559 lines
20 KiB
Python
559 lines
20 KiB
Python
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import networkx as nx
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import numpy as np
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from numpy.lib.stride_tricks import as_strided
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from scipy import ndimage as ndi
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from scipy import sparse
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import math
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from ... import measure, segmentation, util, color
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def _edge_generator_from_csr(csr_matrix):
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"""Yield weighted edge triples for use by NetworkX from a CSR matrix.
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This function is a straight rewrite of
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`networkx.convert_matrix._csr_gen_triples`. Since that is a private
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function, it is safer to include our own here.
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Parameters
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----------
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csr_matrix : scipy.sparse.csr_matrix
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The input matrix. An edge (i, j, w) will be yielded if there is a
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data value for coordinates (i, j) in the matrix, even if that value
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is 0.
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Yields
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------
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i, j, w : (int, int, float) tuples
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Each value `w` in the matrix along with its coordinates (i, j).
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Examples
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--------
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>>> dense = np.eye(2, dtype=np.float)
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>>> csr = sparse.csr_matrix(dense)
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>>> edges = _edge_generator_from_csr(csr)
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>>> list(edges)
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[(0, 0, 1.0), (1, 1, 1.0)]
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"""
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nrows = csr_matrix.shape[0]
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values = csr_matrix.data
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indptr = csr_matrix.indptr
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col_indices = csr_matrix.indices
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for i in range(nrows):
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for j in range(indptr[i], indptr[i + 1]):
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yield i, col_indices[j], values[j]
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def min_weight(graph, src, dst, n):
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"""Callback to handle merging nodes by choosing minimum weight.
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Returns a dictionary with `"weight"` set as either the weight between
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(`src`, `n`) or (`dst`, `n`) in `graph` or the minimum of the two when
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both exist.
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Parameters
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----------
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graph : RAG
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The graph under consideration.
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src, dst : int
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The verices in `graph` to be merged.
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n : int
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A neighbor of `src` or `dst` or both.
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Returns
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-------
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data : dict
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A dict with the `"weight"` attribute set the weight between
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(`src`, `n`) or (`dst`, `n`) in `graph` or the minimum of the two when
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both exist.
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"""
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# cover the cases where n only has edge to either `src` or `dst`
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default = {'weight': np.inf}
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w1 = graph[n].get(src, default)['weight']
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w2 = graph[n].get(dst, default)['weight']
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return {'weight': min(w1, w2)}
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def _add_edge_filter(values, graph):
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"""Create edge in `graph` between central element of `values` and the rest.
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Add an edge between the middle element in `values` and
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all other elements of `values` into `graph`. ``values[len(values) // 2]``
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is expected to be the central value of the footprint used.
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Parameters
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----------
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values : array
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The array to process.
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graph : RAG
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The graph to add edges in.
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Returns
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-------
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0 : float
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Always returns 0. The return value is required so that `generic_filter`
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can put it in the output array, but it is ignored by this filter.
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"""
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values = values.astype(int)
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center = values[len(values) // 2]
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for value in values:
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if value != center and not graph.has_edge(center, value):
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graph.add_edge(center, value)
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return 0.
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class RAG(nx.Graph):
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"""
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The Region Adjacency Graph (RAG) of an image, subclasses
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`networx.Graph <http://networkx.github.io/documentation/latest/reference/classes/graph.html>`_
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Parameters
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----------
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label_image : array of int
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An initial segmentation, with each region labeled as a different
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integer. Every unique value in ``label_image`` will correspond to
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a node in the graph.
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connectivity : int in {1, ..., ``label_image.ndim``}, optional
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The connectivity between pixels in ``label_image``. For a 2D image,
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a connectivity of 1 corresponds to immediate neighbors up, down,
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left, and right, while a connectivity of 2 also includes diagonal
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neighbors. See `scipy.ndimage.generate_binary_structure`.
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data : networkx Graph specification, optional
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Initial or additional edges to pass to the NetworkX Graph
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constructor. See `networkx.Graph`. Valid edge specifications
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include edge list (list of tuples), NumPy arrays, and SciPy
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sparse matrices.
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**attr : keyword arguments, optional
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Additional attributes to add to the graph.
