definition of junction node positions (using the
circumcenter if possible) which works only for triangulations (and
is therefore disabled by default).
For triangulations, it is also possible to include the opposite
vertex of the terminal triangles into the skeleton by setting
`includeTerminalPositions` to True.
If you want to use the rectified CAT (with weak chords being
suppressed), you would use removeWeakChords before calling catMap:
>>> del2 = copy.copy(del1) # if you want to keep the original
>>> removeWeakChords(del2)
>>> rcat2 = delaunay.catMap(del2)
The resulting map will have additional attributes that relate the
skeleton with the original boundary:
subtendedLengths:
This is a list mapping edge labels of the skeleton to the
accumulated lengths of all contour segments within the contours
of the sleeve- and terminal-faces that comprise the sleeve
represented by that skeleton edge.
shapeWidths:
This is a list mapping edge labels of the skeleton to lists of
shape widths at each support point of the polygon (may be None
at the ends). In theory, this allows to reconstruct the
original boundary and thus makes the CAT fully reversible (see
Prasad's papers).
nodeChordLabels:
This is a list mapping node labels of the skeleton to lists of
(sleeveLabel, chordLabel) pairs, where sleeveLabel is the label
of a skeleton edge and chordLabel is the dart label of the first
chord from the `delaunayMap` within that sleeve. (This is
needed for later corrections of the junction node positions
after pruning.)"""
if rectified:
junctionPos = rectifiedJunctionNodePosition
assert not includeTerminalPositions, \
"includeTerminalPositions is not supported for the rectified CAT!"
else:
junctionPos = junctionNodePosition
result = GeoMap(delaunayMap.imageSize())
result.subtendedLengths = [0] # unused Edge 0
result.shapeWidths = [None]
result.nodeChordLabels = []
faceChords = [None] * delaunayMap.maxFaceLabel()
boundaryLength = [None] * delaunayMap.maxFaceLabel()
faceType = [None] * delaunayMap.maxFaceLabel()
nodeLabel = [None] * delaunayMap.maxFaceLabel()
for face in delaunayMap.faceIter(skipInfinite = True):
if face.flag(OUTER_FACE):
continue
assert face.holeCount() == 0
chords = []
bl = 0.0
for dart in face.contour().phiOrbit():
if not dart.edge().flag(CONTOUR_SEGMENT):
chords.append(dart)
else:
bl += dart.edge().length()
boundaryLength[face.label()] = bl
faceChords[face.label()] = chords
# classify into terminal, sleeve, and junction triangles:
if len(chords) < 2:
faceType[face.label()] = "T"
if chords:
nodePos = middlePoint(chords[0]) # (may be changed later)
elif len(chords) == 2:
faceType[face.label()] = "S"
else:
faceType[face.label()] = "J"
nodePos = junctionPos(chords)
# add nodes for non-sleeve triangles:
if faceType[face.label()] != "S" and chords:
nodeLabel[face.label()] = result.addNode(nodePos).label()
result.nodeChordLabels.append([])
for face in delaunayMap.faceIter(skipInfinite = True):
if face.flag(OUTER_FACE):
continue
if faceType[face.label()] != "S":
#print faceType[face.label()] + "-triangle", face.label()
for dart in faceChords[face.label()]:
#print "following limb starting with", dart
startNode = result.node(nodeLabel[face.label()])
startDart = dart.clone()
edgePoints = []
subtendedBoundaryLength = 0.0
shapeWidth = []
if faceType[face.label()] == "T":
subtendedBoundaryLength += boundaryLength[face.label()]
if includeTerminalPositions:
# include opposite position
startNode.setPosition((dart.clone().nextPhi())[-1])
while True:
edgePoints.append(middlePoint(dart))
shapeWidth.append(dart.edge().length())
dart.nextAlpha()
nextFace = dart.leftFace()
if faceType[nextFace.label()] == "S":
subtendedBoundaryLength += boundaryLength[nextFace.label()]
# continue with opposite dart:
if dart == faceChords[nextFace.label()][0]:
dart = faceChords[nextFace.label()][1]
else:
dart = faceChords[nextFace.label()][0]
else:
faceChords[nextFace.label()].remove(dart)
break
endNode = result.node(nodeLabel[nextFace.label()])
if faceType[nextFace.label()] == "T":
subtendedBoundaryLength += boundaryLength[nextFace.label()]
if includeTerminalPositions:
endNode.setPosition((dart.clone().nextPhi())[-1])
flags = 0
if not edgePoints or edgePoints[0] != startNode.position():
edgePoints.insert(0, startNode.position())
shapeWidth.insert(0, None)
flags |= START_NODE_ADDED
if edgePoints[-1] != endNode.position():
edgePoints.append(endNode.position())
shapeWidth.append(None)
flags |= END_NODE_ADDED
if len(edgePoints) < 2:
