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Vighnesh Birodkar
2014-08-09 21:29:41 +05:30
parent 6d0bf723d7
commit 3973b30300
3 changed files with 64 additions and 39 deletions
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skimage/graph/_ncut_cy.pyx
-2
View File
@@ -74,7 +74,5 @@ def cut_cost(cut, W):
row = indices[row_index]
if cut_mask[row] != cut_mask[col]:
cost += data[row_index]
row_index += 1
col += 1
return cost * 0.5
skimage/graph/graph_cut.py
+55 -29
View File
@@ -9,7 +9,7 @@ from . import _ncut_cy
from scipy.sparse import linalg
def cut_threshold(labels, rag, thresh):
def cut_threshold(labels, rag, thresh, in_place=True):
"""Combine regions seperated by weight less than threshold.
Given an image's labels and its RAG, output new labels by
@@ -25,6 +25,10 @@ def cut_threshold(labels, rag, thresh):
thresh : float
The threshold. Regions connected by edges with smaller weights are
combined.
in_place : bool
If set, modifies `rag` in place. The function will remove the edges
with weights less that `thresh`. If set to `False` the function
makes a copy of `rag` before proceeding.
Returns
-------
@@ -47,7 +51,9 @@ def cut_threshold(labels, rag, thresh):
"""
# Because deleting edges while iterating through them produces an error.
rag = rag.copy()
if not in_place:
rag = rag.copy()
to_remove = [(x, y) for x, y, d in rag.edges_iter(data=True)
if d['weight'] >= thresh]
rag.remove_edges_from(to_remove)
@@ -66,7 +72,7 @@ def cut_threshold(labels, rag, thresh):
return map_array[labels]
def cut_normalized(labels, rag, thresh=0.001, num_cuts=10):
def cut_normalized(labels, rag, thresh=0.001, num_cuts=10, in_place=True):
"""Perform Normalized Graph cut on the Region Adjacency Graph.
Given an image's labels and its similarity RAG, recursively perform
@@ -85,6 +91,9 @@ def cut_normalized(labels, rag, thresh=0.001, num_cuts=10):
value of the N-cut exceeds `thresh`.
num_cuts : int
The number or N-cuts to perform before determining the optimal one.
in_place : bool
If set, modifies `rag` in place. For each node `n` the function will
set a new attribute ``rag.node[n]['ncut label]``.
Returns
-------
@@ -106,8 +115,15 @@ def cut_normalized(labels, rag, thresh=0.001, num_cuts=10):
IEEE Transactions on , vol.22, no.8, pp.888,905, August 2000
"""
map_array = np.arange(labels.max() + 1)
_ncut_relabel(rag, thresh, num_cuts, map_array)
if not in_place:
rag = rag.copy()
_ncut_relabel(rag, thresh, num_cuts)
map_array = np.zeros(labels.max() + 1)
# Mapping from old labels to new
for n, d in rag.nodes_iter(data=True):
map_array[d['labels']] = d['ncut label']
return map_array[labels]
@@ -128,6 +144,16 @@ def partition_by_cut(cut, rag):
sub1, sub2 : RAG
The two resulting subgraphs from the bi-partition.
"""
# `cut` is derived from `D` and `W` matrices, which also follow the
# ordering returned by `rag.nodes()` because we use
# nx.to_scipy_sparce_matrix.
# Example
# rag.nodes() = [3, 7, 9, 13]
# cut = [True, False, True, False]
# nodes1 = [3, 9]
# nodes2 = [7, 10]
nodes1 = [n for i, n in enumerate(rag.nodes()) if cut[i]]
nodes2 = [n for i, n in enumerate(rag.nodes()) if not cut[i]]
@@ -153,9 +179,10 @@ def get_min_ncut(ev, d, w, num_cuts):
Returns
-------
threshold, mcut : float
The threshold which produced the minimum ncut, and the value of the
ncut itself.
mask : array
The array of booleans which denotes the bi-partition.
mcut : float
The value of the minimum ncut.
"""
mcut = np.inf
@@ -165,13 +192,21 @@ def get_min_ncut(ev, d, w, num_cuts):
mask = ev > t
cost = _ncut.ncut_cost(mask, d, w)
if cost < mcut:
min_mask = mask
mcut = cost
threshold = t
return threshold, mcut
return min_mask, mcut
def _ncut_relabel(rag, thresh, num_cuts, map_array):
def _label_all(rag, attr_name):
node = rag.nodes()[0]
new_label = rag.node[node]['labels'][0]
for n, d in rag.nodes_iter(data=True):
for l in d['labels']:
d[attr_name] = new_label
def _ncut_relabel(rag, thresh, num_cuts):
"""Perform Normalized Graph cut on the Region Adjacency Graph.
