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# Module: future.graph¶

 skimage.future.graph.rag_mean_color(image, …) Compute the Region Adjacency Graph using mean colors. skimage.future.graph.cut_threshold(labels, …) Combine regions separated by weight less than threshold. skimage.future.graph.cut_normalized(labels, rag) Perform Normalized Graph cut on the Region Adjacency Graph. skimage.future.graph.ncut(labels, rag[, …]) Perform Normalized Graph cut on the Region Adjacency Graph. skimage.future.graph.show_rag(labels, rag, image) Show a Region Adjacency Graph on an image. skimage.future.graph.merge_hierarchical(…) Perform hierarchical merging of a RAG. skimage.future.graph.rag_boundary(labels, …) Comouter RAG based on region boundaries skimage.future.graph.RAG([label_image, …]) The Region Adjacency Graph (RAG) of an image, subclasses networx.Graph

## 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: image : ndarray, shape(M, N, […, P,] 3) Input image. labels : ndarray, 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). 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.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. sigma : float, 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. out : RAG The region adjacency graph.

References

  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)


### Examples using skimage.future.graph.rag_mean_color¶ Normalized Cut RAG Thresholding  RAG Merging

## 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: labels : ndarray The array of labels. rag : RAG The region adjacency graph. thresh : float The threshold. Regions connected by edges with smaller weights are combined. in_place : bool 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. out : ndarray The new labelled array.

References

  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¶ RAG Thresholding

## cut_normalized¶

skimage.future.graph.cut_normalized(labels, rag, thresh=0.001, num_cuts=10, in_place=True, max_edge=1.0)[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: labels : ndarray The array of labels. rag : RAG The region adjacency graph. thresh : float The threshold. A subgraph won’t be further subdivided if the value of the N-cut exceeds thresh. num_cuts : int The number or N-cuts to perform before determining the optimal one. in_place : bool If set, modifies rag in place. For each node n the function will set a new attribute rag.node[n]['ncut label']. max_edge : float, 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. out : ndarray The new labeled array.

References

  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)


### Examples using skimage.future.graph.cut_normalized¶ Normalized Cut

## ncut¶

skimage.future.graph.ncut(labels, rag, thresh=0.001, num_cuts=10, in_place=True, max_edge=1.0)[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: labels : ndarray The array of labels. rag : RAG The region adjacency graph. thresh : float The threshold. A subgraph won’t be further subdivided if the value of the N-cut exceeds thresh. num_cuts : int The number or N-cuts to perform before determining the optimal one. in_place : bool If set, modifies rag in place. For each node n the function will set a new attribute rag.node[n]['ncut label']. max_edge : float, 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. out : ndarray The new labeled array.

References

  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)


## 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: 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 : 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_place : bool, optional If set, the RAG is modified in place. For each node n the function will set a new attribute rag.node[n]['centroid']. ax : matplotlib.axes.Axes, optional The axes to draw on. If not specified, new axes are created and drawn on. 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.

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)


### Examples using skimage.future.graph.show_rag¶ Region Boundary based RAGs  Hierarchical Merging of Region Boundary RAGs

## 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: labels : ndarray The array of labels. rag : RAG The Region Adjacency Graph. thresh : float Regions connected by an edge with weight smaller than thresh are merged. rag_copy : bool If set, the RAG copied before modifying. in_place_merge : bool If set, the nodes are merged in place. Otherwise, a new node is created for each merge.. merge_func : callable 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_func : callable 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. out : ndarray The new labeled array.

### Examples using skimage.future.graph.merge_hierarchical¶ RAG Merging Hierarchical Merging of Region Boundary RAGs

## 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.

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)


### Examples using skimage.future.graph.rag_boundary¶ Region Boundary based RAGs Hierarchical Merging of Region Boundary RAGs

## 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_image : array 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. connectivity : int 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. data : networkx 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. **attr : keyword 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_data : input 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. attr : keyword arguments, optional (default= no attributes) Attributes to add to graph as key=value pairs.

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(u, v, attr_dict=None, **attr)[source]

Add an edge between u and v while updating max node id.

networkx.Graph.add_edge().

add_node(n, attr_dict=None, **attr)[source]

Add node n while updating the maximum node id.

networkx.Graph.add_node().

copy()[source]

Copy the graph with its max node id.

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, dst : int Nodes to be merged. weight_func : callable, 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_place : bool, optional If set to True, the merged node has the id dst, else merged node has a new id which is returned. extra_arguments : sequence, optional The sequence of extra positional arguments passed to weight_func. extra_keywords : dictionary, optional The dict of keyword arguments passed to the weight_func. id : int 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: id : int The id of the new node to be inserted.