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"""
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def __init__(self, label_image=None, connectivity=1, data=None, **attr):
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super(RAG, self).__init__(data, **attr)
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if self.number_of_nodes() == 0:
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self.max_id = 0
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else:
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self.max_id = max(self.nodes())
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if label_image is not None:
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fp = ndi.generate_binary_structure(label_image.ndim, connectivity)
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# In the next ``ndi.generic_filter`` function, the kwarg
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# ``output`` is used to provide a strided array with a single
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# 64-bit floating point number, to which the function repeatedly
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# writes. This is done because even if we don't care about the
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# output, without this, a float array of the same shape as the
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# input image will be created and that could be expensive in
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# memory consumption.
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ndi.generic_filter(
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label_image,
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function=_add_edge_filter,
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footprint=fp,
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mode='nearest',
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output=as_strided(np.empty((1,), dtype=np.float_),
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shape=label_image.shape,
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strides=((0,) * label_image.ndim)),
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extra_arguments=(self,))
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def merge_nodes(self, src, dst, weight_func=min_weight, in_place=True,
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extra_arguments=[], extra_keywords={}):
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"""Merge node `src` and `dst`.
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The new combined node is adjacent to all the neighbors of `src`
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and `dst`. `weight_func` is called to decide the weight of edges
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incident on the new node.
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Parameters
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----------
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src, dst : int
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Nodes to be merged.
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weight_func : callable, optional
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Function to decide the attributes of edges incident on the new
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node. For each neighbor `n` for `src and `dst`, `weight_func` will
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be called as follows: `weight_func(src, dst, n, *extra_arguments,
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**extra_keywords)`. `src`, `dst` and `n` are IDs of vertices in the
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RAG object which is in turn a subclass of `networkx.Graph`. It is
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expected to return a dict of attributes of the resulting edge.
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in_place : bool, optional
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If set to `True`, the merged node has the id `dst`, else merged
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node has a new id which is returned.
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extra_arguments : sequence, optional
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The sequence of extra positional arguments passed to
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`weight_func`.
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extra_keywords : dictionary, optional
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The dict of keyword arguments passed to the `weight_func`.
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Returns
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-------
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id : int
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The id of the new node.
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Notes
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-----
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If `in_place` is `False` the resulting node has a new id, rather than
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`dst`.
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"""
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src_nbrs = set(self.neighbors(src))
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dst_nbrs = set(self.neighbors(dst))
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neighbors = (src_nbrs | dst_nbrs) - {src, dst}
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if in_place:
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new = dst
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else:
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new = self.next_id()
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self.add_node(new)
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for neighbor in neighbors:
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data = weight_func(self, src, new, neighbor, *extra_arguments,
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**extra_keywords)
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self.add_edge(neighbor, new, attr_dict=data)
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self.nodes[new]['labels'] = (self.nodes[src]['labels'] +
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self.nodes[dst]['labels'])
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self.remove_node(src)
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if not in_place:
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self.remove_node(dst)
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return new
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def add_node(self, n, attr_dict=None, **attr):
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"""Add node `n` while updating the maximum node id.
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.. seealso:: :func:`networkx.Graph.add_node`."""
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if attr_dict is None: # compatibility with old networkx
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attr_dict = attr
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else:
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attr_dict.update(attr)
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super(RAG, self).add_node(n, **attr_dict)
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self.max_id = max(n, self.max_id)
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def add_edge(self, u, v, attr_dict=None, **attr):
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"""Add an edge between `u` and `v` while updating max node id.
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.. seealso:: :func:`networkx.Graph.add_edge`."""
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if attr_dict is None: # compatibility with old networkx
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attr_dict = attr
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else:
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attr_dict.update(attr)
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super(RAG, self).add_edge(u, v, **attr_dict)
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self.max_id = max(u, v, self.max_id)
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def copy(self):
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"""Copy the graph with its max node id.
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.. seealso:: :func:`networkx.Graph.copy`."""
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g = super(RAG, self).copy()
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g.max_id = self.max_id
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return g
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def fresh_copy(self):
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"""Return a fresh copy graph with the same data structure.
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A fresh copy has no nodes, edges or graph attributes. It is
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the same data structure as the current graph. This method is
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typically used to create an empty version of the graph.
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This is required when subclassing Graph with networkx v2 and
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does not cause problems for v1. Here is more detail from
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the network migrating from 1.x to 2.x document::
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With the new GraphViews (SubGraph, ReversedGraph, etc)
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you can't assume that ``G.__class__()`` will create a new
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instance of the same graph type as ``G``. In fact, the
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call signature for ``__class__`` differs depending on
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whether ``G`` is a view or a base class. For v2.x you
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should use ``G.fresh_copy()`` to create a null graph of
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the correct type---ready to fill with nodes and edges.