# don't add edges with only 1 point (two adjacent
# T-triangles) - may fail for J-faces?!
# but J-faces should not have nodes on their borders
assert endNode.position() == startNode.position() and \
endNode.isIsolated() and startNode.isIsolated()
nodeLabel[nextFace.label()] = nodeLabel[face.label()]
result.removeIsolatedNode(endNode)
continue
sleeve = result.addEdge(
startNode, endNode, edgePoints)
sleeve.setFlag(flags)
result.subtendedLengths.append(subtendedBoundaryLength)
result.shapeWidths.append(shapeWidth)
if faceType[face.label()] == "J":
result.nodeChordLabels[startNode.label()].append(
(sleeve.label(), startDart.label()))
if faceType[nextFace.label()] == "J":
result.nodeChordLabels[endNode.label()].append(
(sleeve.label(), dart.label()))
result.initializeMap(initLabelImage = False)
return result
def pyCrackEdgeGraph(labelImage,
eightConnectedRegions=True,
progressHook=None):
result = GeoMap(labelImage.size())
cc = crackConnectionImage(labelImage)
if eightConnectedRegions:
for y in range(1, cc.height() - 1):
for x in range(1, cc.width() - 1):
if cc[x, y] == CONN_ALL4:
if labelImage[x, y] == labelImage[x - 1, y - 1]:
cc[x, y] += CONN_DIAG_UPLEFT
if labelImage[x - 1, y] == labelImage[x, y - 1]:
cc[x, y] += CONN_DIAG_UPRIGHT
# crossing regions?
if cc[x,
y] == CONN_ALL4 + CONN_DIAG_UPLEFT + CONN_DIAG_UPRIGHT:
# preserve connectedness of higher label:
if labelImage[x, y - 1] > labelImage[x - 1, y - 1]:
cc[x, y] -= CONN_DIAG_UPLEFT
else:
cc[x, y] -= CONN_DIAG_UPRIGHT
for y in range(cc.height()):
for x in range(cc.width()):
conn = int(cc[x, y])
if degree[conn] > 2:
cc[x, y] = conn | CONN_NODE
elif conn & CONN_ALL4 == (CONN_RIGHT | CONN_DOWN):
cc[x, y] = conn | CONN_MAYBE_NODE
if conn & CONN_DIAG:
cc[x, y] = conn | CONN_MAYBE_NODE
nodeImage = ScalarImage(cc.size())
# nodeImage encoding: each pixel's higher 28 bits encode the
# (label + 1) of a node that has been inserted into the resulting
# GeoMap at the corresponding position (+1 because zero is a valid
# node label), while the lower 4 bits encode the four CONN_
# directions in which a GeoMap edge is already connected to this
# node
progressHook = progressHook and progressHook.rangeTicker(cc.height())
for startAt in (CONN_NODE, CONN_MAYBE_NODE):
for y in range(cc.height()):
if progressHook:
progressHook()
for x in range(cc.width()):
nodeConn = int(cc[x, y])
if nodeConn & startAt:
startNodeInfo = int(nodeImage[x, y])
if startNodeInfo:
startNode = result.node((startNodeInfo >> 4) - 1)
else:
startNode = result.addNode((x - 0.5, y - 0.5))
nodeImage[x, y] = startNodeInfo = \
(startNode.label() + 1) << 4
for direction, startConn in enumerate(connections):
if nodeConn & startConn and not startNodeInfo & startConn:
edge, endPos, endConn = followEdge(
cc, (x, y), direction)
endNodeInfo = int(nodeImage[endPos])
if not endNodeInfo:
endNode = result.addNode(
(endPos[0] - 0.5, endPos[1] - 0.5))
endNodeInfo = (endNode.label() + 1) << 4
else:
assert not endNodeInfo & endConn, "double connection?"
endNode = result.node((endNodeInfo >> 4) - 1)
edge = result.addEdge(startNode, endNode, edge)
startNodeInfo |= startConn
if edge.isLoop():
startNodeInfo |= endConn
nodeImage[x, y] = startNodeInfo
else:
nodeImage[x, y] = startNodeInfo
nodeImage[endPos] = endNodeInfo | endConn
return result
def catMap(delaunayMap,
rectified = True,
includeTerminalPositions = False):
"""catMap(delaunayMap,
rectified = True,
includeTerminalPositions = False)
Extract a CAT (chordal axis transform) from a GeoMap object
containing a Delaunay Triangulation. Implements the rectified
version (from L.Prasad's DGCI'05 article), which also works for
GeoMaps with non-triangular Faces.
