The Center for Nanophase Materials Science and The Institute for Functional Imaging for Materials
Oak Ridge National Laboratory
1/19/2017
Advanced Structural and Chemical Imaging -
https://ascimaging.springeropen.com/articles/10.1186/s40679-018-0052-y
This Jupyter notebook uses pycroscopy to analyze Band Excitation data. We request you to reference the following papers if you use this notebook for your research:
This is a Jupyter Notebook - it contains text and executable code cells
. To learn more about how to use it, please see this video. Please see the image below for some basic tips on using this notebook.
Image courtesy of Jean Bilheux from the neutron imaging GitHub repository.
Note: This notebook was written for the pycroscopy version listed below and is not guaranteed to work on past or future versions of the package
pycroscopy
version: 0.59.8
If you have a different version of pycroscopy
installed, you may consider using the notebook as is and accept the possibility of errors. The cell below will attempt to install the correct versions of the packages. However, if you experience trouble, uninstall the existing version of pycroscopy and install the required version above by executing the following commands in a terminal (Linux / MacOS) / Anaconda prompt (Windows):
pip uninstall pycroscopy
pip install -I pycroscopy==0.59.8
# Make sure needed packages are installed and up-to-date
import sys
!conda install --yes --prefix {sys.prefix} numpy scipy matplotlib scikit-learn Ipython ipywidgets h5py
!{sys.executable} -m pip install -U --no-deps pycroscopy==0.59.8
# Import necessary libraries:
# Ensure python 3 compatibility
from __future__ import division, print_function, absolute_import
# General utilities:
import os
from time import time
from scipy.misc import imsave
# Computation:
import numpy as np
import h5py
from skimage import measure
from scipy.cluster.hierarchy import linkage, dendrogram
from scipy.spatial.distance import pdist
from sklearn.cluster import KMeans
# Visualization:
import matplotlib.pyplot as plt
import matplotlib.patches as patches
from mpl_toolkits.axes_grid1 import make_axes_locatable
from IPython.display import display, HTML
import ipywidgets as widgets
from mpl_toolkits.axes_grid1 import ImageGrid
# Import pyUSID
import pyUSID as usid
# Finally, pycroscopy itself
sys.path.append('..')
import pycroscopy as px
# Make Notebook take up most of page width
display(HTML(data="""
<style>
div#notebook-container { width: 95%; }
div#menubar-container { width: 65%; }
div#maintoolbar-container { width: 99%; }
</style>
"""))
# set up notebook to show plots within the notebook
% matplotlib notebook
This notebook performs some functional fitting whose duration can be substantially decreased by using more memory and CPU cores. We have provided default values below but you may choose to change them if necessary.
max_mem = 1024*8 # Maximum memory to use, in Mbs. Default = 8192
max_cores = None # Number of logical cores to use in fitting. None uses all but 2 available cores.
image_path = px.io_utils.file_dialog('*.png *PNG *TIFF * TIF *tif *tiff *BMP *bmp','Images')
print('Working on: \n{}'.format(image_path))
folder_path, file_name = os.path.split(image_path)
base_name, _ = os.path.splitext(file_name)
Convert the source image file into a pycroscopy compatible hierarchical data format (HDF or .h5) file. This simple translation gives you access to the powerful data functions within pycroscopy
# Check if an HDF5 file with the chosen image already exists.
# Only translate if it does not.
h5_path = os.path.join(folder_path, base_name+'.h5')
need_translation = True
if os.path.exists(h5_path):
try:
h5_file = h5py.File(h5_path, 'r+')
h5_raw = h5_file['Measurement_000']['Channel_000']['Raw_Data']
need_translation = False
print('HDF5 file with Raw_Data found. No need to translate.')
except KeyError:
print('Raw Data not found.')
else:
print('No HDF5 file found.')
if need_translation:
# Initialize the Image Translator
tl = px.ImageTranslator()
# create an H5 file that has the image information in it and get the reference to the dataset
h5_raw = tl.translate(image_path)
# create a reference to the file
h5_file = h5_raw.file
print('HDF5 file is located at {}.'.format(h5_file.filename))
The file contents are stored in a tree structure, just like files on a contemporary computer.
The data is stored as a 2D matrix (position, spectroscopic value) regardless of the dimensionality of the data.
