def test_barcode():
N = 200
N_s = 50
k = int(N/5)
w = .5
r = .6
vertices = get_image('C', 1, size=200, sample_size=N)[0]
tangents = hm.find_tangents(vertices, k)
curve = hm.get_curve(vertices, k = k, w = w)
sparse = sparse_sample(vertices, N_s)
v_s = vertices[sparse,:]
t_s = tangents[sparse]
c_s = curve[sparse]
edges = hm.get_rips_complex(v_s, tangents=t_s, k = k, w = w, r = r)
f, ax = plt.subplots(1,2)
plt_edges, plt_barcode = ax
plt_edges.scatter(v_s[:,0], v_s[:,1], marker = '.', c=c_s, s=200)
for edge in edges:
plt_edges.plot(v_s[edge, 0], v_s[edge, 1], lw = 1, c = 'blue')
plt_edges.invert_yaxis()
ordered_simplices, curve_lookup = hm.get_ordered_simplices(v_s, c_s, edges)
barcode = bc.get_barcode(ordered_simplices, degree_values=c_s[np.argsort(c_s)])
b0 = barcode[barcode[:,2] == 0, :]
bc.plot_barcode_gant(b0, plt=plt_barcode)
plt.show()
def image_preprocessing():
N = 500
N_s = 30
sample, vertices, image, original = get_image('A', 1, size=200, sample_size=N)
f, ax = plt.subplots(2,2, gridspec_kw = {'width_ratios':[1,1]})
ax[0][0].imshow(original, cmap='binary')
ax[0][0].set_xticks([])
ax[0][0].set_yticks([])
ax[0][0].set_title("Original Image")
ax[0][1].imshow(image, cmap='binary')
ax[0][1].set_xticks([])
ax[0][1].set_yticks([])
ax[0][1].set_title("Scaled, Cropped & Thinned")
ax[1][0].scatter(sample[:,0], sample[:,1], marker='.')
ax[1][0].invert_yaxis()
ax[1][0].set_xticks(np.arange(-1, 1.1))
ax[1][0].set_yticks(np.arange(-1, 1.1))
ax[1][0].set_title('Random Sampling')
sparse_idx = sparse_sample(sample, N_s)
sparse = sample[sparse_idx, :]
ax[1][1].scatter(sparse[:,0], sparse[:,1], marker='.')
ax[1][1].invert_yaxis()
ax[1][1].set_xticks(np.arange(-1, 1.1))
ax[1][1].set_yticks(np.arange(-1, 1.1))
ax[1][1].set_title('Downsampled')
plt.tight_layout()
plt.show()
def delaunay_complex_2d(vertices, N_s):
sparse = sparse_sample(vertices, N_s)
landmarks = vertices[sparse, :]
tri = spatial.Delaunay(landmarks)
edges = np.concatenate(
[tri.simplices[:, :2], tri.simplices[:, 1:], tri.simplices[:, [2, 0]]],
axis=0)
return edges, landmarks, sparse
def witness_complex_2d(vertices, N_s):
sparse = sparse_sample(vertices, N_s)
landmarks = vertices[sparse, :]
D = spatial.distance.cdist(vertices, landmarks)
closest = np.argsort(D, axis=1)
edges = closest[:, :2]
edges = remove_duplicate_edges(edges)
return edges, landmarks, sparse
def test_sparse_sampling():
N = 500
vertices = get_image_skeleton('P', 0, size=200, sample_size=N)[0]
plt.scatter(vertices[:,0], vertices[:,1], marker = '.', c='#eeeeee')
sparse = sparse_sample(vertices, 50)
plt.scatter(sparse[:,0], sparse[:,1], marker='+', c='blue')
plt.show()
def get_all_rips_2d(vertices, N_s, k, w, r):
tangents = find_tangents(vertices, k)
curve = find_curve(vertices, tangents, k, w)
sparse = sparse_sample(vertices, N_s)
v_s = vertices[sparse, :]
t_s = tangents[sparse]
c_s = curve[sparse]
edges = rips_complex_2d(v_s, r=r)
return v_s, t_s, c_s, edges
def witness_complex_4d(vertices, tangents, w, N_s):
tspace = get_tspace(vertices, tangents, w)
sparse = sparse_sample(tspace, N_s)
landmarks = tspace[sparse, :]
