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quickmatch_cluster.py
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import numpy as np
from util import euclidean_dist_matrix
def quickmatch_scale(data, n):
"""
calculate the $d_{ik}$ for each point
:param data: [m*n, p] data, m is number of images
for data[x][p], i = x // n, k = x % n
:param n: number of points per image
:return: a $d_{ik}$ array of shape[m*n,]
"""
npoint = data.shape[0]
scale = np.zeros((npoint, ), dtype=np.float32)
for i in range(0, npoint, n):
dsq_i = euclidean_dist_matrix(data[i:i+n], data[i:i+n])
for k in range(0, n):
min_d = 1e5
for y in range(0, n):
if k == y:
continue
min_d = min(min_d, dsq_i[k][y])
scale[i+k] = min_d
return scale
def quickmatch_density(data, scales, rho=0.25, kernel=None,
kernel_support_radius=None,
flag_low_memory=False,
chunk_size=None,
flag_recursive=False):
# scales = dik
sigma = rho * scales
if (not flag_low_memory) or flag_recursive:
dsq = data
dsq = dsq / sigma
if not kernel:
p = dsq
else:
if kernel_support_radius:
p = np.zeros(dsq.shape, dtype=np.float32)
flag = dsq < kernel_support_radius
p[flag] = kernel(-dsq[flag])
else:
p = kernel(-dsq)
tree_density = np.sum(p, axis=1)
else:
# here data is [p, n] raw data
npoint = data.shape[0]
tree_density = np.zeros((npoint,), dtype=np.float32)
for i in range(0, npoint, chunk_size):
j = min(i+chunk_size, npoint)
dsq = euclidean_dist_matrix(data[:, i:j], data)
tree_density[i:j] = quickmatch_density(dsq, scales=scales, rho=rho,
kernel=kernel,
kernel_support_radius=kernel_support_radius,
flag_recursive=True)
return tree_density
def quickmatch_tree(density, dsq, n):
"""
:param density:
:param dsq: distance matrix
:param n: number of points per image
:return:
"""
npoint = density.shape[0]
tree_parent = np.zeros((npoint, ), dtype=np.int32)
tree_distance = np.zeros((npoint, ), dtype=np.float32)
for i in range(npoint):
parent = i
for j in range(npoint):
# parent in the tree is given by the closest point
# with higher density from another image
if density[j] <= density[i] or (i // n) == (j // n):
# density is lower or from the same image
continue
if parent == i or dsq[i][j] < dsq[i][parent]:
parent = j
tree_parent[i] = parent
tree_distance[i] = dsq[i][parent]
return tree_parent, tree_distance
def quickmatch_breaktree_merge(tree_parent, tree_distance, scales, rho_edge=0.5):
npoint = tree_parent.shape[0]
clusters_indicator = np.array([i for i in range(npoint)], dtype=np.int32)
clusters = [[i] for i in range(npoint)]
match_dis = scales
idx_sorted = np.argsort(tree_distance, axis=0)
for i in idx_sorted:
p = tree_parent[i]
c1 = clusters_indicator[i]
c2 = clusters_indicator[p]
if i != p and c1 != c2:
match_dis_c1_c2 = min(match_dis[c1], match_dis[c2])
if tree_distance[i] <= rho_edge * match_dis_c1_c2:
clusters_indicator[clusters[c2]] = c1
clusters[c1] = clusters[c1] + clusters[c2]
clusters[c2] = []
match_dis[c1] = match_dis_c1_c2
res = []
for i in range(len(clusters)):
if clusters[i]:
res.append(clusters[i])
return res
def quickmatch_cluster(data, n, kernel=None, flag_low_memory=False, rho=0.25, rho_edge=0.5):
"""
:param rho:
:param rho_edge:
:param data: [m*n, p]
:param n: number of points per image
:param kernel:
:param flag_low_memory:
:return:
"""
scale = quickmatch_scale(data, n)
dsq = euclidean_dist_matrix(data, data)
tree_density = quickmatch_density(dsq, scales=scale, rho=rho,
kernel=kernel,
flag_low_memory=flag_low_memory)
tree_parents, tree_distance = quickmatch_tree(tree_density, dsq, n)
clusters = quickmatch_breaktree_merge(tree_parents, tree_distance,
scales=scale, rho_edge=rho_edge)
return clusters