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"""
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return RAG()
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def next_id(self):
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"""Returns the `id` for the new node to be inserted.
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The current implementation returns one more than the maximum `id`.
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Returns
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-------
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id : int
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The `id` of the new node to be inserted.
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"""
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return self.max_id + 1
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def _add_node_silent(self, n):
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"""Add node `n` without updating the maximum node id.
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This is a convenience method used internally.
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.. seealso:: :func:`networkx.Graph.add_node`."""
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super(RAG, self).add_node(n)
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def rag_mean_color(image, labels, connectivity=2, mode='distance',
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sigma=255.0):
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"""Compute the Region Adjacency Graph using mean colors.
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Given an image and its initial segmentation, this method constructs the
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corresponding Region Adjacency Graph (RAG). Each node in the RAG
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represents a set of pixels within `image` with the same label in `labels`.
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The weight between two adjacent regions represents how similar or
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dissimilar two regions are depending on the `mode` parameter.
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Parameters
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----------
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image : ndarray, shape(M, N, [..., P,] 3)
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Input image.
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labels : ndarray, shape(M, N, [..., P])
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The labelled image. This should have one dimension less than
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`image`. If `image` has dimensions `(M, N, 3)` `labels` should have
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dimensions `(M, N)`.
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connectivity : int, optional
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Pixels with a squared distance less than `connectivity` from each other
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are considered adjacent. It can range from 1 to `labels.ndim`. Its
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behavior is the same as `connectivity` parameter in
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``scipy.ndimage.generate_binary_structure``.
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mode : {'distance', 'similarity'}, optional
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The strategy to assign edge weights.
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'distance' : The weight between two adjacent regions is the
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:math:`|c_1 - c_2|`, where :math:`c_1` and :math:`c_2` are the mean
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colors of the two regions. It represents the Euclidean distance in
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their average color.
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'similarity' : The weight between two adjacent is
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:math:`e^{-d^2/sigma}` where :math:`d=|c_1 - c_2|`, where
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:math:`c_1` and :math:`c_2` are the mean colors of the two regions.
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It represents how similar two regions are.
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sigma : float, optional
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Used for computation when `mode` is "similarity". It governs how
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close to each other two colors should be, for their corresponding edge
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weight to be significant. A very large value of `sigma` could make
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any two colors behave as though they were similar.
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Returns
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-------
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out : RAG
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The region adjacency graph.
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Examples
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--------
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>>> from skimage import data, segmentation
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>>> from skimage.future import graph
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>>> img = data.astronaut()
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>>> labels = segmentation.slic(img)
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>>> rag = graph.rag_mean_color(img, labels)
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References
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----------
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.. [1] Alain Tremeau and Philippe Colantoni
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"Regions Adjacency Graph Applied To Color Image Segmentation"
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:DOI:`10.1109/83.841950`
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"""
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graph = RAG(labels, connectivity=connectivity)
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for n in graph:
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graph.nodes[n].update({'labels': [n],
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'pixel count': 0,
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'total color': np.array([0, 0, 0],
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dtype=np.double)})
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for index in np.ndindex(labels.shape):
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current = labels[index]
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graph.nodes[current]['pixel count'] += 1
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graph.nodes[current]['total color'] += image[index]
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for n in graph:
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graph.nodes[n]['mean color'] = (graph.nodes[n]['total color'] /
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graph.nodes[n]['pixel count'])
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||
|
|
for x, y, d in graph.edges(data=True):
|
||
|
|
diff = graph.nodes[x]['mean color'] - graph.nodes[y]['mean color']
|
||
|
|
diff = np.linalg.norm(diff)
|
||
|
|
if mode == 'similarity':
|
||
|
|
d['weight'] = math.e ** (-(diff ** 2) / sigma)
|
||
|
|
elif mode == 'distance':
|
||
|
|
d['weight'] = diff
|
||
|
|
else:
|
||
|
|
raise ValueError("The mode '%s' is not recognised" % mode)
|
||
|
|
|
||
|
|
return graph
|
||
|
|
|
||
|
|
|
||
|
|
def rag_boundary(labels, edge_map, connectivity=2):
|
||
|
|
""" Comouter RAG based on region boundaries
|
||
|
|
|
||
|
|
Given an image's initial segmentation and its edge map this method
|
||
|
|
constructs the corresponding Region Adjacency Graph (RAG). Each node in the
|
||
|
|
RAG represents a set of pixels within the image with the same label in
|
||
|
|
`labels`. The weight between two adjacent regions is the average value
|
||
|
|
in `edge_map` along their boundary.