In the case of these 2D images, the data is stored as a N x 1 dataset
The main dataset is always accompanied by four ancillary datasets that explain the position and spectroscopic value of any given element in the dataset. In the case of the 2d images, the positions will be arranged as row0-col0, row0-col1.... row0-colN, row1-col0.... The spectroscopic information is trivial since the data at any given pixel is just a scalar value
print('Datasets and datagroups within the file:')
px.hdf_utils.print_tree(h5_file)
print('\nThe main dataset:')
print(h5_file['/Measurement_000/Channel_000/Raw_Data'])
print('\nThe ancillary datasets:')
print(h5_file['/Measurement_000/Channel_000/Position_Indices'])
print(h5_file['/Measurement_000/Channel_000/Position_Values'])
print(h5_file['/Measurement_000/Channel_000/Spectroscopic_Indices'])
print(h5_file['/Measurement_000/Channel_000/Spectroscopic_Values'])
print('\nMetadata or attributes in a datagroup')
for key in h5_file['/Measurement_000'].attrs:
print('{} : {}'.format(key, h5_file['/Measurement_000'].attrs[key]))
# Initialize the windowing class
iw = px.processing.ImageWindow(h5_raw, max_RAM_mb=max_mem)
# grab position indices from the H5 file
h5_pos = h5_raw.h5_pos_inds
# determine the image size:
num_x, num_y = h5_raw.pos_dim_sizes
# extract figure data and reshape to proper numpy array
raw_image_mat = np.reshape(h5_raw[()], [num_x,num_y]);
Though the source file is actually grayscale image, we will visualize it using a color-scale
fig, axis = plt.subplots(figsize=(10,10))
px.plot_utils.plot_map(axis, raw_image_mat, cmap=px.plot_utils.cmap_jet_white_center())
axis.set_title('Raw Image', fontsize=16)
usid.jupyter_utils.save_fig_filebox_button(fig, 'Raw_Image.png')
num_peaks = 2
win_size , psf_width = iw.window_size_extract(num_peaks, save_plots=False, show_plots=True)
print('Window size = {}'.format(win_size))
# Uncomment this line if you need to manually specify a window size
# win_size = 32
# plot a single window
row_offset = int(0.5*(num_x-win_size))
col_offset = int(0.5*(num_y-win_size))
fig, axis = plt.subplots(figsize=(5, 5))
px.plot_utils.plot_map(axis, raw_image_mat[row_offset:row_offset+win_size,
col_offset:col_offset+win_size],
cmap=px.plot_utils.cmap_jet_white_center())
# the result should be about the size of a unit cell
# if it is the wrong size, just choose on manually by setting the win_size
axis.set_title('Example window', fontsize=18)
usid.jupyter_utils.save_fig_filebox_button(fig, 'Example_window.png')
We do this by sliding a small window across the image. This artificially baloons the size of the data.
windowing_parms = {
'fft_mode': None, # Options are None, 'abs', 'data+abs', or 'complex'
'win_x': win_size,
'win_y': win_size,
'win_step_x': 1,
'win_step_y': 1,
}
win_parms_copy = windowing_parms.copy()
if windowing_parms['fft_mode'] is None:
win_parms_copy['fft_mode'] = 'data'
h5_wins_grp = px.hdf_utils.check_for_old(h5_raw, 'Windowing',
win_parms_copy)
if h5_wins_grp==[]:
print('Windows either do not exist or were created with different parameters')
t0 = time()
h5_wins = iw.do_windowing(win_x=windowing_parms['win_x'],
win_y=windowing_parms['win_y'],
save_plots=False,
show_plots=False,
win_fft=windowing_parms['fft_mode'])
print( 'Windowing took {} seconds.'.format(round(time()-t0, 2)))
else:
print('Taking existing windows dataset')
h5_wins = px.PycroDataset(h5_wins_grp[0]['Image_Windows'])
print('\nRaw data was of shape {} and the windows dataset is now of shape {}'.format(h5_raw.shape, h5_wins.shape))
print('Now each position (window) is descibed by a set of pixels')
# Peek at a few random windows
num_rand_wins = 9
rand_positions = np.random.randint(0, high=h5_wins.shape[0], size=num_rand_wins)
example_wins = np.zeros(shape=(windowing_parms['win_x'], windowing_parms['win_y'], num_rand_wins), dtype=np.float32)
for rand_ind, rand_pos in enumerate(rand_positions):
example_wins[:, :, rand_ind] = np.reshape(h5_wins[rand_pos], (windowing_parms['win_x'], windowing_parms['win_y']))
fig, axes = px.plot_utils.plot_map_stack(example_wins.T, title='Example Windows', cmap=px.plot_utils.cmap_jet_white_center(),
subtitle=['Window # ' + str(win_pos) for win_pos in rand_positions], title_yoffset=0.93)
usid.jupyter_utils.save_fig_filebox_button(fig, 'Example_Windows.png')
SVD decomposes data (arranged as position x value) into a sequence of orthogonal components arranged in descending order of variance. The first component contains the most significant trend in the data. The second component contains the next most significant trend orthogonal to all previous components (just the first component). Each component consists of the trend itself (eigenvector), the spatial variaion of this trend (eigenvalues), and the variance (statistical importance) of the component.
