Module: future.graph
¶

Perform Normalized Graph cut on the Region Adjacency Graph. 

Combine regions separated by weight less than threshold. 
Perform hierarchical merging of a RAG. 


Perform Normalized Graph cut on the Region Adjacency Graph. 

Comouter RAG based on region boundaries 

Compute the Region Adjacency Graph using mean colors. 

Show a Region Adjacency Graph on an image. 

The Region Adjacency Graph (RAG) of an image, subclasses networx.Graph 
cut_normalized¶

skimage.future.graph.
cut_normalized
(labels, rag, thresh=0.001, num_cuts=10, in_place=True, max_edge=1.0, *, random_state=None)[source]¶ Perform Normalized Graph cut on the Region Adjacency Graph.
Given an image’s labels and its similarity RAG, recursively perform a 2way normalized cut on it. All nodes belonging to a subgraph that cannot be cut further are assigned a unique label in the output.
 Parameters
 labelsndarray
The array of labels.
 ragRAG
The region adjacency graph.
 threshfloat
The threshold. A subgraph won’t be further subdivided if the value of the Ncut exceeds thresh.
 num_cutsint
The number or Ncuts to perform before determining the optimal one.
 in_placebool
If set, modifies
rag
in place. For each node n the function will set a new attributerag.nodes[n]['ncut label']
. max_edgefloat, optional
The maximum possible value of an edge in the RAG. This corresponds to an edge between identical regions. This is used to put self edges in the RAG.
 random_stateint, RandomState instance or None, optional
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. The random state is used for the starting point of
scipy.sparse.linalg.eigsh
.
 Returns
 outndarray
The new labeled array.
References
 1
Shi, J.; Malik, J., “Normalized cuts and image segmentation”, Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 22, no. 8, pp. 888905, August 2000.
Examples
>>> from skimage import data, segmentation >>> from skimage.future import graph >>> img = data.astronaut() >>> labels = segmentation.slic(img) >>> rag = graph.rag_mean_color(img, labels, mode='similarity') >>> new_labels = graph.cut_normalized(labels, rag)
Examples using skimage.future.graph.cut_normalized
¶
cut_threshold¶

skimage.future.graph.
cut_threshold
(labels, rag, thresh, in_place=True)[source]¶ Combine regions separated by weight less than threshold.
Given an image’s labels and its RAG, output new labels by combining regions whose nodes are separated by a weight less than the given threshold.
 Parameters
 labelsndarray
The array of labels.
 ragRAG
The region adjacency graph.
 threshfloat
The threshold. Regions connected by edges with smaller weights are combined.
 in_placebool
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 ofrag
before proceeding.
 Returns
 outndarray
The new labelled array.
References
 1
Alain Tremeau and Philippe Colantoni “Regions Adjacency Graph Applied To Color Image Segmentation” DOI:10.1109/83.841950
Examples
>>> from skimage import data, segmentation >>> from skimage.future import graph >>> img = data.astronaut() >>> labels = segmentation.slic(img) >>> rag = graph.rag_mean_color(img, labels) >>> new_labels = graph.cut_threshold(labels, rag, 10)
Examples using skimage.future.graph.cut_threshold
¶
merge_hierarchical¶

skimage.future.graph.
merge_hierarchical
(labels, rag, thresh, rag_copy, in_place_merge, merge_func, weight_func)[source]¶ Perform hierarchical merging of a RAG.
Greedily merges the most similar pair of nodes until no edges lower than thresh remain.
 Parameters
 labelsndarray
The array of labels.
 ragRAG
The Region Adjacency Graph.
 threshfloat
Regions connected by an edge with weight smaller than thresh are merged.
 rag_copybool
If set, the RAG copied before modifying.
 in_place_mergebool
If set, the nodes are merged in place. Otherwise, a new node is created for each merge..
 merge_funccallable
This function is called before merging two nodes. For the RAG graph while merging src and dst, it is called as follows
merge_func(graph, src, dst)
. weight_funccallable
The function to compute the new weights of the nodes adjacent to the merged node. This is directly supplied as the argument weight_func to merge_nodes.
 Returns
 outndarray
The new labeled array.
ncut¶

