def _label(point, centers):
"""
Returns an index such that *centers*[index] is the point in *centers* nearest *point*.
"""
min_sqdist = None
best_label = None
for c in range(len(centers)):
if min_sqdist == None or sqdist(point, centers[c]) < min_sqdist:
min_sqdist = sqdist(point, centers[c])
best_label = c
return best_label
def kmeans(points3, centers, epsilon):
"""
Returns a list of lists of elements of *points3*, k-means clustered in two dimensions
around the k centers in *centers* with points weighted by third dimension coordinate.
Iteration until no center moves more than *epsilon*.
"""
prevcenters = None
while prevcenters == None or max([ sqdist(center, prevcenter)
for (center, prevcenter) in zip(centers, prevcenters)
]) > epsilon**2:
# empty clusters
clusters = []
for center in centers:
clusters.append([])
# recluster points
for point in points3:
clusters[_label(point, centers)].append(point)
# find new centers
prevcenters = deepcopy(centers)
for i in range(len(centers)):
centers[i] = np.average(clusters[i],
axis=0,
weights=[ point[2] for point in clusters[i] ])
return clusters
def local_maxima(points3, radius):
"""
Returns a list of points from *points3* who have no neighbors of greater intensity
within *radius* pixels. Ties are arbitrarily broken.
"""
maxima = []
for p in points3:
neighbor_zs = [ q[2] for q in points3 if q != p and sqdist(p, q) < radius**2 ]
if neighbor_zs == [] or p[2] > max(neighbor_zs):
maxima.append(p)
elif p[2] == max(neighbor_zs):
# break ties
p[2] = 0
return maxima
def best_into_mapping(domain, H, codomain):
"""
Associates each point in *domain* with the point in *codomain* nearest its image
under homography *H*. Returns an ordered list of images corresponding to points
in *domain*, along with some indication of how good or bad the match is.
"""
RANGE = []
total_error = 0
for preimage in domain:
modeled = H * preimage
min_error = None
image = None
for point in codomain:
error = sqdist(htoc(modeled), htoc(point))
if min_error == None or error < min_error:
min_error = error
image = point
total_error += min_error
RANGE.append(image)
return RANGE, total_error
def _nearest(p, points2):
"""
Returns the distance from *p* to the nearest other point in *points2*.
"""
return sqrt(min([ sqdist(p, q) for q in points2 if q != p ]))