PointDirectedGraph¶

class
menpo.shape.
PointDirectedGraph
(points, adjacency_matrix, copy=True, skip_checks=False)[source]¶ Bases:
PointGraph
,DirectedGraph
Class for defining a directed graph with geometry.
 Parameters
points (
(n_vertices, n_dims)
ndarray) – The array representing the points.adjacency_matrix (
(n_vertices, n_vertices, )
ndarray or csr_matrix) – The adjacency matrix of the graph in which the rows represent source vertices and columns represent destination vertices. The nonedges must be represented with zeros and the edges can have a weight value.copy (bool, optional) – If
False
, theadjacency_matrix
will not be copied on assignment.skip_checks (bool, optional) – If
True
, no checks will be performed.
 Raises
ValueError – A point for each graph vertex needs to be passed. Got {n_points} points instead of {n_vertices}.
ValueError – adjacency_matrix must be either a numpy.ndarray or a scipy.sparse.csr_matrix.
ValueError – Graph must have at least two vertices.
ValueError – adjacency_matrix must be square (n_vertices, n_vertices, ), ({adjacency_matrix.shape[0]}, {adjacency_matrix.shape[1]}) given instead.
Examples
The following directed graph
>0<     1<>2   v v 3>4  v 5
can be defined as
import numpy as np adjacency_matrix = np.array([[0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0], [1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) points = np.array([[10, 30], [0, 20], [20, 20], [0, 10], [20, 10], [0, 0]]) graph = PointDirectedGraph(points, adjacency_matrix)
or
from scipy.sparse import csr_matrix adjacency_matrix = csr_matrix(([1] * 8, ([1, 2, 1, 2, 1, 2, 3, 3], [0, 0, 2, 1, 3, 4, 4, 5])), shape=(6, 6)) points = np.array([[10, 30], [0, 20], [20, 20], [0, 10], [20, 10], [0, 0]]) graph = PointDirectedGraph(points, adjacency_matrix)
The following graph with isolated vertices
0<   1 2  v 3>4 5
can be defined as
import numpy as np adjacency_matrix = np.array([[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) points = np.array([[10, 30], [0, 20], [20, 20], [0, 10], [20, 10], [0, 0]]) graph = PointDirectedGraph(points, adjacency_matrix)
or
from scipy.sparse import csr_matrix adjacency_matrix = csr_matrix(([1] * 3, ([2, 2, 3], [0, 4, 4])), shape=(6, 6)) points = np.array([[10, 30], [0, 20], [20, 20], [0, 10], [20, 10], [0, 0]]) graph = PointDirectedGraph(points, adjacency_matrix)

