graph
¶skimage.graph.shortest_path (arr[, reach, …]) 
Find the shortest path through an nd array from one side to another. 
skimage.graph.route_through_array (array, …) 
Simple example of how to use the MCP and MCP_Geometric classes. 
skimage.graph.MCP (costs[, offsets, …]) 
A class for finding the minimum cost path through a given nd costs array. 
skimage.graph.MCP_Geometric (costs[, …]) 
Find distanceweighted minimum cost paths through an nd costs array. 
skimage.graph.MCP_Connect (costs[, offsets, …]) 
Connect source points using the distanceweighted minimum cost function. 
skimage.graph.MCP_Flexible (costs[, offsets, …]) 
Find minimum cost paths through an Nd costs array. 
skimage.graph.
shortest_path
(arr, reach=1, axis=1, output_indexlist=False)[source]¶Find the shortest path through an nd array from one side to another.
Parameters:  arr : ndarray of float64 reach : int, optional
axis : int, optional
output_indexlist: bool, optional


Returns:  p : iterable of int
cost : float

skimage.graph.
route_through_array
(array, start, end, fully_connected=True, geometric=True)[source]¶Simple example of how to use the MCP and MCP_Geometric classes.
See the MCP and MCP_Geometric class documentation for explanation of the pathfinding algorithm.
Parameters:  array : ndarray
start : iterable
end : iterable
fully_connected : bool (optional)
geometric : bool (optional)


Returns:  path : list
cost : float

See also
Examples
>>> import numpy as np
>>> from skimage.graph import route_through_array
>>>
>>> image = np.array([[1, 3], [10, 12]])
>>> image
array([[ 1, 3],
[10, 12]])
>>> # Forbid diagonal steps
>>> route_through_array(image, [0, 0], [1, 1], fully_connected=False)
([(0, 0), (0, 1), (1, 1)], 9.5)
>>> # Now allow diagonal steps: the path goes directly from start to end
>>> route_through_array(image, [0, 0], [1, 1])
([(0, 0), (1, 1)], 9.1923881554251192)
>>> # Cost is the sum of array values along the path (16 = 1 + 3 + 12)
>>> route_through_array(image, [0, 0], [1, 1], fully_connected=False,
... geometric=False)
([(0, 0), (0, 1), (1, 1)], 16.0)
>>> # Larger array where we display the path that is selected
>>> image = np.arange((36)).reshape((6, 6))
>>> image
array([[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 21, 22, 23],
[24, 25, 26, 27, 28, 29],
[30, 31, 32, 33, 34, 35]])
>>> # Find the path with lowest cost
>>> indices, weight = route_through_array(image, (0, 0), (5, 5))
>>> indices = np.array(indices).T
>>> path = np.zeros_like(image)
>>> path[indices[0], indices[1]] = 1
>>> path
array([[1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1]])
MCP
¶skimage.graph.
MCP
(costs, offsets=None, fully_connected=True, sampling=None)¶Bases: object
A class for finding the minimum cost path through a given nd costs array.
Given an nd costs array, this class can be used to find the minimumcost path through that array from any set of points to any other set of points. Basic usage is to initialize the class and call find_costs() with a one or more starting indices (and an optional list of end indices). After that, call traceback() one or more times to find the path from any given endposition to the closest starting index. New paths through the same costs array can be found by calling find_costs() repeatedly.
The cost of a path is calculated simply as the sum of the values of the costs array at each point on the path. The class MCP_Geometric, on the other hand, accounts for the fact that diagonal vs. axial moves are of different lengths, and weights the path cost accordingly.
Array elements with infinite or negative costs will simply be ignored, as will paths whose cumulative cost overflows to infinite.
Parameters:  costs : ndarray offsets : iterable, optional
fully_connected : bool, optional
sampling : tuple, optional


Attributes
offsets  (ndarray) Equivalent to the offsets provided to the constructor, or if none were so provided, the offsets created for the requested nd neighborhood. These are useful for interpreting the traceback array returned by the find_costs() method. 
__init__
(costs, offsets=None, fully_connected=True, sampling=None)¶See class documentation.
find_costs
()¶Find the minimumcost path from the given starting points.
This method finds the minimumcost path to the specified ending indices from any one of the specified starting indices. If no end positions are given, then the minimumcost path to every position in the costs array will be found.
Parameters:  starts : iterable
ends : iterable, optional
find_all_ends : bool, optional


