68 lines
1.8 KiB
Python
68 lines
1.8 KiB
Python
try:
|
|
import networkx as nx
|
|
except ImportError:
|
|
from ..._shared.utils import warn
|
|
warn('RAGs require networkx')
|
|
import numpy as np
|
|
from scipy import sparse
|
|
from . import _ncut_cy
|
|
|
|
|
|
def DW_matrices(graph):
|
|
"""Returns the diagonal and weight matrices of a graph.
|
|
|
|
Parameters
|
|
----------
|
|
graph : RAG
|
|
A Region Adjacency Graph.
|
|
|
|
Returns
|
|
-------
|
|
D : csc_matrix
|
|
The diagonal matrix of the graph. ``D[i, i]`` is the sum of weights of
|
|
all edges incident on `i`. All other entries are `0`.
|
|
W : csc_matrix
|
|
The weight matrix of the graph. ``W[i, j]`` is the weight of the edge
|
|
joining `i` to `j`.
|
|
"""
|
|
# sparse.eighsh is most efficient with CSC-formatted input
|
|
W = nx.to_scipy_sparse_matrix(graph, format='csc')
|
|
entries = W.sum(axis=0)
|
|
D = sparse.dia_matrix((entries, 0), shape=W.shape).tocsc()
|
|
|
|
return D, W
|
|
|
|
|
|
def ncut_cost(cut, D, W):
|
|
"""Returns the N-cut cost of a bi-partition of a graph.
|
|
|
|
Parameters
|
|
----------
|
|
cut : ndarray
|
|
The mask for the nodes in the graph. Nodes corresponding to a `True`
|
|
value are in one set.
|
|
D : csc_matrix
|
|
The diagonal matrix of the graph.
|
|
W : csc_matrix
|
|
The weight matrix of the graph.
|
|
|
|
Returns
|
|
-------
|
|
cost : float
|
|
The cost of performing the N-cut.
|
|
|
|
References
|
|
----------
|
|
.. [1] Normalized Cuts and Image Segmentation, Jianbo Shi and
|
|
Jitendra Malik, IEEE Transactions on Pattern Analysis and Machine
|
|
Intelligence, Page 889, Equation 2.
|
|
"""
|
|
cut = np.array(cut)
|
|
cut_cost = _ncut_cy.cut_cost(cut, W)
|
|
|
|
# D has elements only along the diagonal, one per node, so we can directly
|
|
# index the data attribute with cut.
|
|
assoc_a = D.data[cut].sum()
|
|
assoc_b = D.data[~cut].sum()
|
|
|
|
return (cut_cost / assoc_a) + (cut_cost / assoc_b)
|