Since the data consists of the large sequence of small windows, SVD essentially compares every single window with every other window to find statistically significant trends in the image
# check to make sure number of components is correct:
num_comp = 128
num_comp = min(num_comp,
min(h5_wins.shape)*len(h5_wins.dtype))
proc = px.processing.SVD(h5_wins, num_components=num_comp)
if proc.duplicate_h5_groups==[]:
print('SVD not performed with these parameters')
h5_svd = proc.compute()
else:
print('Taking existing results!')
h5_svd = proc.duplicate_h5_groups
h5_U = h5_svd['U']
h5_S = h5_svd['S']
h5_V = h5_svd['V']
# extract parameters of the SVD results
h5_pos = iw.hdf.file[h5_wins.attrs['Position_Indices']]
num_rows = len(np.unique(h5_pos[:, 0]))
num_cols = len(np.unique(h5_pos[:, 1]))
num_comp = h5_S.size
print("There are a total of {} components.".format(num_comp))
print('\nRaw data was of shape {} and the windows dataset is now of shape {}'.format(h5_raw.shape, h5_wins.shape))
print('Now each position (window) is descibed by a set of pixels')
plot_comps = 49
U_map_stack = np.reshape(h5_U[:, :plot_comps], [num_rows, num_cols, -1])
V_map_stack = np.reshape(h5_V, [num_comp, win_size, win_size])
V_map_stack = np.transpose(V_map_stack,(2,1,0))
The plot below shows the variance or statistical significance of the SVD components. The first few components contain the most significant information while the last few components mainly contain noise.
Note also that the plot below is a log-log plot. The importance of each subsequent component drops exponentially.
fig_S, ax_S = px.plot_utils.plot_scree(h5_S[()]);
usid.jupyter_utils.save_fig_filebox_button(fig_S, 'Scree_of_Windows.png')
The V dataset contains the end members for each component
for field in V_map_stack.dtype.names:
fig_V, ax_V = px.plot_utils.plot_map_stack(V_map_stack[:,:,:][field].T, title='', subtitle='Vector-'+field, num_comps=plot_comps,
color_bar_mode='each', cmap=px.plot_utils.cmap_jet_white_center())
display(usid.jupyter_utils.save_fig_filebox_button(fig_V, 'Vector-{}.png'.format(field)))
The plot below shows the spatial distribution of each component
fig_U, ax_U = px.plot_utils.plot_map_stack(U_map_stack[:,:,:25].T, title='', subtitle='Component', num_comps=plot_comps,
color_bar_mode='each', cmap=px.plot_utils.cmap_jet_white_center())
usid.jupyter_utils.save_fig_filebox_button(fig_U, 'Projection_of_Windows.png')
Since SVD is just a decomposition technique, it is possible to reconstruct the data with U, S, V matrices.
It is also possible to reconstruct a version of the data with a set of components.
Thus, by reconstructing with the first few components, we can remove the statistical noise in the data.
clean_components = range(36) # np.append(range(5,9),(17,18))
num_components=len(clean_components)
# Check if the image has been reconstructed with the same parameters:
# First, gather all groups created by this tool:
h5_clean_image = None
for item in h5_svd:
if item.startswith('Cleaned_Image_') and isinstance(h5_svd[item],h5py.Group):
grp = h5_svd[item]
old_comps = px.hdf_utils.get_attr(grp, 'components_used')
if '-' in old_comps:
start, stop = old_comps.split('-')
old_comps = np.arange(px.hdf_utils.get_attr(h5_svd, 'num_components'))[int(start):int(stop)]
if old_comps.size == num_components:
if np.all(np.isclose(old_comps, np.array(clean_components))):
h5_clean_image = grp['Cleaned_Image']
print( 'Existing clean image found. No need to rebuild.')
