This is an example using scopyon (https://scopyon.readthedocs.io/).
In [1]:
import scopyon
Set the configuration first.
In [2]:
config = scopyon.DefaultConfiguration()
config.default.magnification = 360.0
config.default.detector.exposure_time = 33.0e-3 # second
In [3]:
# config.environ.processes = 20
A field of microscopic view could be calculated as follows:
In [4]:
pixel_length = config.default.detector.pixel_length / config.default.magnification
L_2 = config.default.detector.image_size[0] * pixel_length * 0.5
Randomly generate positions of 1000 molecules on membrane. The diffusion rate D is 0.1e-12.
In [5]:
import numpy
rng = numpy.random.RandomState(1)
num_frames = 50
duration = config.default.detector.exposure_time * 5
t = numpy.linspace(0, duration, num_frames + 1)
In [6]:
N = 1000
D = 0.1e-12 # m ** 2 / s
inputs = scopyon.sample_inputs(t, N=N, lower=-L_2, upper=+L_2, ndim=2, D=D, rng=rng)
scopyon.form_image generates a single image from the given inputs.
In [7]:
# import logging
# logging.basicConfig(level=logging.INFO)
In [8]:
img1 = scopyon.form_image(inputs, config=config, rng=rng)
In [9]:
spots1 = scopyon.analysis.spot_detection(
img1.as_array(), min_sigma=1, max_sigma=4, threshold=40.0, overlap=0.5)
In [10]:
r = 6
shapes = [dict(x=spot[0], y=spot[1], sigma=r, color='red')
for spot in spots1]
img1.show(shapes=shapes)
Take another image at time 't=0.1'.
In [11]:
img2 = scopyon.form_image(inputs, start_time=100e-3, config=config, rng=rng)
In [12]:
spots2 = scopyon.analysis.spot_detection(
img2.as_array(), min_sigma=1, max_sigma=4, threshold=40.0, overlap=0.5)
Compare two images and choose the closest point for each points.
In [13]:
closest = []
for spot in spots1:
distance = spots2[:, : 2] - spot[: 2]
idx = (distance ** 2).sum(axis=1).argmin()
closest.extend(distance[idx])
closest = numpy.array(closest)
In [14]:
closest
Out[14]:
A diffusion rate is estimated based on the average of closest distances (displacements). The units below is a square of pixels per second.
In [15]:
D_ = numpy.average(closest ** 2) / (2 * duration)
D_
Out[15]:
Rescaled into physical units (square meters per second).
In [16]:
D_ * (pixel_length ** 2)
Out[16]:
Plot data with probability densities.
In [17]:
import plotly.graph_objects as go
from scipy.stats import norm
fig = go.Figure()
fig.add_trace(go.Histogram(x=closest, histnorm='probability density', name='Samples'))
x = numpy.linspace(closest.min(), closest.max(), 101)
y = norm.pdf(x, scale=numpy.sqrt(2 * D_ * duration))
fig.add_trace(go.Scatter(x=x, y=y, mode='lines', name='Estimated'))
y = norm.pdf(x, scale=numpy.sqrt(2 * (D / (pixel_length ** 2)) * duration))
fig.add_trace(go.Scatter(x=x, y=y, mode='lines', name='True'))
fig.show()