Recursively partition the graph into 2, until further subdivision
@@ -195,46 +230,37 @@ def _ncut_relabel(rag, thresh, num_cuts, map_array):
the function.
"""
d, w = _ncut.DW_matrices(rag)
stop = False
m = w.shape[0]
if m > 2:
d2 = d.copy()
# Since d is diagonal, we can directly operate on it's data
# the inverse
d2.data = 1.0 / d2.data
# the square root
d2.data = np.sqrt(d2.data)
# the inverse of the square root
d2.data = np.reciprocal(np.sqrt(d2.data, out=d2.data), out=d2.data)
# Refer Shi & Malik 2001, Equation 7, Page 891
vals, vectors = linalg.eigsh(d2 * (d - w) * d2, which='SM',
k=min(100, m - 2))
else:
stop = True
if not stop:
# Pick second smalles eigenvector.
# Pick second smallest eigenvector.
# Refer Shi & Malik 2001, Section 3.2.3, Page 893
vals, vectors = np.real(vals), np.real(vectors)
index2 = _ncut_cy.argmin2(vals)
ev = _ncut.normalize(vectors[:, index2])
threshold, mcut = get_min_ncut(ev, d, w, num_cuts)
cut_mask, mcut = get_min_ncut(ev, d, w, num_cuts)
if (mcut < thresh):
cut_mask = ev > threshold
# Sub divide and perform N-cut again
# Refer Shi & Malik 2001, Section 3.2.5, Page 893
sub1, sub2 = partition_by_cut(cut_mask, rag)
_ncut_relabel(sub1, thresh, num_cuts, map_array)
_ncut_relabel(sub2, thresh, num_cuts, map_array)
_ncut_relabel(sub1, thresh, num_cuts)
_ncut_relabel(sub2, thresh, num_cuts)
return
# The N-cut wasn't small enough, or could not be computed.
# The remaining graph is a region.
# Assign `ncut label` by picking any label from the existing nodes, since
# `labels` are unique, `new_label` is also unique.
node = rag.nodes()[0]
new_label = rag.node[node]['labels'][0]
for n, d in rag.nodes_iter(data=True):
for l in d['labels']:
map_array[l] = new_label
_label_all(rag, 'ncut label')
skimage/graph/rag.py
+9 -8
View File
@@ -2,6 +2,7 @@ try:
import networkx as nx
except ImportError:
msg = "Graph functions require networkx, which is not installed"
class nx:
class Graph:
def __init__(self, *args, **kwargs):
@@ -119,7 +120,7 @@ def _add_edge_filter(values, graph):
return 0
def rag_mean_color(image, labels, connectivity=2, mode='dissimilarity',
def rag_mean_color(image, labels, connectivity=2, mode='distance',
sigma=255.0):
"""Compute the Region Adjacency Graph using mean colors.
@@ -142,15 +143,15 @@ def rag_mean_color(image, labels, connectivity=2, mode='dissimilarity',
are considered adjacent. It can range from 1 to `labels.ndim`. Its
behavior is the same as `connectivity` parameter in
`scipy.ndimage.filters.generate_binary_structure`.
mode : str['similarity' | 'dissimilarity']
mode : {'distance', 'similarity'}, optional
The strategy to assign edge weights.
'similarity' : The weight between two adjacent regions is the
'distance' : The weight between two adjacent regions is the
:math:`|c_1 - c_2|`, where :math:`c_1` and :math:`c_2` are the mean
colors of the two regions. It represents how different two regions
are.
colors of the two regions. It represents the Euclidian distance in
their average color.
'dissimilarity' : The weight between two adjacent is
'similarity' : The weight between two adjacent is
:math:`e^{-d^2/sigma}` where :math:`d=|c_1 - c_2|`, where
:math:`c_1` and :math:`c_2` are the mean colors of the two regions.
It represents how similar two regions are.
@@ -229,9 +230,9 @@ def rag_mean_color(image, labels, connectivity=2, mode='dissimilarity',
diff = np.linalg.norm(diff)
if mode == 'similarity':
d['weight'] = math.e ** (-(diff ** 2) / sigma)
elif mode == 'dissimilarity':
elif mode == 'distance':
d['weight'] = diff
else:
raise ValueError("The mode '%s' is not recodnized" % mode)
raise ValueError("The mode '%s' is not recognised" % mode)
return graph