Expects outer faces of the delaunayMap to be marked with the
OUTER_FACE flag (in order to skip these faces and work only on the
inner parts of the shapes), and edges which belong to the
constrained segments of the CDT to be marked with the
CONTOUR_SEGMENT flag (i.e. an edge is a chord iff
'not edge.flag(CONTOUR_SEGMENT)')
Usually, you will do sth. along:
>>> del1 = delaunay.faceCDTMap(map1.face(173), map1.imageSize())
>>> cat1 = delaunay.catMap(del1, rectified = False)
The optional parameter `rectified` has been set to False here to
use the original definition of junction node positions (using the
circumcenter if possible) which works only for triangulations (and
is therefore disabled by default).
For triangulations, it is also possible to include the opposite
vertex of the terminal triangles into the skeleton by setting
`includeTerminalPositions` to True.
If you want to use the rectified CAT (with weak chords being
suppressed), you would use removeWeakChords before calling catMap:
>>> del2 = copy.copy(del1) # if you want to keep the original
>>> removeWeakChords(del2)
>>> rcat2 = delaunay.catMap(del2)
The resulting map will have additional attributes that relate the
skeleton with the original boundary:
subtendedLengths:
This is a list mapping edge labels of the skeleton to the
accumulated lengths of all contour segments within the contours
of the sleeve- and terminal-faces that comprise the sleeve
represented by that skeleton edge.
shapeWidths:
This is a list mapping edge labels of the skeleton to lists of
shape widths at each support point of the polygon (may be None
at the ends). In theory, this allows to reconstruct the
original boundary and thus makes the CAT fully reversible (see
Prasad's papers).
nodeChordLabels:
This is a list mapping node labels of the skeleton to lists of
(sleeveLabel, chordLabel) pairs, where sleeveLabel is the label
of a skeleton edge and chordLabel is the dart label of the first
chord from the `delaunayMap` within that sleeve. (This is
needed for later corrections of the junction node positions
after pruning.)"""
if rectified:
junctionPos = rectifiedJunctionNodePosition
assert not includeTerminalPositions, \
"includeTerminalPositions is not supported for the rectified CAT!"
else:
junctionPos = junctionNodePosition
result = GeoMap(delaunayMap.imageSize())
result.subtendedLengths = [0] # unused Edge 0
result.shapeWidths = [None]
result.nodeChordLabels = []
faceChords = [None] * delaunayMap.maxFaceLabel()
boundaryLength = [None] * delaunayMap.maxFaceLabel()
faceType = [None] * delaunayMap.maxFaceLabel()
nodeLabel = [None] * delaunayMap.maxFaceLabel()
for face in delaunayMap.faceIter(skipInfinite = True):
if face.flag(OUTER_FACE):
continue
assert face.holeCount() == 0
chords = []
bl = 0.0
for dart in face.contour().phiOrbit():
if not dart.edge().flag(CONTOUR_SEGMENT):
chords.append(dart)
else:
bl += dart.edge().length()
boundaryLength[face.label()] = bl
faceChords[face.label()] = chords
# classify into terminal, sleeve, and junction triangles:
if len(chords) < 2:
faceType[face.label()] = "T"
if chords:
nodePos = middlePoint(chords[0]) # (may be changed later)
elif len(chords) == 2:
faceType[face.label()] = "S"
else:
faceType[face.label()] = "J"
nodePos = junctionPos(chords)
# add nodes for non-sleeve triangles:
if faceType[face.label()] != "S" and chords:
nodeLabel[face.label()] = result.addNode(nodePos).label()
result.nodeChordLabels.append([])
for face in delaunayMap.faceIter(skipInfinite = True):
if face.flag(OUTER_FACE):
continue
if faceType[face.label()] != "S":
#print faceType[face.label()] + "-triangle", face.label()
for dart in faceChords[face.label()]:
#print "following limb starting with", dart
startNode = result.node(nodeLabel[face.label()])
startDart = dart.clone()
edgePoints = []
subtendedBoundaryLength = 0.0
shapeWidth = []
if faceType[face.label()] == "T":
subtendedBoundaryLength += boundaryLength[face.label()]
if includeTerminalPositions:
# include opposite position
startNode.setPosition((dart.clone().nextPhi())[-1])
while True:
edgePoints.append(middlePoint(dart))
shapeWidth.append(dart.edge().length())
dart.nextAlpha()
nextFace = dart.leftFace()
if faceType[nextFace.label()] == "S":
subtendedBoundaryLength += boundaryLength[nextFace.label()]
# continue with opposite dart:
if dart == faceChords[nextFace.label()][0]:
dart = faceChords[nextFace.label()][1]
else:
dart = faceChords[nextFace.label()][0]
else:
faceChords[nextFace.label()].remove(dart)
break
endNode = result.node(nodeLabel[nextFace.label()])
if faceType[nextFace.label()] == "T":
subtendedBoundaryLength += boundaryLength[nextFace.label()]
if includeTerminalPositions:
endNode.setPosition((dart.clone().nextPhi())[-1])
flags = 0
if not edgePoints or edgePoints[0] != startNode.position():
edgePoints.insert(0, startNode.position())
shapeWidth.insert(0, None)
flags |= START_NODE_ADDED
if edgePoints[-1] != endNode.position():
edgePoints.append(endNode.position())
shapeWidth.append(None)
flags |= END_NODE_ADDED
if len(edgePoints) < 2:
