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skeleton_graph_matching.py
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skeleton_graph_matching.py
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import json
from timeit import default_timer as timer
from scipy.optimize import linear_sum_assignment
from modified_skeleton_algorithm import MedialAxisTransformer
import numpy as np
import matplotlib.pyplot as plt
from tqdm import tqdm
from pathlib import Path
from osb import optimal_subsequence_bijection
from utils import (
extract_points_from_file,
sort_counterclockwise,
get_shape_paths,
)
N_SAMPLES = 20
def path_distance(puv_r1: np.ndarray, puv_r2: np.ndarray, l1: float, l2: float, weight_factor=30):
"""Distance between two paths"""
r_diff_sq = np.square(puv_r1 - puv_r2)
r_sum = puv_r1 + puv_r2
ratio = r_diff_sq / (r_sum + 0.00000001)
addend = np.sum(ratio)
augend = weight_factor * ((l1 - l2) ** 2 / (l1 + l2))
return addend + augend
def path_distance_matrix(
vi: int,
g: MedialAxisTransformer,
vj_prime: int,
g_prime: MedialAxisTransformer
) -> np.ndarray:
k = len(g.skeleton_end_points)
n = len(g_prime.skeleton_end_points)
if k > n:
g, g_prime = g_prime, g
vi, vj_prime = vj_prime, vi
k, n = n, k
ks = [g.all_pair_eps_shortest_paths[(vi, x)]
for x in g.skeleton_end_point_indices if x != vi]
ns = [g_prime.all_pair_eps_shortest_paths[(
vj_prime, x)] for x in g_prime.skeleton_end_point_indices if x != vj_prime]
pd_mat = np.zeros((k - 1, n - 1))
for i, lpi in enumerate(ks):
l_k, path_k = lpi
for j, lpj in enumerate(ns):
l_n, path_n = lpj
rn1 = g.sampled_radii_vector_along_path(path_k, l_k, N_SAMPLES)
rn2 = g_prime.sampled_radii_vector_along_path(
path_n, l_n, N_SAMPLES)
pd_mat[i, j] = path_distance(rn1, rn2, l_k, l_n)
return pd_mat
def main1():
input_file1 = "shapes/horse-1.txt"
input_file2 = "shapes/horse-19.txt"
points1 = extract_points_from_file(input_file1)
points2 = extract_points_from_file(input_file2)
ma_skeleton1 = MedialAxisTransformer.from_boundary_points(points1)
ma_skeleton2 = MedialAxisTransformer.from_boundary_points(points2)
adjacency_map1 = ma_skeleton1.skeleton_graph
end_points1 = ma_skeleton1.skeleton_end_point_indices
adjacency_map2 = ma_skeleton2.skeleton_graph
end_points2 = ma_skeleton2.skeleton_end_point_indices
eps1 = np.array([ma_skeleton1.medial_axis_point_idx_map[i]
for i in end_points1])
eps1 = sort_counterclockwise(eps1)
plt.scatter(eps1[:, 0], eps1[:, 1])
for i, label in enumerate(end_points1):
plt.annotate(str(label), tuple(eps1[i]))
plt.show()
# find shortest path between an endpoint and all the points in the graph
all_ep_pair_sps1 = get_shape_paths(end_points1.copy(), adjacency_map1)
all_ep_pair_sps2 = get_shape_paths(end_points2.copy(), adjacency_map2)
# seen_lengths = defaultdict(list)
# for ep in product(end_points1, end_points1):
# _, path = all_ep_pair_sps1[ep]
# if len(path) > 1:
# seen_lengths[len(path)].append(ep)
# for ep in product(end_points2, end_points2):
# _, path = all_ep_pair_sps2[ep]
# if len(path) in seen_lengths:
# print(f"This {ep}: {len(path)}")
# print(f"Possible matches {seen_lengths[len(path)]}")
l1, path1 = all_ep_pair_sps1[(13, 40)]
l2, path2 = all_ep_pair_sps2[(12, 43)]
r1 = ma_skeleton1.get_radii_vector_along_path(path1)
r2 = ma_skeleton2.get_radii_vector_along_path(path2)
print(path_distance(r1, r2, l1, l2))
def compare_skeletons(mas1: MedialAxisTransformer, mas2: MedialAxisTransformer, comp_name: str):
end_points1, end_points2 = mas1.skeleton_end_points, mas2.skeleton_end_points
k = len(end_points1)
n = len(end_points2)
if k > n:
end_points1, end_points2 = end_points2, end_points1
k, n = n, k
corr = np.zeros((n, n))
for i, ep1 in enumerate(mas1.skeleton_end_point_indices):