break
if h5_clean_image is None:
t0 = time()
#h5_clean_image = iw.clean_and_build_batch(h5_win=h5_wins, components=clean_components)
h5_clean_image = iw.clean_and_build_separate_components(h5_win=h5_wins, components=clean_components)
print( 'Cleaning and rebuilding image took {} seconds.'.format(round(time()-t0, 2)))
# Building a stack of images from here:
image_vec_components = h5_clean_image[()]
# summing over the components:
for comp_ind in range(1, h5_clean_image.shape[1]):
image_vec_components[:, comp_ind] = np.sum(h5_clean_image[:, :comp_ind+1], axis=1)
# converting to 3D:
image_components = np.reshape(image_vec_components, [num_x, num_y, -1])
# calculating the removed noise:
noise_components = image_components - np.reshape(np.tile(h5_raw[()], [1, h5_clean_image.shape[1]]), image_components.shape)
# defining a helper function to get the FFTs of a stack of images
def get_fft_stack(image_stack):
blackman_window_rows = np.blackman(image_stack.shape[0])
blackman_window_cols = np.blackman(image_stack.shape[1])
fft_stack = np.zeros(image_stack.shape, dtype=np.float)
for image_ind in range(image_stack.shape[2]):
layer = image_stack[:, :, image_ind]
windowed = blackman_window_rows[:, np.newaxis] * layer * blackman_window_cols[np.newaxis, :]
fft_stack[:, :, image_ind] = np.abs(np.fft.fftshift(np.fft.fft2(windowed, axes=(0,1)), axes=(0,1)))
return fft_stack
# get the FFT of the cleaned image and the removed noise:
fft_image_components = get_fft_stack(image_components)
fft_noise_components = get_fft_stack(noise_components)
fig, ax = px.plot_utils.plot_map_stack(image_components[:,:,:25].T, title='', evenly_spaced=False,
subtitle='Upto component', num_comps=plot_comps, color_bar_mode='single',
cmap=px.plot_utils.cmap_jet_white_center())
usid.jupyter_utils.save_fig_filebox_button(fig, 'Reconstructed_Components.png')
slide the bar to pick the the number of components such that the noise is removed while maintaining the integrity of the image
num_comps = min(16, image_components.shape[2])
img_stdevs = 3
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(14, 14))
axes.flat[0].loglog(h5_S[()], '*-')
axes.flat[0].set_xlim(left=1, right=h5_S[()].size)
axes.flat[0].set_ylim(bottom=np.min(h5_S[()]), top=np.max(h5_S[()]))
axes.flat[0].set_title('Variance', fontsize=16)
vert_line = axes.flat[0].axvline(x=num_comps, color='r')
clean_image_mat = image_components[:, :, num_comps]
img_clean = axes.flat[1].imshow(clean_image_mat, cmap=px.plot_utils.cmap_jet_white_center(), origin='lower')
mean_val = np.mean(clean_image_mat)
std_val = np.std(clean_image_mat)
img_clean.set_clim(vmin=mean_val-img_stdevs*std_val, vmax=mean_val+img_stdevs*std_val)
axes.flat[1].get_yaxis().set_visible(False)
axes.flat[1].get_xaxis().set_visible(False)
axes.flat[1].set_title('Cleaned Image', fontsize=16)
fft_std_dev = np.max(np.std(fft_image_components[:, :, num_comps]))
img_noise_fft = axes.flat[2].imshow(fft_noise_components[:, :, num_comps], cmap=plt.cm.jet,
vmin=0, vmax=4*fft_std_dev, origin='lower')
axes.flat[2].get_yaxis().set_visible(False)
axes.flat[2].get_xaxis().set_visible(False)
axes.flat[2].set_title('FFT of removed noise', fontsize=16)
img_clean_fft = axes.flat[3].imshow(fft_image_components[:, :, num_comps], cmap=plt.cm.jet,
vmin=0, vmax=4*fft_std_dev, origin='lower')
axes.flat[3].set_title('FFT of cleaned image', fontsize=16)
axes.flat[3].get_yaxis().set_visible(False)
axes.flat[3].get_xaxis().set_visible(False)
plt.show()
def move_comp_line(num_comps):
vert_line.set_xdata((num_comps, num_comps))
clean_image_mat = image_components[:, :, num_comps]
