1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
|
# Copyright (c) DataLab Platform Developers, BSD 3-Clause license, see LICENSE file.
"""
Geometric analysis module
-------------------------
This module provides functions for geometric analysis of images, including
centroid detection, shape fitting, and spatial measurements.
Features include:
- Various centroid detection algorithms (Fourier-based, projected profile,
automatic selection)
- Enclosing circle calculation for thresholded regions
- Radial profile extraction around specified centers
- Absolute level calculation from relative thresholds
These tools support precise geometric measurements and shape analysis
for scientific and technical image analysis applications.
"""
from __future__ import annotations
from typing import Literal
import numpy as np
from skimage import measure
from sigima.tools.checks import check_2d_array
from sigima.tools.image.preprocessing import get_absolute_level
@check_2d_array
def get_centroid_fourier(data: np.ndarray) -> tuple[float, float]:
"""Return image centroid using Fourier algorithm
Args:
data: Input data
Returns:
Centroid coordinates (row, col)
"""
# Fourier transform method as discussed by Weisshaar et al.
# (http://www.mnd-umwelttechnik.fh-wiesbaden.de/pig/weisshaar_u5.pdf)
rows, cols = data.shape
if rows == 1 or cols == 1:
return 0, 0
i = np.arange(0, rows).reshape(1, rows)
sin_a = np.sin((i - 1) * 2 * np.pi / (rows - 1)).T
cos_a = np.cos((i - 1) * 2 * np.pi / (rows - 1)).T
j = np.arange(0, cols).reshape(cols, 1)
sin_b = np.sin((j - 1) * 2 * np.pi / (cols - 1)).T
cos_b = np.cos((j - 1) * 2 * np.pi / (cols - 1)).T
a = np.nansum((cos_a * data))
b = np.nansum((sin_a * data))
c = np.nansum((data * cos_b))
d = np.nansum((data * sin_b))
rphi = (0 if b > 0 else 2 * np.pi) if a > 0 else np.pi
cphi = (0 if d > 0 else 2 * np.pi) if c > 0 else np.pi
if a * c == 0.0:
return 0, 0
row = (np.arctan(b / a) + rphi) * (rows - 1) / (2 * np.pi) + 1
col = (np.arctan(d / c) + cphi) * (cols - 1) / (2 * np.pi) + 1
row = np.nan if row is np.ma.masked else row
col = np.nan if col is np.ma.masked else col
return row, col
@check_2d_array
def get_projected_profile_centroid(
data: np.ndarray, smooth_ratio: float = 1 / 40, method: str = "median"
) -> tuple[float, float]:
"""
Estimate centroid from smoothed 1D projections.
Args:
data: 2D image array
smooth_ratio: Ratio of smoothing window size (default: 1/40)
method: 'median' (default) or 'barycenter'
Returns:
(y, x) coordinates
"""
x_profile = data.sum(axis=0)
y_profile = data.sum(axis=1)
window_size = max(1, int(min(data.shape) * smooth_ratio))
kernel = np.ones(window_size) / window_size
x_profile = np.convolve(x_profile, kernel, mode="same")
y_profile = np.convolve(y_profile, kernel, mode="same")
x_profile -= np.min(x_profile)
y_profile -= np.min(y_profile)
if method == "median":
x_integral = np.cumsum(x_profile)
y_integral = np.cumsum(y_profile)
x_center = np.interp(
0.5 * x_integral[-1], x_integral, np.arange(len(x_integral))
)
y_center = np.interp(
0.5 * y_integral[-1], y_integral, np.arange(len(y_integral))
)
elif method == "barycenter": # pragma: no cover
# (ignored for coverage because median gives better results)
x_center = np.sum(np.arange(len(x_profile)) * x_profile) / np.sum(x_profile)
y_center = np.sum(np.arange(len(y_profile)) * y_profile) / np.sum(y_profile)
else:
raise ValueError("Unknown method: choose 'median' or 'barycenter'")
return float(y_center), float(x_center)
@check_2d_array
def get_centroid_auto(
data: np.ndarray,
return_method: bool = False,
) -> tuple[float, float] | tuple[float, float, Literal["fourier", "skimage"]]:
"""
Automatically select the most reliable centroid estimation method:
- Prefer Fourier if it is more consistent with the projected median.
- Fallback to scikit-image centroid if Fourier is less coherent.
Args:
data: 2D image array.
return_method: If True, also return the name of the selected method.
Returns:
(row, col): Estimated centroid coordinates (float).
Optionally, the selected method as string: "fourier" or "skimage".
"""
try:
row_f, col_f = get_centroid_fourier(data)
except Exception: # pylint: disable=broad-except
row_f, col_f = float("nan"), float("nan")
row_m, col_m = get_projected_profile_centroid(data, method="median")
row_s, col_s = measure.centroid(data)
dist_f = np.hypot(row_f - row_m, col_f - col_m)
dist_s = np.hypot(row_s - row_m, col_s - col_m)
if not (np.isnan(row_f) or np.isnan(col_f)) and dist_f < dist_s:
result = (row_f, col_f)
method = "fourier"
else:
result = (row_s, col_s)
method = "skimage"
return result + (method,) if return_method else result
@check_2d_array(non_constant=True)
def get_enclosing_circle(
data: np.ndarray, level: float = 0.5
) -> tuple[int, int, float]:
"""Return (x, y, radius) for the circle contour enclosing image
values above threshold relative level (.5 means FWHM)
Args:
data: Input data
level: Relative level (default: 0.5)
Returns:
A tuple (x, y, radius)
Raises:
ValueError: No contour was found
"""
data_th = data.copy()
data_th[data <= get_absolute_level(data, level)] = 0.0
contours = measure.find_contours(data_th)
model = measure.CircleModel()
result = None
max_radius = 1.0
for contour in contours:
if model.estimate(contour):
yc, xc, radius = model.params
if radius > max_radius:
result = (int(xc), int(yc), radius)
max_radius = radius
if result is None:
raise ValueError("No contour was found")
return result
|
