def test_distance_matrix():
metric = dipysmetric.SumPointwiseEuclideanMetric()
for dtype in [np.int32, np.int64, np.float32, np.float64]:
# Compute distances of all tuples spawn by the Cartesian product
# of `data` with itself.
data = (np.random.rand(4, 10, 3) * 10).astype(dtype)
D = dipysmetric.distance_matrix(metric, data)
assert_equal(D.shape, (len(data), len(data)))
assert_array_equal(np.diag(D), np.zeros(len(data)))
if metric.is_order_invariant:
# Distance matrix should be symmetric
assert_array_equal(D, D.T)
for i in range(len(data)):
for j in range(len(data)):
assert_equal(D[i, j], dipysmetric.dist(metric, data[i],
data[j]))
# Compute distances of all tuples spawn by the Cartesian product
# of `data` with `data2`.
data2 = (np.random.rand(3, 10, 3) * 10).astype(dtype)
D = dipysmetric.distance_matrix(metric, data, data2)
assert_equal(D.shape, (len(data), len(data2)))
for i in range(len(data)):
for j in range(len(data2)):
assert_equal(D[i, j],
dipysmetric.dist(metric, data[i], data2[j]))
def mdf(s1, s2):
""" Computes the MDF (Minimum average Direct-Flip) distance
[Garyfallidis12]_ between two streamlines.
Streamlines must have the same number of points.
Parameters
----------
s1 : 2D array
A streamline (sequence of N-dimensional points).
s2 : 2D array
A streamline (sequence of N-dimensional points).
Returns
-------
double
Distance between two streamlines.
References
----------
.. [Garyfallidis12] Garyfallidis E. et al., QuickBundles a method for
tractography simplification, Frontiers in Neuroscience,
vol 6, no 175, 2012.
"""
return dist(MinimumAverageDirectFlipMetric(), s1, s2)
def mdf(s1, s2):
""" Computes the MDF (Minimum average Direct-Flip) distance
[Garyfallidis12]_ between two streamlines.
Streamlines must have the same number of points.
Parameters
----------
s1 : 2D array
A streamline (sequence of N-dimensional points).
s2 : 2D array
A streamline (sequence of N-dimensional points).
Returns
-------
double
Distance between two streamlines.
References
----------
.. [Garyfallidis12] Garyfallidis E. et al., QuickBundles a method for
tractography simplification, Frontiers in Neuroscience,
vol 6, no 175, 2012.
"""
return dist(MinimumAverageDirectFlipMetric(), s1, s2)
def test_metric_minimum_average_direct_flip():
feature = dipysfeature.IdentityFeature()
class MinimumAverageDirectFlipMetric(dipysmetric.Metric):
def __init__(self, feature):
super(MinimumAverageDirectFlipMetric,
self).__init__(feature=feature)
@property
def is_order_invariant(self):
return True # Ordering is handled in the distance computation
def are_compatible(self, shape1, shape2):
return shape1[0] == shape2[0]
def dist(self, v1, v2):
def average_euclidean(x, y):
return np.mean(norm(x - y, axis=1))
dist_direct = average_euclidean(v1, v2)
dist_flipped = average_euclidean(v1, v2[::-1])
return min(dist_direct, dist_flipped)
for metric in [
MinimumAverageDirectFlipMetric(feature),
dipysmetric.MinimumAverageDirectFlipMetric(feature)
]:
# Test special cases of the MDF distance.
assert_equal(metric.dist(s, s), 0.)
assert_equal(metric.dist(s, s[::-1]), 0.)
# Translation
offset = np.array([0.8, 1.3, 5], dtype=dtype)
assert_almost_equal(metric.dist(s, s + offset), norm(offset), 5)
# Scaling
M_scaling = np.diag([1.2, 2.8, 3]).astype(dtype)
s_mean = np.mean(s, axis=0)
s_zero_mean = s - s_mean
s_scaled = np.dot(M_scaling, s_zero_mean.T).T + s_mean
d = np.mean(norm((np.diag(M_scaling) - 1) * s_zero_mean, axis=1))
assert_almost_equal(metric.dist(s, s_scaled), d, 5)
# Rotation
from dipy.core.geometry import rodrigues_axis_rotation
rot_axis = np.array([1, 2, 3], dtype=dtype)
M_rotation = rodrigues_axis_rotation(rot_axis, 60.).astype(dtype)
s_mean = np.mean(s, axis=0)
s_zero_mean = s - s_mean
s_rotated = np.dot(M_rotation, s_zero_mean.T).T + s_mean
opposite = norm(np.cross(rot_axis, s_zero_mean),
axis=1) / norm(rot_axis)
distances = np.sqrt(2 * opposite**2 *
(1 - np.cos(60. * np.pi / 180.))).astype(dtype)
d = np.mean(distances)
assert_almost_equal(metric.dist(s, s_rotated), d, 5)
# All possible pairs
for s1, s2 in itertools.product(*[streamlines] * 2):
# Extract features since metric doesn't work
# directly on streamlines
f1 = metric.feature.extract(s1)
f2 = metric.feature.extract(s2)
# Test method are_compatible
same_nb_points = f1.shape[0] == f2.shape[0]
assert_equal(metric.are_compatible(f1.shape, f2.shape),
same_nb_points)
# Test method dist if features are compatible
if metric.are_compatible(f1.shape, f2.shape):
distance = metric.dist(f1, f2)
if np.all(f1 == f2):
assert_equal(distance, 0.)
