def locally_extreme_points(coords,
data,
neighbourhood,
lookfor='max',
p_norm=2.):
# Description
# Find local maxima of points in a pointcloud. Ties result in both points passing through the filter.
#
# Not to be used for high-dimensional data. It will be slow.
#
# coords: A shape (n_points, n_dims) array of point locations
# data: A shape (n_points, ) vector of point values
# neighbourhood: The (scalar) size of the neighbourhood in which to search.
# lookfor: Either 'max', or 'min', depending on whether you want local maxima or minima
# p_norm: The p-norm to use for measuring distance (e.g. 1=Manhattan, 2=Euclidian)
#
# returns
# filtered_coords: The coordinates of locally extreme points
# filtered_data: The values of these points
assert coords.shape[0] == data.shape[
0], 'You must have one coordinate per data point'
extreme_fcn = {'min': np.min, 'max': np.max}[lookfor]
kdtree = KDTree(coords)
neighbours = kdtree.query_ball_tree(kdtree, r=neighbourhood, p=p_norm)
i_am_extreme = [
data[i] == extreme_fcn(data[n]) for i, n in enumerate(neighbours)
]
extrema, = np.nonzero(
i_am_extreme) # This line just saves time on indexing
return coords[extrema], data[extrema]
def locally_extreme_points(coords,
data,
radius,
smoothing_radius=None,
min_neighbourhood_size=-1,
lookfor='max',
p_norm=2):
'''
Find local maxima of points in a pointcloud. Ties result in both points passing through the filter.
Not to be used for high-dimensional data. It will be slow.
coords: A shape (n_points, n_dims) array of point locations
data: A shape (n_points, ) vector of point values
radius: The (scalar) size of the neighbourhood in which to search.
min_neighbourhood_size: Extrema whose neighbourhood has less than min_neighbourhood_size points are discarded
lookfor: Either 'max', or 'min', depending on whether you want local maxima or minima
p_norm: The p-norm to use for measuring distance (e.g. 1=Manhattan, 2=Euclidian)
returns
filtered_coords: The coordinates of locally extreme points
filtered_data: The values of these points
'''
assert coords.shape[0] == data.shape[
0], 'You must have one coordinate per data point'
extreme_fcn = {'min': np.min, 'max': np.max}[lookfor]
kdtree = KDTree(coords)
if smoothing_radius is not None:
smoothing_neighbours = kdtree.query_ball_tree(kdtree,
r=smoothing_radius,
p=p_norm)
smooth_data = np.array(
[np.mean(data[n]) for n in smoothing_neighbours])
else:
smooth_data = data
neighbours = kdtree.query_ball_tree(kdtree, r=radius, p=p_norm)
i_am_extreme = [
(np.nonzero(np.equal(n, i))[0][0] == np.argmax(smooth_data[n])) &
(len(n) > min_neighbourhood_size) for i, n in enumerate(neighbours)
]
extrema, = np.nonzero(
i_am_extreme) # This line just saves time on indexing
return coords[extrema], data[extrema]
def kdtree_density(points, radius, return_tree=False):
""" Returns the density calculated sing a Ball Tree.
Higher is denser.
Scales according to the dimension of the points.
see: https://stackoverflow.com/questions/14070565/calculating-point-density-using-python
If `return_tree` is `True` returns a tuple of the density and the KDTree.
"""
tree = KDTree(points)
n = points.shape[-1]
ball_trees = tree.query_ball_tree(tree, radius)
frequency = np.array([len(neighbours) for neighbours in ball_trees])
density = frequency / radius**n
if return_tree:
return np.mean(density), tree
return np.mean(density)
