Module: future.graph

`skimage.future.graph.cut_normalized`(labels, rag)	Perform Normalized Graph cut on the Region Adjacency Graph.
`skimage.future.graph.cut_threshold`(labels, …)	Combine regions separated by weight less than threshold.
`skimage.future.graph.merge_hierarchical`(…)	Perform hierarchical merging of a RAG.
`skimage.future.graph.ncut`(labels, rag[, …])	Perform Normalized Graph cut on the Region Adjacency Graph.
`skimage.future.graph.rag_boundary`(labels, …)	Comouter RAG based on region boundaries
`skimage.future.graph.rag_mean_color`(image, …)	Compute the Region Adjacency Graph using mean colors.
`skimage.future.graph.show_rag`(labels, rag, image)	Show a Region Adjacency Graph on an image.
`skimage.future.graph.RAG`([label_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 2-way 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 N-cut exceeds thresh.
num_cutsint: The number or N-cuts 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 attribute rag.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. 888-905, 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)

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 of rag 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)

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.

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 N-cut exceeds thresh.
num_cutsint: The number or N-cuts 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 attribute rag.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. 888-905, 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_cmapmatplotlib.colors.Colormap, optional: Any matplotlib colormap with which the edges are drawn.
img_cmapmatplotlib.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'].
axmatplotlib.axes.Axes, optional: The axes to draw on. If not specified, new axes are created and drawn on.

Returns

lcmatplotlib.collections.LineCollection: A colection of lines that represent the edges of the graph. It can be passed to the 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)

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. See scipy.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__(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.

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(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(n, attr_dict=None, **attr) [source]: Add node n while updating the maximum node id.

See also

networkx.Graph.add_node().

copy() [source]: Copy the graph with its max node id.

See also

networkx.Graph.copy().

fresh_copy() [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 type---ready to fill with nodes and edges.

merge_nodes(src, dst, weight_func=<function min_weight>, 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.

next_id() [source]

Returns the id for the new node to be inserted.

The current implementation returns one more than the maximum id.

Returns

idint: The id of the new node to be inserted.

© 2019 the scikit-image team
Licensed under the BSD 3-clause License.
https://scikit-image.org/docs/0.18.x/api/skimage.future.graph.html