|
||
|
|
|
||
|
|
labels : ndarray
|
||
|
|
The labelled image.
|
||
|
|
edge_map : ndarray
|
||
|
|
This should have the same shape as that of `labels`. For all pixels
|
||
|
|
along the boundary between 2 adjacent regions, the average value of the
|
||
|
|
corresponding pixels in `edge_map` is the edge weight between them.
|
||
|
|
connectivity : int, optional
|
||
|
|
Pixels with a squared distance less than `connectivity` from each other
|
||
|
|
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`.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from skimage import data, segmentation, filters, color
|
||
|
|
>>> from skimage.future import graph
|
||
|
|
>>> img = data.chelsea()
|
||
|
|
>>> labels = segmentation.slic(img)
|
||
|
|
>>> edge_map = filters.sobel(color.rgb2gray(img))
|
||
|
|
>>> rag = graph.rag_boundary(labels, edge_map)
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
conn = ndi.generate_binary_structure(labels.ndim, connectivity)
|
||
|
|
eroded = ndi.grey_erosion(labels, footprint=conn)
|
||
|
|
dilated = ndi.grey_dilation(labels, footprint=conn)
|
||
|
|
boundaries0 = (eroded != labels)
|
||
|
|
boundaries1 = (dilated != labels)
|
||
|
|
labels_small = np.concatenate((eroded[boundaries0], labels[boundaries1]))
|
||
|
|
labels_large = np.concatenate((labels[boundaries0], dilated[boundaries1]))
|
||
|
|
n = np.max(labels_large) + 1
|
||
|
|
|
||
|
|
# use a dummy broadcast array as data for RAG
|
||
|
|
ones = as_strided(np.ones((1,), dtype=np.float), shape=labels_small.shape,
|
||
|
|
strides=(0,))
|
||
|
|
count_matrix = sparse.coo_matrix((ones, (labels_small, labels_large)),
|
||
|
|
dtype=np.int_, shape=(n, n)).tocsr()
|
||
|
|
data = np.concatenate((edge_map[boundaries0], edge_map[boundaries1]))
|
||
|
|
|
||
|
|
data_coo = sparse.coo_matrix((data, (labels_small, labels_large)))
|
||
|
|
graph_matrix = data_coo.tocsr()
|
||
|
|
graph_matrix.data /= count_matrix.data
|
||
|
|
|
||
|
|
rag = RAG()
|
||
|
|
rag.add_weighted_edges_from(_edge_generator_from_csr(graph_matrix),
|
||
|
|
weight='weight')
|
||
|
|
rag.add_weighted_edges_from(_edge_generator_from_csr(count_matrix),
|
||
|
|
weight='count')
|
||
|
|
|
||
|
|
for n in rag.nodes():
|
||
|
|
rag.nodes[n].update({'labels': [n]})
|
||
|
|
|
||
|
|
return rag
|
||
|
|
|
||
|
|
|
||
|
|
def show_rag(labels, rag, image, border_color='black', edge_width=1.5,
|
||
|
|
edge_cmap='magma', img_cmap='bone', in_place=True, ax=None):
|
||
|
|
"""Show a Region Adjacency Graph on an image.
|
||
|
|
|
||
|
|
Given a labelled image and its corresponding RAG, show the nodes and edges
|
||
|
|
of the RAG on the image with the specified colors. Edges are displayed between
|
||
|
|
the centroid of the 2 adjacent regions in the image.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
labels : ndarray, shape (M, N)
|
||
|
|
The labelled image.
|
||
|
|
rag : RAG
|
||
|
|
The Region Adjacency Graph.
|
||
|
|
image : ndarray, shape (M, N[, 3])
|
||
|
|
Input image. If `colormap` is `None`, the image should be in RGB
|
||
|
|
format.
|
||
|
|
border_color : color spec, optional
|
||
|
|
Color with which the borders between regions are drawn.
|
||
|
|
edge_width : float, optional
|
||
|
|
The thickness with which the RAG edges are drawn.
|
||
|
|
edge_cmap : :py:class:`matplotlib.colors.Colormap`, optional
|
||
|
|
Any matplotlib colormap with which the edges are drawn.
|
||
|
|
img_cmap : :py:class:`matplotlib.colors.Colormap`, optional
|
||
|
|
Any matplotlib colormap with which the image is draw. If set to `None`
|
||
|
|
the image is drawn as it is.
