# Testing basic functions of Motion Clouds

## Motion Clouds: raw principles¶

Motion Clouds are synthesized textures which aim at having similar characteristics as natural images but with controlled parameters. There are many ways to achieve these results and this notebook aims at showing that different procedures from different communities (neurioscience, modelling, computer vision, ...) may produce similar results.

In [1]:
import numpy as np
np.set_printoptions(precision=3, suppress=True)
import pylab
import matplotlib.pyplot as plt
%matplotlib inline


### Using Fourier ("official Motion Clouds")¶

In [2]:
import MotionClouds as mc
fx, fy, ft = mc.get_grids(mc.N_X, mc.N_Y, mc.N_frame)


### Using mixtures of images¶

In [3]:
from scipy.misc import face
lena = face()
print(lena.shape)
lena = lena[:, (1024-768):, :].mean(axis=-1)
print(lena.shape)
lena -= lena.mean()
lena /= lena.std()
print(lena.shape)

(768, 1024, 3)
(768, 768)
(768, 768)

In [4]:
plt.imshow(lena, cmap=plt.cm.gray)

Out[4]:
<matplotlib.image.AxesImage at 0x103200d68>
In [5]:
lena.shape

Out[5]:
(768, 768)
In [6]:
lena[0, :]

Out[6]:
array([ 0.723,  0.824,  1.025,  1.132,  0.895,  0.45 ,  0.159,  0.1  ,
-0.185, -0.292, -0.392, -0.339, -0.143,  0.124,  0.343,  0.45 ,
0.907,  1.405,  1.529,  1.138,  0.444, -0.446, -0.908, -0.736,
0.011,  0.367,  0.402, -0.114, -0.47 , -0.238,  0.26 ,  0.58 ,
0.883,  0.491,  0.064, -0.096,  0.011,  0.171,  0.171,  0.1  ,
0.474,  0.349,  0.082, -0.292, -0.665, -0.932, -1.075, -1.11 ,
-0.499, -0.214,  0.106,  0.207,  0.064, -0.131, -0.22 , -0.22 ,
-0.315, -0.327, -0.339, -0.297, -0.22 , -0.161, -0.137, -0.161,
0.07 , -0.048, -0.137, -0.226, -0.155,  0.201,  0.438,  0.367,
0.248,  0.296,  0.402,  0.539,  0.646,  0.663,  0.58 ,  0.527,
0.527,  0.402,  0.136, -0.025,  0.136,  0.385,  0.26 , -0.06 ,
-0.007, -0.042,  0.171,  0.325, -0.066, -0.742, -0.956, -0.725,
-0.558, -0.416, -0.452, -0.63 , -0.665, -0.505, -0.416, -0.517,
-0.713, -0.73 , -0.819, -0.926, -0.897, -0.879, -1.039, -1.252,
-1.235, -0.505,  0.189,  0.029, -0.576, -0.713, -0.375, -0.143,
-0.197, -0.398, -0.487, -0.452, -0.398, -0.22 , -0.203, -0.381,
-0.096, -0.078, -0.042, -0.203, -0.47 , -0.487, -0.452, -0.558,
-0.416, -0.381, -0.416, -0.363, -0.007,  0.313,  0.064, -0.434,
-0.529, -0.458, -0.386, -0.28 , -0.173, -0.155, -0.297, -0.475,
-0.262, -0.369, -0.44 , -0.386, -0.262, -0.084,  0.183,  0.45 ,
0.242, -0.09 , -0.321, -0.321, -0.339, -0.464, -0.446, -0.274,
-0.114,  0.242,  0.58 ,  0.628,  0.432,  0.219,  0.076,  0.005,
-0.072, -0.41 , -0.819, -0.98 , -0.819, -0.535, -0.41 , -0.41 ,
-0.161,  0.319,  0.462, -0.09 , -0.784, -0.908, -0.428,  0.07 ,
0.165,  0.076, -0.037, -0.037, -0.066, -0.226, -0.042,  0.438,