_view_2d
(figure_id=None, new_figure=False, image_view=True, render_lines=True, line_colour='r', line_style='', line_width=1.0, render_markers=True, marker_style='o', marker_size=5, marker_face_colour='k', marker_edge_colour='k', marker_edge_width=1.0, render_numbering=False, numbers_horizontal_align='center', numbers_vertical_align='bottom', numbers_font_name='sansserif', numbers_font_size=10, numbers_font_style='normal', numbers_font_weight='normal', numbers_font_colour='k', render_axes=True, axes_font_name='sansserif', axes_font_size=10, axes_font_style='normal', axes_font_weight='normal', axes_x_limits=None, axes_y_limits=None, axes_x_ticks=None, axes_y_ticks=None, figure_size=(7, 7), label=None, **kwargs)¶ Visualization of the PointGraph in 2D.
 Returns
figure_id (object, optional) – The id of the figure to be used.
new_figure (bool, optional) – If
True
, a new figure is created.image_view (bool, optional) – If
True
the PointGraph will be viewed as if it is in the image coordinate system.render_lines (bool, optional) – If
True
, the edges will be rendered.line_colour (See Below, optional) – The colour of the lines. Example options:
{r, g, b, c, m, k, w} or (3, ) ndarray
line_style (
{'', '', '.', ':'}
, optional) – The style of the lines.line_width (float, optional) – The width of the lines.
render_markers (bool, optional) – If
True
, the markers will be rendered.marker_style (See Below, optional) –
The style of the markers. Example options
{., ,, o, v, ^, <, >, +, x, D, d, s, p, *, h, H, 1, 2, 3, 4, 8}
marker_size (int, optional) – The size of the markers in points.
marker_face_colour (See Below, optional) – The face (filling) colour of the markers. Example options
{r, g, b, c, m, k, w} or (3, ) ndarray
marker_edge_colour (See Below, optional) – The edge colour of the markers. Example options
{r, g, b, c, m, k, w} or (3, ) ndarray
marker_edge_width (float, optional) – The width of the markers’ edge.
render_numbering (bool, optional) – If
True
, the landmarks will be numbered.numbers_horizontal_align (
{center, right, left}
, optional) – The horizontal alignment of the numbers’ texts.numbers_vertical_align (
{center, top, bottom, baseline}
, optional) – The vertical alignment of the numbers’ texts.numbers_font_name (See Below, optional) –
The font of the numbers. Example options
{serif, sansserif, cursive, fantasy, monospace}
numbers_font_size (int, optional) – The font size of the numbers.
numbers_font_style (
{normal, italic, oblique}
, optional) – The font style of the numbers.numbers_font_weight (See Below, optional) – The font weight of the numbers. Example options
{ultralight, light, normal, regular, book, medium, roman, semibold, demibold, demi, bold, heavy, extra bold, black}
numbers_font_colour (See Below, optional) – The font colour of the numbers. Example options
{r, g, b, c, m, k, w} or (3, ) ndarray
render_axes (bool, optional) – If
True
, the axes will be rendered.axes_font_name (See Below, optional) – The font of the axes. Example options
{serif, sansserif, cursive, fantasy, monospace}
axes_font_size (int, optional) – The font size of the axes.
axes_font_style ({
normal
,italic
,oblique
}, optional) – The font style of the axes.axes_font_weight (See Below, optional) – The font weight of the axes. Example options
{ultralight, light, normal, regular, book, medium, roman, semibold, demibold, demi, bold, heavy, extra bold, black}
axes_x_limits (float or (float, float) or
None
, optional) – The limits of the x axis. If float, then it sets padding on the right and left of the PointGraph as a percentage of the PointGraph’s width. If tuple or list, then it defines the axis limits. IfNone
, then the limits are set automatically.axes_y_limits ((float, float) tuple or
None
, optional) – The limits of the y axis. If float, then it sets padding on the top and bottom of the PointGraph as a percentage of the PointGraph’s height. If tuple or list, then it defines the axis limits. IfNone
, then the limits are set automatically.axes_x_ticks (list or tuple or
None
, optional) – The ticks of the x axis.axes_y_ticks (list or tuple or
None
, optional) – The ticks of the y axis.figure_size ((float, float) tuple or
None
, optional) – The size of the figure in inches.label (str, optional) – The name entry in case of a legend.
 Returns
viewer (
PointGraphViewer2d
) – The viewer object.