|
||
|
|
in_place : bool, optional
|
||
|
|
If set, the RAG is modified in place. For each node `n` the function
|
||
|
|
will set a new attribute ``rag.nodes[n]['centroid']``.
|
||
|
|
ax : :py:class:`matplotlib.axes.Axes`, optional
|
||
|
|
The axes to draw on. If not specified, new axes are created and drawn
|
||
|
|
on.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
lc : :py:class:`matplotlib.collections.LineCollection`
|
||
|
|
A colection of lines that represent the edges of the graph. It can be
|
||
|
|
passed to the :meth:`matplotlib.figure.Figure.colorbar` function.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from skimage import data, segmentation
|
||
|
|
>>> from skimage.future import graph
|
||
|
|
>>> import matplotlib.pyplot as plt
|
||
|
|
>>>
|
||
|
|
>>> img = data.coffee()
|
||
|
|
>>> labels = segmentation.slic(img)
|
||
|
|
>>> g = graph.rag_mean_color(img, labels)
|
||
|
|
>>> lc = graph.show_rag(labels, g, img)
|
||
|
|
>>> cbar = plt.colorbar(lc)
|
||
|
|
"""
|
||
|
|
from matplotlib import colors, cm
|
||
|
|
from matplotlib import pyplot as plt
|
||
|
|
from matplotlib.collections import LineCollection
|
||
|
|
|
||
|
|
if not in_place:
|
||
|
|
rag = rag.copy()
|
||
|
|
|
||
|
|
if ax is None:
|
||
|
|
fig, ax = plt.subplots()
|
||
|
|
out = util.img_as_float(image, force_copy=True)
|
||
|
|
|
||
|
|
if img_cmap is None:
|
||
|
|
if image.ndim < 3 or image.shape[2] not in [3, 4]:
|
||
|
|
msg = 'If colormap is `None`, an RGB or RGBA image should be given'
|
||
|
|
raise ValueError(msg)
|
||
|
|
# Ignore the alpha channel
|
||
|
|
out = image[:, :, :3]
|
||
|
|
else:
|
||
|
|
img_cmap = cm.get_cmap(img_cmap)
|
||
|
|
out = color.rgb2gray(image)
|
||
|
|
# Ignore the alpha channel
|
||
|
|
out = img_cmap(out)[:, :, :3]
|
||
|
|
|
||
|
|
edge_cmap = cm.get_cmap(edge_cmap)
|
||
|
|
|
||
|
|
# Handling the case where one node has multiple labels
|
||
|
|
# offset is 1 so that regionprops does not ignore 0
|
||
|
|
offset = 1
|
||
|
|
map_array = np.arange(labels.max() + 1)
|
||
|
|
for n, d in rag.nodes(data=True):
|
||
|
|
for label in d['labels']:
|
||
|
|
map_array[label] = offset
|
||
|
|
offset += 1
|
||
|
|
|
||
|
|
rag_labels = map_array[labels]
|
||
|
|
regions = measure.regionprops(rag_labels)
|
||
|
|
|
||
|
|
for (n, data), region in zip(rag.nodes(data=True), regions):
|
||
|
|
data['centroid'] = tuple(map(int, region['centroid']))
|
||
|
|
|
||
|
|
cc = colors.ColorConverter()
|
||
|
|
if border_color is not None:
|
||
|
|
border_color = cc.to_rgb(border_color)
|
||
|
|
out = segmentation.mark_boundaries(out, rag_labels, color=border_color)
|
||
|
|
|
||
|
|
ax.imshow(out)
|
||
|
|
|
||
|
|
# Defining the end points of the edges
|
||
|
|
# The tuple[::-1] syntax reverses a tuple as matplotlib uses (x,y)
|
||
|
|
# convention while skimage uses (row, column)
|
||
|
|
lines = [[rag.nodes[n1]['centroid'][::-1], rag.nodes[n2]['centroid'][::-1]]
|
||
|
|
for (n1, n2) in rag.edges()]
|
||
|
|
|
||
|
|
lc = LineCollection(lines, linewidths=edge_width, cmap=edge_cmap)
|
||
|
|
edge_weights = [d['weight'] for x, y, d in rag.edges(data=True)]
|
||
|
|
lc.set_array(np.array(edge_weights))
|
||
|
|
ax.add_collection(lc)
|
||
|
|
|
||
|
|
return lc
|