0.367,  0.171, -0.137, -0.155,  0.219,  0.598,  0.918,  1.239,
1.156,  0.978,  0.711,  0.497,  0.444,  0.462,  0.402,  0.26 ,
0.242,  0.1  , -0.149, -0.523, -0.914, -0.986, -0.487,  0.118,
0.141,  0.497,  0.681,  0.752,  0.764,  0.414,  0.112,  0.195,
0.195,  0.064,  0.005, -0.114, -0.274, -0.173, -0.001,  0.017,
0.094,  0.165,  0.219,  0.13 , -0.066, -0.155, -0.013,  0.219,
0.521,  0.29 ,  0.094,  0.183,  0.503,  0.752,  0.752,  0.628,
-0.019, -0.001,  0.248,  0.782,  1.227,  1.227,  0.764,  0.296,
-0.096,  0.242,  0.847,  1.452,  1.595,  1.221,  0.669,  0.313,
0.646,  1.108,  1.28 ,  0.96 ,  0.569,  0.396,  0.628,  1.037,
1.405,  1.28 ,  0.77 ,  0.278,  0.207,  0.248,  0.201,  0.183,
-0.084, -0.031,  0.379,  0.788,  0.966,  1.126,  0.913,  0.308,
0.361,  0.895,  1.268,  1.322,  1.268,  0.984,  0.61 ,  0.432,
0.527,  0.491,  0.343,  0.213,  0.302,  0.592,  0.776,  0.829,
0.604,  0.337,  0.159,  0.373,  0.776,  0.936,  0.776,  0.527,
0.426,  0.551,  0.853,  1.162,  1.179,  0.841,  0.48 ,  0.284,
0.622,  0.408,  0.296,  0.509,  0.889,  1.12 ,  1.031,  0.853,
0.515,  0.497,  0.337, -0.001, -0.297, -0.286, -0.037,  0.224,
0.883,  0.966,  1.031,  1.049,  0.996,  0.705,  0.13 , -0.422,
-0.019,  0.017, -0.001, -0.072, -0.019,  0.195,  0.355,  0.408,
0.462,  0.764,  0.996,  0.907,  0.675,  0.515,  0.462,  0.444,
0.254,  0.094, -0.084, -0.143, -0.072, -0.06 , -0.185, -0.363,
0.183,  0.521,  0.835,  0.907,  0.764,  0.515,  0.195, -0.037,
-0.096, -0.143, -0.131,  0.064,  0.396,  0.669,  0.628,  0.468,
0.355,  0.355,  0.408,  0.491,  0.438,  0.26 ,  0.094,  0.023,
0.011,  0.1  ,  0.1  , -0.001,  0.035,  0.189,  0.29 ,  0.254,
0.195,  0.213,  0.236,  0.254,  0.337,  0.408,  0.373,  0.313,
0.118, -0.007, -0.078, -0.025,  0.023,  0.041,  0.094,  0.195,
0.23 ,  0.213,  0.195,  0.195,  0.177,  0.118,  0.029, -0.06 ,
-0.078, -0.096, -0.078,  0.047,  0.159,  0.106, -0.09 , -0.274,
-0.452, -0.167,  0.136,  0.224,  0.171,  0.183,  0.219,  0.236,
-0.108, -0.09 , -0.037,  0.052,  0.141,  0.177,  0.177,  0.159,
-0.037, -0.179, -0.25 , -0.161, -0.09 , -0.125, -0.25 , -0.321,
-0.428, -0.357, -0.143,  0.047, -0.078, -0.363, -0.511, -0.493,
-0.381, -0.47 , -0.517, -0.428, -0.292, -0.238, -0.327, -0.452,
-0.452, -0.434, -0.416, -0.434, -0.434, -0.434, -0.398, -0.363,
-0.363, -0.381, -0.398, -0.47 , -0.541, -0.576, -0.612, -0.612,
-0.547, -0.529, -0.511, -0.493, -0.493, -0.511, -0.529, -0.529,
-0.653, -0.636, -0.618, -0.618, -0.636, -0.618, -0.582, -0.547,
-0.594, -0.63 , -0.689, -0.725, -0.742, -0.76 , -0.796, -0.814,
-0.814, -0.814, -0.814, -0.831, -0.861, -0.879, -0.897, -0.914,
-0.903, -0.92 , -0.938, -0.956, -0.938, -0.903, -0.849, -0.814,