_view_landmarks_2d
(group=None, with_labels=None, without_labels=None, figure_id=None, new_figure=False, image_view=True, render_lines=True, line_colour='k', line_style='', line_width=2, render_markers=True, marker_style='s', marker_size=7, marker_face_colour='k', marker_edge_colour='k', marker_edge_width=1.0, render_lines_lms=True, line_colour_lms=None, line_style_lms='', line_width_lms=1, render_markers_lms=True, marker_style_lms='o', marker_size_lms=5, marker_face_colour_lms=None, marker_edge_colour_lms=None, marker_edge_width_lms=1.0, render_numbering=False, numbers_horizontal_align='center', numbers_vertical_align='bottom', numbers_font_name='sansserif', numbers_font_size=10, numbers_font_style='normal', numbers_font_weight='normal', numbers_font_colour='k', render_legend=False, legend_title='', legend_font_name='sansserif', legend_font_style='normal', legend_font_size=10, legend_font_weight='normal', legend_marker_scale=None, legend_location=2, legend_bbox_to_anchor=(1.05, 1.0), legend_border_axes_pad=None, legend_n_columns=1, legend_horizontal_spacing=None, legend_vertical_spacing=None, legend_border=True, legend_border_padding=None, legend_shadow=False, legend_rounded_corners=False, render_axes=False, axes_font_name='sansserif', axes_font_size=10, axes_font_style='normal', axes_font_weight='normal', axes_x_limits=None, axes_y_limits=None, axes_x_ticks=None, axes_y_ticks=None, figure_size=(7, 7))¶ Visualize the landmarks. This method will appear on the PointGraph as
view_landmarks
. Parameters
group (str or``None`` optional) – The landmark group to be visualized. If
None
and there are more than one landmark groups, an error is raised.with_labels (
None
or str or list of str, optional) – If notNone
, only show the given label(s). Should not be used with thewithout_labels
kwarg.without_labels (
None
or str or list of str, optional) – If notNone
, show all except the given label(s). Should not be used with thewith_labels
kwarg.figure_id (object, optional) – The id of the figure to be used.
new_figure (bool, optional) – If
True
, a new figure is created.image_view (bool, optional) – If
True
the PointCloud will be viewed as if it is in the image coordinate system.render_lines (bool, optional) – If
True
, the edges will be rendered.line_colour (See Below, optional) –
The colour of the lines. Example options:
{r, g, b, c, m, k, w} or (3, ) ndarray
line_style (
{, , ., :}
, optional) – The style of the lines.line_width (float, optional) – The width of the lines.
render_markers (bool, optional) – If
True
, the markers will be rendered.marker_style (See Below, optional) –
The style of the markers. Example options
{., ,, o, v, ^, <, >, +, x, D, d, s, p, *, h, H, 1, 2, 3, 4, 8}
marker_size (int, optional) – The size of the markers in points.
marker_face_colour (See Below, optional) –
The face (filling) colour of the markers. Example options
{r, g, b, c, m, k, w} or (3, ) ndarray
marker_edge_colour (See Below, optional) –
The edge colour of the markers. Example options
{r, g, b, c, m, k, w} or (3, ) ndarray
marker_edge_width (float, optional) – The width of the markers’ edge.
render_lines_lms (bool, optional) – If
True
, the edges of the landmarks will be rendered.line_colour_lms (See Below, optional) –
The colour of the lines of the landmarks. Example options:
{r, g, b, c, m, k, w} or (3, ) ndarray
line_style_lms (
{, , ., :}
, optional) – The style of the lines of the landmarks.line_width_lms (float, optional) – The width of the lines of the landmarks.
render_markers – If
True
, the markers of the landmarks will be rendered.marker_style –
The style of the markers of the landmarks. Example options
{., ,, o, v, ^, <, >, +, x, D, d, s, p, *, h, H, 1, 2, 3, 4, 8}
marker_size – The size of the markers of the landmarks in points.
marker_face_colour –
The face (filling) colour of the markers of the landmarks. Example options
{r, g, b, c, m, k, w} or (3, ) ndarray
marker_edge_colour –
The edge colour of the markers of the landmarks. Example options
{r, g, b, c, m, k, w} or (3, ) ndarray
marker_edge_width – The width of the markers’ edge of the landmarks.
render_numbering (bool, optional) – If
True
, the landmarks will be numbered.numbers_horizontal_align (
{center, right, left}
, optional) – The horizontal alignment of the numbers’ texts.numbers_vertical_align (
{center, top, bottom, baseline}
, optional) – The vertical alignment of the numbers’ texts.numbers_font_name (See Below, optional) –
The font of the numbers. Example options
{serif, sansserif, cursive, fantasy, monospace}
numbers_font_size (int, optional) – The font size of the numbers.
numbers_font_style (
{normal, italic, oblique}
, optional) – The font style of the numbers.numbers_font_weight (See Below, optional) –
The font weight of the numbers. Example options
{ultralight, light, normal, regular, book, medium, roman, semibold, demibold, demi, bold, heavy, extra bold, black}
numbers_font_colour (See Below, optional) –
The font colour of the numbers. Example options
{r, g, b, c, m, k, w} or (3, ) ndarray
render_legend (bool, optional) – If
True
, the legend will be rendered.legend_title (str, optional) – The title of the legend.
legend_font_name (See below, optional) –
The font of the legend. Example options
{serif, sansserif, cursive, fantasy, monospace}
legend_font_style (
{normal, italic, oblique}
, optional) – The font style of the legend.legend_font_size (int, optional) – The font size of the legend.
legend_font_weight (See Below, optional) –
The font weight of the legend. Example options
{ultralight, light, normal, regular, book, medium, roman, semibold, demibold, demi, bold, heavy, extra bold, black}
legend_marker_scale (float, optional) – The relative size of the legend markers with respect to the original
legend_location (int, optional) –
The location of the legend. The predefined values are:
’best’
0
’upper right’
1
’upper left’
2
’lower left’
3
’lower right’
4
’right’
5
’center left’
6
’center right’
7
’lower center’
8
’upper center’
9
’center’
10
legend_bbox_to_anchor ((float, float) tuple, optional) – The bbox that the legend will be anchored.
legend_border_axes_pad (float, optional) – The pad between the axes and legend border.
legend_n_columns (int, optional) – The number of the legend’s columns.
legend_horizontal_spacing (float, optional) – The spacing between the columns.
legend_vertical_spacing (float, optional) – The vertical space between the legend entries.
legend_border (bool, optional) – If
True
, a frame will be drawn around the legend.legend_border_padding (float, optional) – The fractional whitespace inside the legend border.
legend_shadow (bool, optional) – If
True
, a shadow will be drawn behind legend.legend_rounded_corners (bool, optional) – If
True
, the frame’s corners will be rounded (fancybox).render_axes (bool, optional) – If
True
, the axes will be rendered.axes_font_name (See Below, optional) –
The font of the axes. Example options
{serif, sansserif, cursive, fantasy, monospace}
axes_font_size (int, optional) – The font size of the axes.
axes_font_style (
{normal, italic, oblique}
, optional) – The font style of the axes.axes_font_weight (See Below, optional) –
The font weight of the axes. Example options
{ultralight, light, normal, regular, book, medium, roman, semibold,demibold, demi, bold, heavy, extra bold, black}
axes_x_limits (float or (float, float) or
None
, optional) – The limits of the x axis. If float, then it sets padding on the right and left of the PointCloud as a percentage of the PointCloud’s width. If tuple or list, then it defines the axis limits. IfNone
, then the limits are set automatically.axes_y_limits ((float, float) tuple or
None
, optional) – The limits of the y axis. If float, then it sets padding on the top and bottom of the PointCloud as a percentage of the PointCloud’s height. If tuple or list, then it defines the axis limits. IfNone
, then the limits are set automatically.axes_x_ticks (list or tuple or
None
, optional) – The ticks of the x axis.axes_y_ticks (list or tuple or
None
, optional) – The ticks of the y axis.figure_size ((float, float) tuple or
None
optional) – The size of the figure in inches.
 Raises
ValueError – If both
with_labels
andwithout_labels
are passed.ValueError – If the landmark manager doesn’t contain the provided group label.