for j, ep2 in enumerate(mas2.skeleton_end_point_indices):
pd_mat = path_distance_matrix(ep1, mas1, ep2, mas2)
corr[i, j] = optimal_subsequence_bijection(pd_mat)
const = np.mean(corr)
if n > k:
corr[k:n, :] = const
_, gp = linear_sum_assignment(np.array(corr))
total_cost = 0
for i, j in enumerate(gp):
if i < len(mas1.skeleton_end_point_indices):
total_cost += corr[i, j]
return comp_name, total_cost
def main2(f1, f2):
start = timer()
g_pts, gprime_pts = map(extract_points_from_file, [f1, f2])
mas1, mas2 = map(MedialAxisTransformer.from_boundary_points, [
g_pts, gprime_pts])
end_points1, end_points2 = mas1.skeleton_end_points, mas2.skeleton_end_points
if len(end_points1) > len(end_points2):
end_points1, end_points2 = end_points2, end_points1
mas1, mas2 = mas2, mas1
g_pts, gprime_pts = gprime_pts, g_pts
k = len(end_points1)
n = len(end_points2)
corr = np.zeros((n, n))
for i, ep1 in enumerate(mas1.skeleton_end_point_indices):
for j, ep2 in enumerate(mas2.skeleton_end_point_indices):
pd_mat = path_distance_matrix(ep1, mas1, ep2, mas2)
corr[i, j] = optimal_subsequence_bijection(pd_mat)
const = np.mean(corr)
if n > k:
corr[k:n, :] = const
_, gp = linear_sum_assignment(np.array(corr))
pairs = []
total_cost = 0
for i, j in enumerate(gp):
if i < len(mas1.skeleton_end_point_indices):
gi = mas1.skeleton_end_point_indices[i]
gj = mas2.skeleton_end_point_indices[j]
total_cost += corr[i, j]
pairs.append((gi, gj))
fig, ax = plt.subplots(2, 2, sharex=True, sharey=True)
fig.set_size_inches((9.6, 7.2))
ax[0, 0].scatter(end_points1[:, 0], end_points1[:, 1], c="b")
ax[0, 0].axis('off')
ax[0, 1].scatter(end_points2[:, 0], end_points2[:, 1], c="r")
ax[0, 1].axis('off')
gp1, gp2 = map(np.array, (g_pts, gprime_pts))
ax[1, 0].scatter(gp1[:, 0], gp1[:, 1])
ax[1, 0].axis('off')
ax[1, 1].scatter(gp2[:, 0], gp2[:, 1])
ax[1, 1].axis('off')
for pt in end_points1:
ax[0, 0].annotate(str(mas1.medial_axis_point_idx_map[tuple(pt)]), pt)
for pt in end_points2:
ax[0, 1].annotate(str(mas2.medial_axis_point_idx_map[tuple(pt)]), pt)
end = timer()
plt.suptitle(str(pairs))
plt.show()
print(f"Total Cost: {total_cost}")
print(f"Time taken = {round(end - start, 2)}")
def select_ref_images():
for file in Path("shapes").glob("*1.txt"):
if "11" not in file.name:
plt.rcParams["figure.figsize"] = (9.6, 7.2)
plt.figure(num=file.stem)
pts = extract_points_from_file(str(file))
pts = np.array(pts)
plt.scatter(pts[:, 0], pts[:, 1])
plt.title(file.name)
plt.gca().set_xlim([-1, 11])
plt.gca().set_ylim([-1, 11])
plt.show()
def match_shape(query_image="shapes/camel/camel_2.txt"):
query_pts = extract_points_from_file(query_image)
query_skeleton = MedialAxisTransformer.from_boundary_points(query_pts)
match_score = {}
ref_files = [file for file in Path(
"reference_shapes/all_shapes").glob("*.txt")]
ref_pts = list(map(extract_points_from_file, ref_files))
ref_skeletons = list(map(
MedialAxisTransformer.from_boundary_points, ref_pts))
fargs = list(zip(ref_skeletons, [file.stem for file in ref_files]))
for skel, skel_name in tqdm(fargs):
try:
img_class, score = compare_skeletons(
query_skeleton, skel, skel_name)
except Exception as e:
e
continue
match_score[img_class] = score
imclasses = list(match_score.keys())
scores = np.array(list(match_score.values()))
exp_scores = np.power(np.euler_gamma, scores)
probs = exp_scores / np.sum(exp_scores)
# best_match = imclasses[np.argmax(probs)]
print(f"Best matches for {Path(query_image).stem}")
for ic, pr in zip(imclasses, probs):
match_score[ic] = round(pr * 100, 2)
top_5_matches = {k: n for k, n in sorted(
match_score.items(), key=lambda x: x[1], reverse=True)[:5]}
print(json.dumps(top_5_matches, indent="\t"))
if __name__ == "__main__":
# main2(if1, if2)
match_shape()