img_clean.set_data(clean_image_mat)
mean_val = np.mean(clean_image_mat)
std_val = np.std(clean_image_mat)
img_clean.set_clim(vmin=mean_val-img_stdevs*std_val, vmax=mean_val+img_stdevs*std_val)
img_noise_fft.set_data(fft_noise_components[:, :, num_comps])
img_clean_fft.set_data(fft_image_components[:, :, num_comps])
clean_components = range(num_comps)
fig.canvas.draw()
# display(fig)
widgets.interact(move_comp_line, num_comps=(1, image_components.shape[2]-1, 1));
usid.jupyter_utils.save_fig_filebox_button(fig, 'Clean_Image_Tool.png')
num_comps = 24
fig, axis = plt.subplots(figsize=(7, 7))
clean_image_mat = image_components[:, :, num_comps]
_ = px.plot_utils.plot_map(axis, clean_image_mat, cmap=px.plot_utils.cmap_jet_white_center())
axis.set_title('Cleaned Image', fontsize=16);
usid.jupyter_utils.save_fig_filebox_button(fig, 'Cleaned_Image.png')
We will attempt to find the positions and the identities of atoms in the image now
Clustering divides data into k clusters such that the variance within each cluster is minimized.
Here, we will be performing k-means clustering on a set of components in the U matrix from SVD.
We want a large enough number of clusters so that K-means identifies fine nuances in the data. At the same time, we want to minimize computational time by reducing the number of clusters. We recommend 32 - 64 clusters.
num_clusters = 4
estimator = px.processing.Cluster(h5_U, KMeans(n_clusters=num_clusters), num_comps=num_comps)
if estimator.duplicate_h5_groups==[]:
t0 = time()
h5_kmeans = estimator.compute()
print('kMeans took {} seconds.'.format(round(time()-t0, 2)))
else:
h5_kmeans = estimator.duplicate_h5_groups[-1]
print( 'Using existing results.')
print( 'Clustering results in {}.'.format(h5_kmeans.name))
half_wind = int(win_size*0.5)
# generate a cropped image that was effectively the area that was used for pattern searching
# Need to get the math righ on the counting
cropped_clean_image = clean_image_mat[half_wind:-half_wind + 1, half_wind:-half_wind + 1]
# Plot cluster results Get the labels dataset
labels_mat = np.reshape(h5_kmeans['Labels'][()], [num_rows, num_cols])
fig, axes = plt.subplots(ncols=2, figsize=(14,7))
axes[0].imshow(cropped_clean_image,cmap=px.plot_utils.cmap_jet_white_center(), origin='lower')
axes[0].set_title('Cleaned Image', fontsize=16)
axes[1].imshow(labels_mat, aspect=1, interpolation='none',cmap=px.plot_utils.cmap_jet_white_center(), origin='lower')
axes[1].set_title('K-means cluster labels', fontsize=16);
for axis in axes:
axis.get_yaxis().set_visible(False)
axis.get_xaxis().set_visible(False)
usid.jupyter_utils.save_fig_filebox_button(fig, 'Clustered_Clean_Image.png')
The vertical length of the branches indicates the relative separation between neighboring clusters.
# Plot dendrogram here
#Get the distrance between cluster means
distance_mat = pdist(h5_kmeans['Mean_Response'][()])
#get hierachical pairings of clusters
linkage_pairing = linkage(distance_mat,'weighted')
# Normalize the pairwise distance with the maximum distance
linkage_pairing[:,2] = linkage_pairing[:,2]/max(linkage_pairing[:,2])
# Visualize dendrogram
fig = plt.figure(figsize=(10,3))
retval = dendrogram(linkage_pairing, count_sort=True,
distance_sort=True, leaf_rotation=90)
#fig.axes[0].set_title('Dendrogram')
fig.axes[0].set_xlabel('Cluster number', fontsize=20)
fig.axes[0].set_ylabel('Cluster separation', fontsize=20)
px.plot_utils.set_tick_font_size(fig.axes[0], 12)
usid.jupyter_utils.save_fig_filebox_button(fig, 'Cluster_Dendrogram.png')
Here, we will interactively identify N windows, each centered on a distinct class / kind of atom.