as_vector
(**kwargs)¶ Returns a flattened representation of the object as a single vector.
 Returns
vector ((N,) ndarray) – The core representation of the object, flattened into a single vector. Note that this is always a view back on to the original object, but is not writable.

bounding_box
()¶ Return a bounding box from two corner points as a directed graph. In the case of a 2D pointcloud, first point (0) should be nearest the origin. In the case of an image, this ordering would appear as:
0<3  ^   v  1>2
In the case of a pointcloud, the ordering will appear as:
3<2  ^   v  0>1
In the case of a 3D pointcloud, the first point (0) should be the near closest to the origin and the second point is the far opposite corner.
 Returns
bounding_box (
PointDirectedGraph
) – The axis aligned bounding box of the PointCloud.

bounds
(boundary=0)¶ The minimum to maximum extent of the PointCloud. An optional boundary argument can be provided to expand the bounds by a constant margin.
 Parameters
boundary (float) – A optional padding distance that is added to the bounds. Default is
0
, meaning the max/min of tightest possible containing square/cube/hypercube is returned. Returns
min_b (
(n_dims,)
ndarray) – The minimum extent of thePointCloud
and boundary along each dimensionmax_b (
(n_dims,)
ndarray) – The maximum extent of thePointCloud
and boundary along each dimension

centre
()¶ The mean of all the points in this PointCloud (centre of mass).
 Returns
centre (
(n_dims)
ndarray) – The mean of this PointCloud’s points.

centre_of_bounds
()¶ The centre of the absolute bounds of this PointCloud. Contrast with
centre()
, which is the mean point position. Returns
centre (
n_dims
ndarray) – The centre of the bounds of this PointCloud.

