Utility functions for graph and images¶

`graph_4_adjacency_2_khalimsky`(graph, …[, …])	Create a contour image in the Khalimsky grid from a 4 adjacency edge-weighted graph.
`khalimsky_2_graph_4_adjacency`(khalimsky[, …])	Create a 4 adjacency edge-weighted graph from a contour image in the Khalimsky grid.
`get_4_adjacency_graph`(shape)	Create an explicit undirected 4 adjacency graph of the given shape.
`get_8_adjacency_graph`(shape)	Create an explicit undirected 8 adjacency graph of the given shape.
`get_4_adjacency_implicit_graph`(shape)	Create an implicit undirected 4 adjacency graph of the given shape (edges are not stored).
`get_8_adjacency_implicit_graph`(shape)	Create an implicit undirected 8 adjacency graph of the given shape (edges are not stored).
`get_nd_regular_graph`(shape, neighbour_list)	Creates a regular graph of the given `shape` with the adjacency given as a `neighbour_list`.
`get_nd_regular_implicit_graph`(shape, …)	Creates an implicit regular graph of the given `shape` with the adjacency given as a `neighbour_list`.
`mask_2_neighbours`(mask[, center])	Converts as a neighbouring mask as a neighbour list.

graph_4_adjacency_2_khalimsky(graph, edge_weights, shape, add_extra_border=False)[source]¶

Create a contour image in the Khalimsky grid from a 4 adjacency edge-weighted graph.

Parameters:

graph – must be a 4 adjacency 2d graph (Concept CptGridGraph)
edge_weights – edge weights of the graph
shape – shape of the graph (deduced from CptGridGraph)
add_extra_border – if False result size is 2 * shape - 1 and 2 * shape + 1 otherwise

Returns:

a 2d array

khalimsky_2_graph_4_adjacency(khalimsky, extra_border=False)[source]¶

Create a 4 adjacency edge-weighted graph from a contour image in the Khalimsky grid.

Parameters:

khalimsky – a 2d array
extra_border – if False the shape of the Khalimsky image is 2 * shape - 1 and 2 * shape + 1 otherwise, where shape is the shape of the resulting grid graph

Returns:

a graph (Concept CptGridGraph) and its edge weights

get_4_adjacency_graph(shape)[source]¶

Create an explicit undirected 4 adjacency graph of the given shape.

Parameters:: shape – a pair (height, width)
Returns:: a graph (Concept CptGridGraph)

get_8_adjacency_graph(shape)[source]¶

Create an explicit undirected 8 adjacency graph of the given shape.

Parameters:: shape – a pair (height, width)
Returns:: a graph (Concept CptGridGraph)

get_4_adjacency_implicit_graph(shape)[source]¶

Create an implicit undirected 4 adjacency graph of the given shape (edges are not stored).

Parameters:: shape – a pair (height, width)
Returns:: a graph (Concept CptGridGraph)

get_8_adjacency_implicit_graph(shape)[source]¶

Create an implicit undirected 8 adjacency graph of the given shape (edges are not stored).

Parameters:: shape – a pair (height, width)
Returns:: a graph (Concept CptGridGraph)

get_nd_regular_graph(shape, neighbour_list)[source]¶

Creates a regular graph of the given shape with the adjacency given as a neighbour_list.

See the helper function mask_2_neighbours() to create a suitable neighbour_list.

Example:

Create a 2d 4-adjacency implicit graph of size (13, 24):

>>> graph = get_nd_regular_graph((13, 24), ((-1, 0), (0, -1), (0, 1), (1, 0)))

Create a 3d 6-adjacency implicit graph of size (10, 13, 24):

>>> mask = [[[0, 0, 0], [0, 1, 0], [0, 0, 0]],
>>>         [[0, 1, 0], [1, 0, 1], [0, 1, 0]],
>>>         [[0, 0, 0], [0, 1, 0], [0, 0, 0]]]
>>> neighbours = mask_2_neighbours(mask)
>>> graph = get_nd_regular_graph((10, 13, 24), neighbours)

Parameters:

shape – a tuple of \(n\) elements representing the dimension of the graph vertices.
neighbour_list – a 2d array of \(k\) \(n\)-d integer vectors

Returns:

a regular graph

get_nd_regular_implicit_graph(shape, neighbour_list)[source]¶

Creates an implicit regular graph of the given shape with the adjacency given as a neighbour_list.

See the helper function mask_2_neighbours() to create a suitable neighbour_list.

Example:

Create a 2d 4-adjacency implicit graph of size (13, 24):

>>> graph = get_nd_regular_implicit_graph((13, 24), ((-1, 0), (0, -1), (0, 1), (1, 0)))

Create a 3d 6-adjacency implicit graph of size (10, 13, 24):

>>> mask = [[[0, 0, 0], [0, 1, 0], [0, 0, 0]],
>>>         [[0, 1, 0], [1, 0, 1], [0, 1, 0]],
>>>         [[0, 0, 0], [0, 1, 0], [0, 0, 0]]]
>>> neighbours = mask_2_neighbours(mask)
>>> graph = get_nd_regular_implicit_graph((10, 13, 24), neighbours)

Parameters:

shape – a tuple of \(n\) elements representing the dimension of the graph vertices.
neighbour_list – a 2d array of \(k\) \(n\)-d integer vectors

Returns:

an implicit regular graph

mask_2_neighbours(mask, center=None)[source]¶

Converts as a neighbouring mask as a neighbour list. A neighbouring mask is a \(n\)-d matrix where each strictly positive value represent a neighbour of the center point. The neighbour list is obtained by offsetting the coordinates of those positive values by the coordinates of the center.

The default center is the center of the mask matrix: i.e. mask.shape // 2.

Example:

>>> mask = [[0, 1, 0], [1, 0, 1], [0, 1, 0]]
>>> hg.mask_2_neighbours(mask)
array([[-1, 0], [0, -1], [0, 1], [1, 0]])

>>> mask = [[0, 1, 0], [1, 0, 1], [0, 1, 0]]
>>> center = [2, 1]
>>> hg.mask_2_neighbours(mask)
array([[-2, 0], [-1, -1], [-1, 1], [0, 0]])

>>> mask = [[[0, 0, 0], [0, 1, 0], [0, 0, 0]],
>>>         [[0, 1, 0], [1, 0, 1], [0, 1, 0]],
>>>         [[0, 0, 0], [0, 1, 0], [0, 0, 0]]]
>>> hg.mask_2_neighbours(mask)
array([[-1, 0, 0], [1, 0, 0], [0, -1, 0], [0, 1, 0], [0, 0, -1], [0, 0, 1]])

Parameters:

mask – a \(n\)-d matrix
center – a 1d array of size \(n\) (optional)

Returns:

a list of point coordinates