Returns:  cumulative_costs : ndarray
traceback : ndarray

goal_reached
()¶int goal_reached(int index, float cumcost) This method is called each iteration after popping an index from the heap, before examining the neighbours.
This method can be overloaded to modify the behavior of the MCP algorithm. An example might be to stop the algorithm when a certain cumulative cost is reached, or when the front is a certain distance away from the seed point.
This method should return 1 if the algorithm should not check the current point’s neighbours and 2 if the algorithm is now done.
traceback
(end)¶Trace a minimum cost path through the precalculated traceback array.
This convenience function reconstructs the the minimum cost path to a given end position from one of the starting indices provided to find_costs(), which must have been called previously. This function can be called as many times as desired after find_costs() has been run.
Parameters:  end : iterable


Returns:  traceback : list of nd tuples

MCP_Geometric
¶skimage.graph.
MCP_Geometric
(costs, offsets=None, fully_connected=True)¶Bases: skimage.graph._mcp.MCP
Find distanceweighted minimum cost paths through an nd costs array.
See the documentation for MCP for full details. This class differs from MCP in that the cost of a path is not simply the sum of the costs along that path.
This class instead assumes that the costs array contains at each position the “cost” of a unit distance of travel through that position. For example, a move (in 2d) from (1, 1) to (1, 2) is assumed to originate in the center of the pixel (1, 1) and terminate in the center of (1, 2). The entire move is of distance 1, half through (1, 1) and half through (1, 2); thus the cost of that move is (1/2)*costs[1,1] + (1/2)*costs[1,2].
On the other hand, a move from (1, 1) to (2, 2) is along the diagonal and is sqrt(2) in length. Half of this move is within the pixel (1, 1) and the other half in (2, 2), so the cost of this move is calculated as (sqrt(2)/2)*costs[1,1] + (sqrt(2)/2)*costs[2,2].
These calculations don’t make a lot of sense with offsets of magnitude greater than 1. Use the sampling argument in order to deal with anisotropic data.
__init__
(costs, offsets=None, fully_connected=True, sampling=None)¶See class documentation.
MCP_Connect
¶skimage.graph.
MCP_Connect
(costs, offsets=None, fully_connected=True)¶Bases: skimage.graph._mcp.MCP
Connect source points using the distanceweighted minimum cost function.
A front is grown from each seed point simultaneously, while the origin of the front is tracked as well. When two fronts meet, create_connection() is called. This method must be overloaded to deal with the found edges in a way that is appropriate for the application.
__init__
($self, /, *args, **kwargs)¶Initialize self. See help(type(self)) for accurate signature.
create_connection
()¶create_connection id1, id2, pos1, pos2, cost1, cost2)
Overload this method to keep track of the connections that are found during MCP processing. Note that a connection with the same ids can be found multiple times (but with different positions and costs).
At the time that this method is called, both points are “frozen” and will not be visited again by the MCP algorithm.
Parameters:  id1 : int
id2 : int
pos1 : tuple
pos2 : tuple
cost1 : float
cost2 : float


MCP_Flexible
¶skimage.graph.
MCP_Flexible
(costs, offsets=None, fully_connected=True)¶Bases: skimage.graph._mcp.MCP
Find minimum cost paths through an Nd costs array.
See the documentation for MCP for full details. This class differs from MCP in that several methods can be overloaded (from pure Python) to modify the behavior of the algorithm and/or create custom algorithms based on MCP. Note that goal_reached can also be overloaded in the MCP class.
__init__
(costs, offsets=None, fully_connected=True, sampling=None)¶See class documentation.
examine_neighbor
(index, new_index, offset_length)¶This method is called once for every pair of neighboring nodes, as soon as both nodes are frozen.
This method can be overloaded to obtain information about neightboring nodes, and/or to modify the behavior of the MCP algorithm. One example is the MCP_Connect class, which checks for meeting fronts using this hook.
travel_cost
(old_cost, new_cost, offset_length)¶This method calculates the travel cost for going from the current node to the next. The default implementation returns new_cost. Overload this method to adapt the behaviour of the algorithm.
update_node
(index, new_index, offset_length)¶This method is called when a node is updated, right after new_index is pushed onto the heap and the traceback map is updated.
This method can be overloaded to keep track of other arrays that are used by a specific implementation of the algorithm. For instance the MCP_Connect class uses it to update an id map.