children
(vertex, skip_checks=False)¶ Returns the children of the selected vertex.
 Parameters
vertex (int) – The selected vertex.
skip_checks (bool, optional) – If
False
, the given vertex will be checked.
 Returns
children (list) – The list of children.
 Raises
ValueError – The vertex must be between 0 and {n_vertices1}.

constrain_to_bounds
(bounds)¶ Returns a copy of this PointCloud, constrained to lie exactly within the given bounds. Any points outside the bounds will be ‘snapped’ to lie exactly on the boundary.
 Parameters
bounds (
(n_dims, n_dims)
tuple of scalars) – The bounds to constrain this pointcloud within. Returns
constrained (
PointCloud
) – The constrained pointcloud.

copy
()¶ Generate an efficient copy of this object.
Note that Numpy arrays and other
Copyable
objects onself
will be deeply copied. Dictionaries and sets will be shallow copied, and everything else will be assigned (no copy will be made).Classes that store state other than numpy arrays and immutable types should overwrite this method to ensure all state is copied.
 Returns
type(self)
– A copy of this object

distance_to
(pointcloud, **kwargs)¶ Returns a distance matrix between this PointCloud and another. By default the Euclidean distance is calculated  see scipy.spatial.distance.cdist for valid kwargs to change the metric and other properties.
 Parameters
pointcloud (
PointCloud
) – The second pointcloud to compute distances between. This must be of the same dimension as this PointCloud. Returns
distance_matrix (
(n_points, n_points)
ndarray) – The symmetric pairwise distance matrix between the two PointClouds s.t.distance_matrix[i, j]
is the distance between the i’th point of this PointCloud and the j’th point of the input PointCloud.

find_all_paths
(start, end, path=[])¶ Returns a list of lists with all the paths (without cycles) found from start vertex to end vertex.
 Parameters
start (int) – The vertex from which the paths start.
end (int) – The vertex from which the paths end.
path (list, optional) – An existing path to append to.
 Returns
paths (list of list) – The list containing all the paths from start to end.

find_all_shortest_paths
(algorithm='auto', unweighted=False)¶ Returns the distances and predecessors arrays of the graph’s shortest paths.
 Parameters
algorithm ('str', see below, optional) –
The algorithm to be used. Possible options are:
’dijkstra’
Dijkstra’s algorithm with Fibonacci heaps
’bellmanford’
BellmanFord algorithm
’johnson’
Johnson’s algorithm
’floydwarshall’
FloydWarshall algorithm
’auto’
Select the best among the above
unweighted (bool, optional) – If
True
, then find unweighted distances. That is, rather than finding the path between each vertex such that the sum of weights is minimized, find the path such that the number of edges is minimized.
 Returns
distances (
(n_vertices, n_vertices,)
ndarray) – The matrix of distances between all graph vertices.distances[i,j]
gives the shortest distance from vertexi
to vertexj
along the graph.predecessors (
(n_vertices, n_vertices,)
ndarray) – The matrix of predecessors, which can be used to reconstruct the shortest paths. Each entrypredecessors[i, j]
gives the index of the previous vertex in the path from vertexi
to vertexj
. If no path exists between verticesi
andj
, thenpredecessors[i, j] = 9999
.

find_path
(start, end, method='bfs', skip_checks=False)¶ Returns a list with the first path (without cycles) found from the
start
vertex to theend
vertex. It can employ either depthfirst search or breadthfirst search. Parameters
start (int) – The vertex from which the path starts.
end (int) – The vertex to which the path ends.
method ({
bfs
,dfs
}, optional) – The method to be used.skip_checks (bool, optional) – If
True
, then input arguments won’t pass through checks. Useful for efficiency.
 Returns
path (list) – The path’s vertices.
 Raises
ValueError – Method must be either bfs or dfs.

find_shortest_path
(start, end, algorithm='auto', unweighted=False, skip_checks=False)¶ Returns a list with the shortest path (without cycles) found from
start
vertex toend
vertex. Parameters
start (int) – The vertex from which the path starts.
end (int) – The vertex to which the path ends.
algorithm ('str', see below, optional) –
The algorithm to be used. Possible options are:
’dijkstra’
Dijkstra’s algorithm with Fibonacci heaps
’bellmanford’
BellmanFord algorithm
’johnson’
Johnson’s algorithm
’floydwarshall’
FloydWarshall algorithm
’auto’
Select the best among the above
unweighted (bool, optional) – If
True
, then find unweighted distances. That is, rather than finding the path such that the sum of weights is minimized, find the path such that the number of edges is minimized.skip_checks (bool, optional) – If
True
, then input arguments won’t pass through checks. Useful for efficiency.
 Returns
path (list) – The shortest path’s vertices, including
start
andend
. If there was not path connecting the vertices, then an empty list is returned.distance (int or float) – The distance (cost) of the path from
start
toend
.