skimage.future.graph.
ncut
(labels, rag, thresh=0.001, num_cuts=10, in_place=True, max_edge=1.0, *, random_state=None)[source]¶ Perform Normalized Graph cut on the Region Adjacency Graph.
Given an image’s labels and its similarity RAG, recursively perform a 2way normalized cut on it. All nodes belonging to a subgraph that cannot be cut further are assigned a unique label in the output.
 Parameters
 labelsndarray
The array of labels.
 ragRAG
The region adjacency graph.
 threshfloat
The threshold. A subgraph won’t be further subdivided if the value of the Ncut exceeds thresh.
 num_cutsint
The number or Ncuts to perform before determining the optimal one.
 in_placebool
If set, modifies
rag
in place. For each node n the function will set a new attributerag.nodes[n]['ncut label']
. max_edgefloat, optional
The maximum possible value of an edge in the RAG. This corresponds to an edge between identical regions. This is used to put self edges in the RAG.
 random_stateint, RandomState instance or None, optional
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. The random state is used for the starting point of
scipy.sparse.linalg.eigsh
.
 Returns
 outndarray
The new labeled array.
References
 1
Shi, J.; Malik, J., “Normalized cuts and image segmentation”, Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 22, no. 8, pp. 888905, August 2000.
Examples
>>> from skimage import data, segmentation >>> from skimage.future import graph >>> img = data.astronaut() >>> labels = segmentation.slic(img) >>> rag = graph.rag_mean_color(img, labels, mode='similarity') >>> new_labels = graph.cut_normalized(labels, rag)
rag_boundary¶

skimage.future.graph.
rag_boundary
(labels, edge_map, connectivity=2)[source]¶ 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.
 labelsndarray
The labelled image.
 edge_mapndarray
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.
 connectivityint, 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)
rag_mean_color¶

skimage.future.graph.
rag_mean_color
(image, labels, connectivity=2, mode='distance', sigma=255.0)[source]¶ Compute the Region Adjacency Graph using mean colors.
Given an image and its initial segmentation, this method constructs the corresponding Region Adjacency Graph (RAG). Each node in the RAG represents a set of pixels within image with the same label in labels. The weight between two adjacent regions represents how similar or dissimilar two regions are depending on the mode parameter.
 Parameters
 imagendarray, shape(M, N, […, P,] 3)
Input image.
 labelsndarray, shape(M, N, […, P])
The labelled image. This should have one dimension less than image. If image has dimensions (M, N, 3) labels should have dimensions (M, N).
 connectivityint, 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.generate_binary_structure
. mode{‘distance’, ‘similarity’}, optional
The strategy to assign edge weights.
‘distance’ : The weight between two adjacent regions is the \(c_1  c_2\), where \(c_1\) and \(c_2\) are the mean colors of the two regions. It represents the Euclidean distance in their average color.
‘similarity’ : The weight between two adjacent is \(e^{d^2/sigma}\) where \(d=c_1  c_2\), where \(c_1\) and \(c_2\) are the mean colors of the two regions. It represents how similar two regions are.
 sigmafloat, optional
Used for computation when mode is “similarity”. It governs how close to each other two colors should be, for their corresponding edge weight to be significant. A very large value of sigma could make any two colors behave as though they were similar.
 Returns
 outRAG
The region adjacency graph.
References
 1
Alain Tremeau and Philippe Colantoni “Regions Adjacency Graph Applied To Color Image Segmentation” DOI:10.1109/83.841950
Examples
>>> from skimage import data, segmentation >>> from skimage.future import graph >>> img = data.astronaut() >>> labels = segmentation.slic(img) >>> rag = graph.rag_mean_color(img, labels)
show_rag¶

skimage.future.graph.
show_rag
(labels, rag, image, border_color='black', edge_width=1.5, edge_cmap='magma', img_cmap='bone', in_place=True, ax=None)[source]¶ 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
 labelsndarray, shape (M, N)
The labelled image.
 ragRAG
The Region Adjacency Graph.
 imagendarray, shape (M, N[, 3])
Input image. If colormap is None, the image should be in RGB format.
 border_colorcolor spec, optional
Color with which the borders between regions are drawn.
 edge_widthfloat, optional
The thickness with which the RAG edges are drawn.
 edge_cmap
matplotlib.colors.Colormap
, optional Any matplotlib colormap with which the edges are drawn.
 img_cmap
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_placebool, 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
matplotlib.axes.Axes
, optional The axes to draw on. If not specified, new axes are created and drawn on.
 Returns
 lc
matplotlib.collections.LineCollection
A colection of lines that represent the edges of the graph. It can be passed to the
matplotlib.figure.Figure.colorbar()
function.
 lc
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)
RAG
¶