Use the coarse and fine positions sliders to center the window onto target atoms. Click the "Set as motif" button to add this window to the list of patterns we will search for in the next step. Avoid duplicates.
motif_win_size = win_size
half_wind = int(motif_win_size*0.5)
row, col = [int(0.5*cropped_clean_image.shape[0]), int(0.5*cropped_clean_image.shape[1])]
fig, axes = plt.subplots(ncols=2, figsize=(14,7))
clean_img = axes[0].imshow(cropped_clean_image,cmap=px.plot_utils.cmap_jet_white_center(), origin='lower')
axes[0].set_title('Cleaned Image', fontsize=16)
axes[1].set_title('Zoomed area', fontsize=16)
vert_line = axes[0].axvline(x=col, color='k')
hor_line = axes[0].axhline(y=row, color='k')
motif_box = axes[0].add_patch(patches.Rectangle((col - half_wind, row - half_wind),
motif_win_size, motif_win_size, fill=False,
color='black', linewidth=2))
indices = (slice(row - half_wind, row + half_wind),
slice(col - half_wind, col + half_wind))
motif_img = axes[1].imshow(cropped_clean_image[indices],cmap=px.plot_utils.cmap_jet_white_center(),
vmax=np.max(cropped_clean_image), vmin=np.min(cropped_clean_image), origin='lower')
axes[1].axvline(x=half_wind, color='k')
axes[1].axhline(y=half_wind, color='k')
plt.show()
def _update_motif_img(row, col):
indices = (slice(row - half_wind, row + half_wind),
slice(col - half_wind, col + half_wind))
motif_box.set_x(col - half_wind)
motif_box.set_y(row - half_wind)
motif_img.set_data(cropped_clean_image[indices])
def move_zoom_box(event):
if not clean_img.axes.in_axes(event):
return
col = int(round(event.xdata))
row = int(round(event.ydata))
vert_line.set_xdata((col, col))
hor_line.set_ydata((row, row))
_update_motif_img(row, col)
fig.canvas.draw()
def _motif_fine_select(event):
if not motif_img.axes.in_axes(event):
return
col_shift = int(round(event.xdata)) - half_wind
row_shift = int(round(event.ydata)) - half_wind
col = vert_line.get_xdata()[0] + col_shift
row = hor_line.get_ydata()[0] + row_shift
vert_line.set_xdata((col, col))
hor_line.set_ydata((row, row))
_update_motif_img(row, col)
fig.canvas.draw()
motif_win_centers = list()
add_motif_button = widgets.Button(description="Set as motif")
display(add_motif_button)
def add_motif(butt):
row = hor_line.get_ydata()[0]
col = vert_line.get_xdata()[0]
#print("Setting motif with coordinates ({}, {})".format(current_center[0], current_center[1]))
axes[0].add_patch(patches.Rectangle((col - int(0.5*motif_win_size),
row - int(0.5*motif_win_size)),
motif_win_size, motif_win_size, fill=False,
color='black', linewidth=2))
motif_win_centers.append((row, col))
cid = clean_img.figure.canvas.mpl_connect('button_press_event', move_zoom_box)
cid2 = motif_img.figure.canvas.mpl_connect('button_press_event', _motif_fine_select)
add_motif_button.on_click(add_motif)
usid.jupyter_utils.save_fig_filebox_button(fig, 'Clean_Image_Atom_Motifs.png')
# select motifs from the cluster labels using the component list:
# motif_win_centers = [(117, 118), (109, 110)]
print('Coordinates of the centers of the chosen motifs:')
print(motif_win_centers)
motif_win_size = win_size
half_wind = int(motif_win_size*0.5)
# Effectively, we end up cropping the image again by the window size while matching patterns so:
double_cropped_image = cropped_clean_image[half_wind:-half_wind, half_wind:-half_wind]
# motif_win_size = 15 # Perhaps the motif should be smaller than the original window
num_motifs = len(motif_win_centers)
motifs = list()
fig, axes = plt.subplots(ncols=3, nrows=num_motifs, figsize=(14,6 * num_motifs))
for window_center, ax_row in zip(motif_win_centers, np.atleast_2d(axes)):
indices = (slice(window_center[0] - half_wind, window_center[0] + half_wind),