from_mask
(mask)[source]¶ A 1D boolean array with the same number of elements as the number of points in the PointDirectedGraph. This is then broadcast across the dimensions of the PointDirectedGraph and returns a new PointDirectedGraph containing only those points that were
True
in the mask. Parameters
mask (
(n_points,)
ndarray) – 1D array of booleans Returns
pointgraph (
PointDirectedGraph
) – A new pointgraph that has been masked. Raises
ValueError – Mask must be a 1D boolean array of the same number of entries as points in this PointDirectedGraph.

from_vector
(vector)¶ Build a new instance of the object from it’s vectorized state.
self
is used to fill out the missing state required to rebuild a full object from it’s standardized flattened state. This is the default implementation, which is which is adeepcopy
of the object followed by a call tofrom_vector_inplace()
. This method can be overridden for a performance benefit if desired. Parameters
vector (
(n_parameters,)
ndarray) – Flattened representation of the object. Returns
object (
type(self)
) – An new instance of this class.

from_vector_inplace
(vector)¶ Deprecated. Use the nonmutating API,
from_vector
.For internal usage in performancesensitive spots, see _from_vector_inplace()
 Parameters
vector (
(n_parameters,)
ndarray) – Flattened representation of this object

get_adjacency_list
()¶ Returns the adjacency list of the graph, i.e. a list of length
n_vertices
that for each vertex has a list of the vertex neighbours. If the graph is directed, the neighbours are children. Returns
adjacency_list (list of list of length
n_vertices
) – The adjacency list of the graph.

h_points
()¶ Convert poincloud to a homogeneous array:
(n_dims + 1, n_points)
 Type
type(self)

has_cycles
()¶ Checks if the graph has at least one cycle.
 Returns
has_cycles (bool) –
True
if the graph has cycles.

has_isolated_vertices
()¶ Whether the graph has any isolated vertices, i.e. vertices with no edge connections.
 Returns
has_isolated_vertices (bool) –
True
if the graph has at least one isolated vertex.

has_nan_values
()¶ Tests if the vectorized form of the object contains
nan
values or not. This is particularly useful for objects with unknown values that have been mapped tonan
values. Returns
has_nan_values (bool) – If the vectorized object contains
nan
values.

classmethod
init_2d_grid
(shape, spacing=None, adjacency_matrix=None, skip_checks=False)¶ Create a PointGraph that exists on a regular 2D grid. The first dimension is the number of rows in the grid and the second dimension of the shape is the number of columns.
spacing
optionally allows the definition of the distance between points (uniform over points). The spacing may be different for rows and columns.If no adjacency matrix is provided, the default connectivity will be a 4connected lattice.
 Parameters
shape (tuple of 2 int) – The size of the grid to create, this defines the number of points across each dimension in the grid. The first element is the number of rows and the second is the number of columns.
spacing (int or tuple of 2 int, optional) – The spacing between points. If a single int is provided, this is applied uniformly across each dimension. If a tuple is provided, the spacing is applied nonuniformly as defined e.g.
(2, 3)
gives a spacing of 2 for the rows and 3 for the columns.adjacency_matrix (
(n_vertices, n_vertices)
ndarray or csr_matrix, optional) –The adjacency matrix of the graph in which the rows represent source vertices and columns represent destination vertices. The nonedges must be represented with zeros and the edges can have a weight value.
The adjacency matrix of an undirected graph must be symmetric.
skip_checks (bool, optional) – If
True
, no checks will be performed. Only considered if no adjacency matrix is provided.
 Returns
pgraph (PointGraph) – A pointgraph arranged in a grid.