D = spatial.distance.cdist(tspace, landmarks)
closest = np.argsort(D, axis=1)
edges = closest[:, :2]
edges = remove_duplicate_edges(edges)
return edges, landmarks, sparse
def delaunay_complex_4d(vertices, tangents, w, N_s):
tspace = get_tspace(vertices, tangents, w)
sparse = sparse_sample(tspace, N_s)
landmarks = tspace[sparse, :]
tri = spatial.Delaunay(landmarks)
edges = np.concatenate([
tri.simplices[:, 0:2], tri.simplices[:, 1:3], tri.simplices[:, 2:4],
tri.simplices[:, 3:5], tri.simplices[:, [4, 0]]
],
axis=0)
return edges, landmarks, sparse
def test_edges():
N = 200
N_s = 50
k = int(N/5)
w = .5
r = .6
vertices = get_image('A', 2, size=200, sample_size=N)[0]
tangents = hm.find_tangents(vertices, k)
sparse = sparse_sample(vertices, N_s)
v_s = vertices[sparse,:]
t_s = tangents[sparse]
edges = hm.get_rips_complex(v_s, tangents=t_s, k = k, w = w, r = r)
plot_edges(v_s, edges, plt)
plt.gca().invert_yaxis()
plt.show()
def test_delaunay():
N = 200
N_s = 50
k = int(N/5)
w = .5
r = .6
vertices = get_image('B', 2, size=200, sample_size=N)[0]
sparse = sparse_sample(vertices, N_s)
v_s = vertices[sparse,:]
edges = hm.delaunay_complex_2d(v_s)
plt.scatter(vertices[:,0], vertices[:,1], marker='.', c='gray')
plt.scatter(v_s[:,0], v_s[:,1], marker='+', c='red')
for edge in edges:
plt.plot(v_s[edge,0], v_s[edge,1], lw = 1, c = 'blue')
plt.gca().invert_yaxis()
plt.show()
def test_tangent():
N = 200
k = int(N/5)
vertices, all_points, img, _ = get_image('B', 0, size=200, sample_size=N)
tspace = hm.get_tangents(vertices, k = k)
sparse = sparse_sample(vertices, 50)
plot_tangent_space_2d(tspace[sparse,:])
# plot_tangent_space_3d(tspace[sparse,:])
# f, ax = plt.subplots(1, 3)
# ax[0].scatter(vertices[:,0], vertices[:,1], marker='.', c=tspace[:,3])
# ax[0].invert_yaxis()
# idx = np.argwhere(tspace[:,3] < 0.25).flatten()
# print(idx.shape)
# v = vertices[idx,:]
# print(v.shape)
# ax[1].scatter(v[:,0], v[:,1], marker='.')
# ax[1].invert_yaxis()
plt.show()
return
def test_filtration():
N = 200
N_s = 50
k = int(N/5)
w = .5
r = .6
vertices = get_image('A', 2, size=200, sample_size=N)[0]
tangents = hm.find_tangents(vertices, k)
curve = hm.get_curve(vertices, k = k, w = w)
sparse = sparse_sample(vertices, N_s)
v_s = vertices[sparse,:]
t_s = tangents[sparse]
c_s = curve[sparse]
edges = hm.get_rips_complex(v_s, tangents=t_s, k = k, w = w, r = r)
simplices, curve_lookup = hm.get_ordered_simplices(v_s, c_s, edges)
max_degree = np.max(simplices[:,3])
degree_step = math.ceil(max_degree/16.0)
verts_degree = simplices[simplices[:,4] == 0,0:3]
f, ax = plt.subplots(4,4, sharex=True, sharey=True)
ax[0][0].invert_yaxis()
for i in range(4):
for j in range(4):
idx = i*4 + j
deg = min(idx * degree_step, max_degree)
plot_simplices(simplices, deg, v_s, ax[i][j])
ax[i][j].set_title("κ={0:1.4f}".format(curve[verts_degree[deg,0]]), fontsize=8)
ax[i][j].set_xticklabels([])
ax[i][j].set_yticklabels([])
plt.tight_layout()
plt.figure()
barcode = bc.get_barcode(simplices, degree_values=c_s[np.argsort(c_s)])
b0 = barcode[barcode[:,2] == 0, :]
bc.plot_barcode_gant(b0, plt=plt)
plt.show()