slice(window_center[1] - half_wind, window_center[1] + half_wind))
motifs.append(labels_mat[indices])
# ax_row[0].hold(True)
ax_row[0].imshow(cropped_clean_image, interpolation='none',cmap=px.plot_utils.cmap_jet_white_center(), origin='lower')
ax_row[0].add_patch(patches.Rectangle((window_center[1] - int(0.5*motif_win_size),
window_center[0] - int(0.5*motif_win_size)),
motif_win_size, motif_win_size, fill=False,
color='black', linewidth=2))
# ax_row[0].hold(False)
# ax_row[1].hold(True)
ax_row[1].imshow(cropped_clean_image[indices], interpolation='none',cmap=px.plot_utils.cmap_jet_white_center(),
vmax=np.max(cropped_clean_image), vmin=np.min(cropped_clean_image), origin='lower')
ax_row[1].plot([0, motif_win_size-2],[int(0.5*motif_win_size), int(0.5*motif_win_size)], 'k--')
ax_row[1].plot([int(0.5*motif_win_size), int(0.5*motif_win_size)], [0, motif_win_size-2], 'k--')
# ax_row[1].axis('tight')
ax_row[1].set_title('Selected window for motif around (row {}, col {})'.format(window_center[0], window_center[1]))
# ax_row[1].hold(False)
ax_row[2].imshow(labels_mat[indices], interpolation='none',cmap=px.plot_utils.cmap_jet_white_center(),
vmax=num_clusters-1, vmin=0, origin='lower')
ax_row[2].set_title('Motif from K-means labels');
usid.jupyter_utils.save_fig_filebox_button(fig, 'Chosen_Motifs.png')
We do this by sliding each motif across the cluster labels image to find how the motif matches with the image
motif_match_coeffs = list()
for motif_mat in motifs:
match_mat = np.zeros(shape=(num_rows-motif_win_size, num_cols-motif_win_size))
for row_count, row_pos in enumerate(range(half_wind, num_rows - half_wind - 1, 1)):
for col_count, col_pos in enumerate(range(half_wind, num_cols - half_wind - 1, 1)):
local_cluster_mat = labels_mat[row_pos-half_wind : row_pos+half_wind,
col_pos-half_wind : col_pos+half_wind]
match_mat[row_count, col_count] = np.sum(local_cluster_mat == motif_mat)
# Normalize the dataset:
match_mat = match_mat/np.max(match_mat)
motif_match_coeffs.append(match_mat)
Note: If a pair of motifs are always matching for the same set of atoms, perhaps this may be a duplicate motif. Alternatively, if these motifs do indeed identify distinct classes of atoms, consider:
show_legend = True
base_color_map = plt.cm.get_cmap('jet')
fig = plt.figure(figsize=(8, 8))
plt.imshow(double_cropped_image, cmap="gray", origin='lower')
if num_motifs > 1:
motif_colors = [base_color_map(int(255 * motif_ind / (num_motifs - 1))) for motif_ind in range(num_motifs)]
else:
motif_colors = [base_color_map(0)]
handles = list()
for motif_ind, current_solid_color, match_mat in zip(range(num_motifs), motif_colors, motif_match_coeffs):
my_cmap = px.plot_utils.make_linear_alpha_cmap('fdfd', current_solid_color, 1)
plt.imshow(match_mat, cmap=my_cmap, origin='lower');
current_solid_color = list(current_solid_color)
current_solid_color[3] = 0.5 # maximum alpha value
handles.append(patches.Patch(color=current_solid_color, label='Motif {}'.format(motif_ind)))
if show_legend:
plt.legend(handles=handles, bbox_to_anchor=(1.01, 1), loc=2, borderaxespad=0., fontsize=14)
axis = fig.get_axes()[0]
axis.set_title('Pattern matching scores', fontsize=22)
axis.set_xticklabels([])
axis.set_yticklabels([])
axis.get_xaxis().set_visible(False)
axis.get_yaxis().set_visible(False)
plt.show()
usid.jupyter_utils.save_fig_filebox_button(fig, 'Motif_Matching_Scores.png')
We do this by thresholding the matching scores such that a score beyond the threshold is set to 1 and all other values are set to 0.
The goal is to set the thresholds such that we avoid overlaps between two clusters and also shrink the blobs such that they are only centered over a single atom wherever possible.