classmethod
init_from_depth_image
(depth_image, spacing=None, adjacency_matrix=None, skip_checks=False)¶ Return a 3D point graph from the given depth image. The depth image is assumed to represent height/depth values and the XY coordinates are assumed to unit spaced and represent image coordinates. This is particularly useful for visualising depth values that have been recovered from images.
If no adjacency matrix is provided, the default connectivity will be a 4connected lattice.
 Parameters
depth_image (
Image
or subclass) – A single channel image that contains depth values  as commonly returned by RGBD cameras, for example.spacing (int or tuple of 2 int, optional) – The spacing between points. If a single int is provided, this is applied uniformly across each dimension. If a tuple is provided, the spacing is applied nonuniformly as defined e.g.
(2, 3)
gives a spacing of 2 for the rows and 3 for the columns.adjacency_matrix (
(n_vertices, n_vertices)
ndarray or csr_matrix, optional) –The adjacency matrix of the graph in which the rows represent source vertices and columns represent destination vertices. The nonedges must be represented with zeros and the edges can have a weight value.
The adjacency matrix of an undirected graph must be symmetric.
skip_checks (bool, optional) – If
True
, no checks will be performed. Only considered if no adjacency matrix is provided.
 Returns
depth_cloud (
type(cls)
) – A new 3D PointGraph with unit XY coordinates and the given depth values as Z coordinates.

classmethod
init_from_edges
(points, edges, copy=True, skip_checks=False)¶ Construct a PointGraph from edges array.
 Parameters
points (
(n_vertices, n_dims, )
ndarray) – The array of point locations.edges (
(n_edges, 2, )
ndarray) – The ndarray of edges, i.e. all the pairs of vertices that are connected with an edge.copy (bool, optional) – If
False
, theadjacency_matrix
will not be copied on assignment.skip_checks (bool, optional) – If
True
, no checks will be performed.
Examples
The following undirected graph
0     12     34   5
can be defined as
from menpo.shape import PointUndirectedGraph import numpy as np points = np.array([[10, 30], [0, 20], [20, 20], [0, 10], [20, 10], [0, 0]]) edges = np.array([[0, 1], [1, 0], [0, 2], [2, 0], [1, 2], [2, 1], [1, 3], [3, 1], [2, 4], [4, 2], [3, 4], [4, 3], [3, 5], [5, 3]]) graph = PointUndirectedGraph.init_from_edges(points, edges)
The following directed graph
>0<     1<>2   v v 3>4  v 5
can be represented as
from menpo.shape import PointDirectedGraph import numpy as np points = np.array([[10, 30], [0, 20], [20, 20], [0, 10], [20, 10], [0, 0]]) edges = np.array([[1, 0], [2, 0], [1, 2], [2, 1], [1, 3], [2, 4], [3, 4], [3, 5]]) graph = PointDirectedGraph.init_from_edges(points, edges)
Finally, the following graph with isolated vertices
0   1 2   34 5
can be defined as
from menpo.shape import PointUndirectedGraph import numpy as np points = np.array([[10, 30], [0, 20], [20, 20], [0, 10], [20, 10], [0, 0]]) edges = np.array([[0, 2], [2, 0], [2, 4], [4, 2], [3, 4], [4, 3]]) graph = PointUndirectedGraph.init_from_edges(points, edges)

is_edge
(vertex_1, vertex_2, skip_checks=False)¶ Whether there is an edge between the provided vertices.
 Parameters
vertex_1 (int) – The first selected vertex. Parent if the graph is directed.
vertex_2 (int) – The second selected vertex. Child if the graph is directed.
skip_checks (bool, optional) – If
False
, the given vertices will be checked.
 Returns
is_edge (bool) –
True
if there is an edge connectingvertex_1
andvertex_2
. Raises
ValueError – The vertex must be between 0 and {n_vertices1}.

is_tree
()¶ Checks if the graph is tree.
 Returns
is_true (bool) – If the graph is a tree.

isolated_vertices
()¶ Returns the isolated vertices of the graph (if any), i.e. the vertices that have no edge connections.
 Returns
isolated_vertices (list) – A list of the isolated vertices. If there aren’t any, it returns an empty list.

n_children
(vertex, skip_checks=False)¶ Returns the number of children of the selected vertex.
 Parameters
vertex (int) – The selected vertex.
 Returns
n_children (int) – The number of children.
skip_checks (bool, optional) – If
False
, the given vertex will be checked.
 Raises
ValueError – The vertex must be in the range
[0, n_vertices  1]
.