class
skimage.future.graph.
RAG
(label_image=None, connectivity=1, data=None, **attr)[source]¶ Bases:
networkx.classes.graph.Graph
The Region Adjacency Graph (RAG) of an image, subclasses networx.Graph
 Parameters
 label_imagearray of int
An initial segmentation, with each region labeled as a different integer. Every unique value in
label_image
will correspond to a node in the graph. connectivityint in {1, …,
label_image.ndim
}, optional The connectivity between pixels in
label_image
. For a 2D image, a connectivity of 1 corresponds to immediate neighbors up, down, left, and right, while a connectivity of 2 also includes diagonal neighbors. Seescipy.ndimage.generate_binary_structure
. datanetworkx Graph specification, optional
Initial or additional edges to pass to the NetworkX Graph constructor. See
networkx.Graph
. Valid edge specifications include edge list (list of tuples), NumPy arrays, and SciPy sparse matrices. **attrkeyword arguments, optional
Additional attributes to add to the graph.

__init__
(self, label_image=None, connectivity=1, data=None, **attr)[source]¶ Initialize a graph with edges, name, or graph attributes.
 Parameters
 incoming_graph_datainput graph (optional, default: None)
Data to initialize graph. If None (default) an empty graph is created. The data can be an edge list, or any NetworkX graph object. If the corresponding optional Python packages are installed the data can also be a NumPy matrix or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz graph.
 attrkeyword arguments, optional (default= no attributes)
Attributes to add to graph as key=value pairs.
See also
convert
Examples
>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G = nx.Graph(name='my graph') >>> e = [(1, 2), (2, 3), (3, 4)] # list of edges >>> G = nx.Graph(e)
Arbitrary graph attribute pairs (key=value) may be assigned
>>> G = nx.Graph(e, day="Friday") >>> G.graph {'day': 'Friday'}

add_edge
(self, u, v, attr_dict=None, **attr)[source]¶ Add an edge between u and v while updating max node id.
See also
networkx.Graph.add_edge()
.

add_node
(self, n, attr_dict=None, **attr)[source]¶ Add node n while updating the maximum node id.
See also
networkx.Graph.add_node()
.

fresh_copy
(self)[source]¶ Return a fresh copy graph with the same data structure.
A fresh copy has no nodes, edges or graph attributes. It is the same data structure as the current graph. This method is typically used to create an empty version of the graph.
This is required when subclassing Graph with networkx v2 and does not cause problems for v1. Here is more detail from the network migrating from 1.x to 2.x document:
With the new GraphViews (SubGraph, ReversedGraph, etc) you can't assume that ``G.__class__()`` will create a new instance of the same graph type as ``G``. In fact, the call signature for ``__class__`` differs depending on whether ``G`` is a view or a base class. For v2.x you should use ``G.fresh_copy()`` to create a null graph of the correct typeready to fill with nodes and edges.

merge_nodes
(self, src, dst, weight_func=<function min_weight at 0x7f8fc5a869d8>, in_place=True, extra_arguments=[], extra_keywords={})[source]¶ Merge node src and dst.
The new combined node is adjacent to all the neighbors of src and dst. weight_func is called to decide the weight of edges incident on the new node.
 Parameters
 src, dstint
Nodes to be merged.
 weight_funccallable, optional
Function to decide the attributes of edges incident on the new node. For each neighbor n for src and `dst, weight_func will be called as follows: weight_func(src, dst, n, *extra_arguments, **extra_keywords). src, dst and n are IDs of vertices in the RAG object which is in turn a subclass of
networkx.Graph
. It is expected to return a dict of attributes of the resulting edge. in_placebool, optional
If set to True, the merged node has the id dst, else merged node has a new id which is returned.
 extra_argumentssequence, optional
The sequence of extra positional arguments passed to weight_func.
 extra_keywordsdictionary, optional
The dict of keyword arguments passed to the weight_func.
 Returns
 idint
The id of the new node.
Notes
If in_place is False the resulting node has a new id, rather than dst.