From 23c6111ad321fc022c1bb6219ba32a75cf0885e4 Mon Sep 17 00:00:00 2001
From: Vighnesh Birodkar <vighneshbirodkar@gmail.com>
Date: Wed, 3 Jun 2015 21:58:26 +0530
Subject: [PATCH] Fixing error in ncut when subgraph as all equal weights
 (#1538)

---
 skimage/future/graph/_ncut.py          | 20 ++------------------
 skimage/future/graph/graph_cut.py      | 11 +++++++++--
 skimage/future/graph/tests/test_rag.py | 20 ++++++++++++++++++++
 3 files changed, 31 insertions(+), 20 deletions(-)

diff --git a/skimage/future/graph/_ncut.py b/skimage/future/graph/_ncut.py
index 05be8cd1..e18e9595 100644
--- a/skimage/future/graph/_ncut.py
+++ b/skimage/future/graph/_ncut.py
@@ -29,6 +29,8 @@ def DW_matrices(graph):
     W = nx.to_scipy_sparse_matrix(graph, format='csc')
     entries = W.sum(axis=0)
     D = sparse.dia_matrix((entries, 0), shape=W.shape).tocsc()
+    #print("D = ",D.todense())
+    #print("W = ",W.todense())
     return D, W
 
 
@@ -65,21 +67,3 @@ def ncut_cost(cut, D, W):
     assoc_b = D.data[~cut].sum()
 
     return (cut_cost / assoc_a) + (cut_cost / assoc_b)
-
-
-def normalize(a):
-    """Normalize values in an array between `0` and `1`.
-
-    Parameters
-    ----------
-    a : ndarray
-        The array to be normalized.
-
-    Returns
-    -------
-    out : ndarray
-        The normalized array.
-    """
-    mi = a.min()
-    mx = a.max()
-    return (a - mi) / (mx - mi)
diff --git a/skimage/future/graph/graph_cut.py b/skimage/future/graph/graph_cut.py
index d727eeac..6a4ba03e 100644
--- a/skimage/future/graph/graph_cut.py
+++ b/skimage/future/graph/graph_cut.py
@@ -195,10 +195,17 @@ def get_min_ncut(ev, d, w, num_cuts):
         The value of the minimum ncut.
     """
     mcut = np.inf
+    mn = ev.min()
+    mx = ev.max()
+
+    # If all values in `ev` are equal, the loop does not assign a value to
+    # `min_mask`. This implies that the graph can't be further sub-divided
+    # In this case the bi-partition is the the graph itself and an empty set.
+    min_mask = np.zeros_like(ev, dtype=np.bool)
 
     # Refer Shi & Malik 2001, Section 3.1.3, Page 892
     # Perform evenly spaced n-cuts and determine the optimal one.
-    for t in np.linspace(0, 1, num_cuts, endpoint=False):
+    for t in np.linspace(mn, mx, num_cuts, endpoint=False):
         mask = ev > t
         cost = _ncut.ncut_cost(mask, d, w)
         if cost < mcut:
@@ -266,7 +273,7 @@ def _ncut_relabel(rag, thresh, num_cuts):
         # 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])
+        ev = vectors[:, index2]
 
         cut_mask, mcut = get_min_ncut(ev, d, w, num_cuts)
         if (mcut < thresh):
diff --git a/skimage/future/graph/tests/test_rag.py b/skimage/future/graph/tests/test_rag.py
index 1cac2b2d..3c5d12b1 100644
--- a/skimage/future/graph/tests/test_rag.py
+++ b/skimage/future/graph/tests/test_rag.py
@@ -159,3 +159,23 @@ def test_rag_hierarchical():
 
     result = graph.cut_threshold(labels, g, thresh)
     assert np.all(result == result[0, 0])
+
+
+@skipif(not is_installed('networkx'))
+def test_ncut_stable_subgraph():
+    """ Test to catch an error thrown when subgraph has all eqal edges. """
+
+    img = np.zeros((100, 100, 3), dtype='uint8')
+
+    labels = np.zeros((100, 100), dtype='uint8')
+    labels[...] = 0
+    labels[:50, :50] = 1
+    labels[:50, 50:] = 2
+
+    rag = graph.rag_mean_color(img, labels, mode='similarity')
+    print(rag.edges(data=True))
+
+    new_labels = graph.cut_normalized(labels, rag, in_place=False)
+    new_labels, _, _ = segmentation.relabel_sequential(new_labels)
+    # Two labels
+    assert new_labels.max() == 0