n_parents
(vertex, skip_checks=False)¶ Returns the number of parents of the selected vertex.
 Parameters
vertex (int) – The selected vertex.
skip_checks (bool, optional) – If
False
, the given vertex will be checked.
 Returns
n_parents (int) – The number of parents.
 Raises
ValueError – The vertex must be in the range
[0, n_vertices  1]
.

n_paths
(start, end)¶ Returns the number of all the paths (without cycles) existing from start vertex to end vertex.
 Parameters
start (int) – The vertex from which the paths start.
end (int) – The vertex from which the paths end.
 Returns
paths (int) – The paths’ numbers.

norm
(**kwargs)¶ Returns the norm of this PointCloud. This is a translation and rotation invariant measure of the point cloud’s intrinsic size  in other words, it is always taken around the point cloud’s centre.
By default, the Frobenius norm is taken, but this can be changed by setting kwargs  see
numpy.linalg.norm
for valid options. Returns
norm (float) – The norm of this
PointCloud

parents
(vertex, skip_checks=False)¶ Returns the parents of the selected vertex.
 Parameters
vertex (int) – The selected vertex.
skip_checks (bool, optional) – If
False
, the given vertex will be checked.
 Returns
parents (list) – The list of parents.
 Raises
ValueError – The vertex must be in the range
[0, n_vertices  1]
.

range
(boundary=0)¶ The range of the extent of the PointCloud.
 Parameters
boundary (float) – A optional padding distance that is used to extend the bounds from which the range is computed. Default is
0
, no extension is performed. Returns
range (
(n_dims,)
ndarray) – The range of thePointCloud
extent in each dimension.

relative_location_edge
(parent, child)[source]¶ Returns the relative location between the provided vertices. That is if vertex j is the parent and vertex i is its child and vector l denotes the coordinates of a vertex, then
l_i  l_j = [[x_i], [y_i]]  [[x_j], [y_j]] = = [[x_i  x_j], [y_i  y_j]]
 Parameters
parent (int) – The first selected vertex which is considered as the parent.
child (int) – The second selected vertex which is considered as the child.
 Returns
relative_location (
(2,)
ndarray) – The relative location vector. Raises
ValueError – Vertices
parent
andchild
are not connected with an edge.

relative_locations
()[source]¶ Returns the relative location between the vertices of each edge. If vertex j is the parent and vertex i is its child and vector l denotes the coordinates of a vertex, then:
l_i  l_j = [[x_i], [y_i]]  [[x_j], [y_j]] = = [[x_i  x_j], [y_i  y_j]]
 Returns
relative_locations (
(n_vertexes, 2)
ndarray) – The relative locations vector.

tojson
()¶ Convert this PointGraph to a dictionary representation suitable for inclusion in the LJSON landmark format.
 Returns
json (dict) – Dictionary with
points
andconnectivity
keys.

with_dims
(dims)¶ Return a copy of this shape with only particular dimensions retained.
 Parameters
dims (valid numpy array slice) – The slice that will be used on the dimensionality axis of the shape under transform. For example, to go from a 3D shape to a 2D one, [0, 1] could be provided or np.array([True, True, False]).
 Returns
copy of self, with only the requested dims

property
edges
¶ Returns the ndarray of edges, i.e. all the pairs of vertices that are connected with an edge.
 Type
(n_edges, 2, )
ndarray

property
has_landmarks
¶ Whether the object has landmarks.
 Type
bool

property
landmarks
¶ The landmarks object.
 Type

property
lms
¶ Deprecated. Maintained for compatibility, will be removed in a future version. Returns a copy of this object, which previously would have held the ‘underlying’
PointCloud
subclass. Type
self

property
n_dims
¶ The number of dimensions in the pointcloud.
 Type
int

property
n_edges
¶ Returns the number of edges.
 Type
int

property
n_landmark_groups
¶ The number of landmark groups on this object.
 Type
int

property
n_parameters
¶ The length of the vector that this object produces.
 Type
int

property
n_points
¶ The number of points in the pointcloud.
 Type
int

property
n_vertices
¶ Returns the number of vertices.
 Type
int

property
vertices
¶ Returns the list of vertices.
 Type
list