assert_almost_equal(distance, dipysmetric.dist(metric, s1, s2))
assert_almost_equal(distance, dipymetric.mdf(s1, s2))
assert_greater_equal(distance, 0.)
# This metric type is order invariant
assert_true(metric.is_order_invariant)
# All possible pairs
for s1, s2 in itertools.product(*[streamlines] * 2):
f1 = metric.feature.extract(s1)
f2 = metric.feature.extract(s2)
if not metric.are_compatible(f1.shape, f2.shape):
continue
f1_flip = metric.feature.extract(s1[::-1])
f2_flip = metric.feature.extract(s2[::-1])
distance = metric.dist(f1, f2)
assert_almost_equal(metric.dist(f1_flip, f2_flip), distance)
if not np.all(f1_flip == f2_flip):
assert_true(np.allclose(metric.dist(f1, f2_flip), distance))
assert_true(np.allclose(metric.dist(f1_flip, f2), distance))
def test_metric_cosine():
feature = dipysfeature.VectorOfEndpointsFeature()
class CosineMetric(dipysmetric.Metric):
def __init__(self, feature):
super(CosineMetric, self).__init__(feature=feature)
def are_compatible(self, shape1, shape2):
# Cosine metric works on vectors.
return shape1 == shape2 and shape1[0] == 1
def dist(self, v1, v2):
# Check if we have null vectors
if norm(v1) == 0:
return 0. if norm(v2) == 0 else 1.
v1_normed = v1.astype(np.float64) / norm(v1.astype(np.float64))
v2_normed = v2.astype(np.float64) / norm(v2.astype(np.float64))
cos_theta = np.dot(v1_normed, v2_normed.T)
# Make sure it's in [-1, 1], i.e. within domain of arccosine
cos_theta = np.minimum(cos_theta, 1.)
cos_theta = np.maximum(cos_theta, -1.)
return np.arccos(cos_theta) / np.pi # Normalized cosine distance
for metric in [CosineMetric(feature), dipysmetric.CosineMetric(feature)]:
# Test special cases of the cosine distance.
v0 = np.array([[0, 0, 0]], dtype=np.float32)
v1 = np.array([[1, 2, 3]], dtype=np.float32)
v2 = np.array([[1, -1. / 2, 0]], dtype=np.float32)
v3 = np.array([[-1, -2, -3]], dtype=np.float32)
assert_equal(metric.dist(v0, v0), 0.) # dot-dot
assert_equal(metric.dist(v0, v1), 1.) # dot-line
assert_equal(metric.dist(v1, v1), 0.) # collinear
assert_equal(metric.dist(v1, v2), 0.5) # orthogonal
assert_equal(metric.dist(v1, v3), 1.) # opposite
# All possible pairs
for s1, s2 in itertools.product(*[streamlines] * 2):
# Extract features since metric doesn't
# work directly on streamlines
f1 = metric.feature.extract(s1)
f2 = metric.feature.extract(s2)
# Test method are_compatible
are_vectors = f1.shape[0] == 1 and f2.shape[0] == 1
same_dimension = f1.shape[1] == f2.shape[1]
assert_equal(metric.are_compatible(f1.shape, f2.shape), are_vectors
and same_dimension)
# Test method dist if features are compatible
if metric.are_compatible(f1.shape, f2.shape):
distance = metric.dist(f1, f2)
if np.all(f1 == f2):
assert_almost_equal(distance, 0.)
assert_almost_equal(distance, dipysmetric.dist(metric, s1, s2))
assert_greater_equal(distance, 0.)
assert_less_equal(distance, 1.)
# This metric type is not order invariant
assert_false(metric.is_order_invariant)
# All possible pairs
for s1, s2 in itertools.product(*[streamlines] * 2):
f1 = metric.feature.extract(s1)
f2 = metric.feature.extract(s2)
if not metric.are_compatible(f1.shape, f2.shape):
continue
f1_flip = metric.feature.extract(s1[::-1])
f2_flip = metric.feature.extract(s2[::-1])
distance = metric.dist(f1, f2)
assert_almost_equal(metric.dist(f1_flip, f2_flip), distance)
if not np.all(f1_flip == f2_flip):
assert_false(metric.dist(f1, f2_flip) == distance)
assert_false(metric.dist(f1_flip, f2) == distance)