# don't add edges with only 1 point (two adjacent
# T-triangles) - may fail for J-faces?!
# but J-faces should not have nodes on their borders
assert endNode.position() == startNode.position() and \
endNode.isIsolated() and startNode.isIsolated()
nodeLabel[nextFace.label()] = nodeLabel[face.label()]
result.removeIsolatedNode(endNode)
continue
sleeve = result.addEdge(
startNode, endNode, edgePoints)
sleeve.setFlag(flags)
result.subtendedLengths.append(subtendedBoundaryLength)
result.shapeWidths.append(shapeWidth)
if faceType[face.label()] == "J":
result.nodeChordLabels[startNode.label()].append(
(sleeve.label(), startDart.label()))
if faceType[nextFace.label()] == "J":
result.nodeChordLabels[endNode.label()].append(
(sleeve.label(), dart.label()))
result.initializeMap(initLabelImage = False)
return result
def pyCrackEdgeGraph(labelImage, eightConnectedRegions = True,
progressHook = None):
result = GeoMap(labelImage.size())
cc = crackConnectionImage(labelImage)
if eightConnectedRegions:
for y in range(1, cc.height()-1):
for x in range(1, cc.width()-1):
if cc[x,y] == CONN_ALL4:
if labelImage[x,y] == labelImage[x-1,y-1]:
cc[x,y] += CONN_DIAG_UPLEFT
if labelImage[x-1,y] == labelImage[x,y-1]:
cc[x,y] += CONN_DIAG_UPRIGHT
# crossing regions?
if cc[x,y] == CONN_ALL4 + CONN_DIAG_UPLEFT + CONN_DIAG_UPRIGHT:
# preserve connectedness of higher label:
if labelImage[x,y-1] > labelImage[x-1,y-1]:
cc[x,y] -= CONN_DIAG_UPLEFT
else:
cc[x,y] -= CONN_DIAG_UPRIGHT
for y in range(cc.height()):
for x in range(cc.width()):
conn = int(cc[x,y])
if degree[conn] > 2:
cc[x,y] = conn | CONN_NODE
elif conn & CONN_ALL4 == (CONN_RIGHT | CONN_DOWN):
cc[x,y] = conn | CONN_MAYBE_NODE
if conn & CONN_DIAG:
cc[x,y] = conn | CONN_MAYBE_NODE
nodeImage = ScalarImage(cc.size())
# nodeImage encoding: each pixel's higher 28 bits encode the
# (label + 1) of a node that has been inserted into the resulting
# GeoMap at the corresponding position (+1 because zero is a valid
# node label), while the lower 4 bits encode the four CONN_
# directions in which a GeoMap edge is already connected to this
# node
progressHook = progressHook and progressHook.rangeTicker(cc.height())
for startAt in (CONN_NODE, CONN_MAYBE_NODE):
for y in range(cc.height()):
if progressHook:
progressHook()
for x in range(cc.width()):
nodeConn = int(cc[x, y])
if nodeConn & startAt:
startNodeInfo = int(nodeImage[x, y])
if startNodeInfo:
startNode = result.node((startNodeInfo >> 4) - 1)
else:
startNode = result.addNode((x - 0.5, y - 0.5))
nodeImage[x, y] = startNodeInfo = \
(startNode.label() + 1) << 4
for direction, startConn in enumerate(connections):
if nodeConn & startConn and not startNodeInfo & startConn:
edge, endPos, endConn = followEdge(
cc, (x, y), direction)
endNodeInfo = int(nodeImage[endPos])
if not endNodeInfo:
endNode = result.addNode((endPos[0] - 0.5, endPos[1] - 0.5))
endNodeInfo = (endNode.label() + 1) << 4
else:
assert not endNodeInfo & endConn, "double connection?"
endNode = result.node((endNodeInfo >> 4) - 1)
edge = result.addEdge(startNode, endNode, edge)
startNodeInfo |= startConn
if edge.isLoop():
startNodeInfo |= endConn
nodeImage[x, y] = startNodeInfo
else:
nodeImage[x, y] = startNodeInfo
nodeImage[endPos] = endNodeInfo | endConn
return result