Use the sliders below to interactively set the threshold values
thresholds = [0.25 for x in range(num_motifs)]
thresholded_maps = list()
motif_imgs = list()
base_color_map = plt.cm.jet
fig = plt.figure(figsize=(10, 10))
plt.imshow(double_cropped_image, cmap="gray")
axis = plt.gca()
handles = list()
if num_motifs > 1:
motif_colors = [base_color_map(int(255 * motif_ind / (num_motifs - 1))) for motif_ind in range(num_motifs)]
else:
motif_colors = [base_color_map(0)]
for motif_ind, match_mat, t_hold, current_solid_color in zip(range(num_motifs), motif_match_coeffs,
thresholds, motif_colors):
my_cmap = px.plot_utils.make_linear_alpha_cmap('fdfd', current_solid_color, 1, max_alpha=0.5)
bin_map = np.where(match_mat > t_hold,
np.ones(shape=match_mat.shape, dtype=np.uint8),
np.zeros(shape=match_mat.shape, dtype=np.uint8))
thresholded_maps.append(bin_map)
motif_imgs.append(plt.imshow(bin_map, interpolation='none', cmap=my_cmap))
current_solid_color = list(current_solid_color)
current_solid_color[3] = 0.5
handles.append(patches.Patch(color=current_solid_color,label='Motif {}'.format(motif_ind)))
axis.set_xticklabels([])
axis.set_yticklabels([])
axis.get_xaxis().set_visible(False)
axis.get_yaxis().set_visible(False)
plt.legend(handles=handles, bbox_to_anchor=(1.01, 1), loc=2, borderaxespad=0.)
def threshold_images(thresholds):
# thresholded_maps = list()
# empty the thresholded maps:
del thresholded_maps[:]
for motif_ind, match_mat, t_hold, current_solid_color in zip(range(num_motifs), motif_match_coeffs, thresholds, motif_colors):
my_cmap = px.plot_utils.make_linear_alpha_cmap('fdfd', current_solid_color, 1, max_alpha=0.5)
bin_map = np.where(match_mat > t_hold,
np.ones(shape=match_mat.shape, dtype=np.uint8),
np.zeros(shape=match_mat.shape, dtype=np.uint8))
thresholded_maps.append(bin_map)
def interaction_unpacker(**kwargs):
#threshs = range(num_motifs)
for motif_ind in range(num_motifs):
thresholds[motif_ind] = kwargs['Motif ' + str(motif_ind)]
threshold_images(thresholds)
for img_handle, th_image in zip(motif_imgs, thresholded_maps):
img_handle.set_data(th_image)
fig.canvas.draw()
temp_thresh = dict()
for motif_ind in range(num_motifs):
temp_thresh['Motif ' + str(motif_ind)] = (0,1,0.025)
widgets.interact(interaction_unpacker, **temp_thresh)
usid.jupyter_utils.save_fig_filebox_button(fig, 'Motif_Threshold_Maps.png')
The centers of the atoms will be inferred from the centroid of each of the blobs.
print(thresholds)
atom_labels = list()
for thresh_map in thresholded_maps:
labled_atoms = measure.label(thresh_map, background=0)
map_props = measure.regionprops(labled_atoms)
atom_centroids = np.zeros(shape=(len(map_props),2))
for atom_ind, atom in enumerate(map_props):
atom_centroids[atom_ind] = np.array(atom.centroid)
atom_labels.append(atom_centroids)
# overlay atom positions on original image
fig, axis = plt.subplots(figsize=(8,8))
col_map = plt.cm.jet
axis.imshow(double_cropped_image, interpolation='none',cmap="gray")
legend_handles = list()
for atom_type_ind, atom_centroids in enumerate(atom_labels):
axis.scatter(atom_centroids[:,1], atom_centroids[:,0], color=col_map(int(255 * atom_type_ind / (num_motifs-1))),
label='Motif {}'.format(atom_type_ind), s=30)
axis.set_xlim(0, double_cropped_image.shape[0])
axis.set_ylim(0, double_cropped_image.shape[1]);
axis.invert_yaxis()
axis.set_xticklabels([])
axis.set_yticklabels([])
axis.get_xaxis().set_visible(False)
axis.get_yaxis().set_visible(False)
axis.legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=14)
axis.set_title('Atom Positions', fontsize=22)
fig.tight_layout()
usid.jupyter_utils.save_fig_filebox_button(fig, 'Atomic_Positions.png')
h5_file.close()