-0.938, -0.938, -0.956, -0.974, -0.991, -1.009, -1.027, -1.045,
-1.009, -0.956, -0.831, -0.725, -0.653, -0.677, -0.748, -0.819,
-0.849, -0.849, -0.855, -0.837, -0.819, -0.766, -0.736, -0.695,
-0.855, -0.873, -0.873, -0.891, -0.867, -0.843, -0.796, -0.766,
-0.742, -0.73 , -0.683, -0.677, -0.671, -0.671, -0.647, -0.63 ,
-0.606, -0.564, -0.523, -0.446, -0.381, -0.345, -0.327, -0.309,
-0.333, -0.404, -0.517, -0.612, -0.683, -0.677, -0.636, -0.606,
-0.736, -0.689, -0.606, -0.529, -0.464, -0.41 , -0.327, -0.286,
-0.268, -0.179, -0.072,  0.029,  0.082,  0.165,  0.254,  0.349,
0.396,  0.361,  0.325,  0.325,  0.313,  0.284,  0.213,  0.147,
0.13 ,  0.141,  0.124,  0.106,  0.082,  0.082,  0.124,  0.195,
0.106, -0.535, -1.229, -1.478, -1.324, -1.027, -0.908, -0.956,
-0.855, -0.962, -1.152, -1.312, -1.407, -1.472, -1.49 , -1.508,
-1.407, -1.508, -1.596, -1.543, -1.43 , -1.359, -1.401, -1.478,
-1.223, -1.68 , -1.834, -1.531, -0.481,  0.468,  0.764,  0.646,
0.379, -0.297, -1.158, -1.561, -1.436, -1.098, -1.015, -1.14 ,
-1.057, -1.051, -1.051, -1.051, -1.063, -1.08 , -1.098, -1.098,
-1.039, -1.069, -1.069, -1.051, -1.027, -1.021, -1.027, -1.045,
-0.956, -0.956, -0.962, -0.944, -0.938, -0.932, -0.95 , -0.938,
-1.069, -1.08 , -1.08 , -1.092, -1.098, -1.098, -1.086, -1.086,
-1.158, -1.134, -1.128, -1.116, -1.104, -1.14 , -1.146, -1.163,
-1.152, -1.169, -1.205, -1.223, -1.223, -1.169, -1.134, -1.11 ,
-1.027, -0.974, -0.903, -0.867, -0.867, -0.903, -0.92 , -0.92 ,
-1.039, -0.997, -0.997, -1.075, -1.033, -0.873, -0.671, -0.576,
-0.309, -0.256, -0.292, -0.392, -0.475, -0.47 , -0.47 , -0.523,
-0.475, -0.458, -0.44 , -0.404, -0.327, -0.173, -0.007,  0.106,
0.171, -0.025, -0.191, -0.179,  0.035,  0.367,  0.752,  1.037,
0.954,  0.99 ,  0.972,  0.883,  0.901,  0.942,  0.913,  0.806,
0.752,  0.58 ,  0.302,  0.052, -0.054, -0.001,  0.177,  0.319])
In [7]:
def noise(image=lena):
for axis in [0, 1]:
image = np.roll(image, np.random.randint(image.shape[axis]), axis=axis)
return image

In [8]:
plt.imshow(noise(), cmap=plt.cm.gray)

Out[8]:
<matplotlib.image.AxesImage at 0x109532cc0>
In [9]:
plt.imshow(noise(), cmap=plt.cm.gray)

Out[9]:
<matplotlib.image.AxesImage at 0x109f67b38>

### Using ARMA processes¶

Now, we define the ARMA process as an averaging process with a certain time constant $\tau=30.$ (in frames).

In [10]:
def ARMA(image, tau=30.):
image = (1 - 1/tau)* image + 1/tau * noise()
return image


initializing

In [11]:
image = ARMA(lena)
plt.imshow(image, cmap=plt.cm.gray)

Out[11]:
<matplotlib.image.AxesImage at 0x10cea6390>
In [12]:
for _ in range(1000): image = ARMA(image)
plt.imshow(image, cmap=plt.cm.gray)

Out[12]:
<matplotlib.image.AxesImage at 0x10ddb2160>