Image cleaning and atom finding using pycroscopy

Suhas Somnath, Chris R. Smith, Stephen Jesse

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

References:

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:

  • Arxiv paper titled "USID and Pycroscopy - Open frameworks for storing and analyzing spectroscopic and imaging data"
  • Advanced Structural and Chemical Imaging paper titled "Feature extraction via similarity search: application to atom finding and denoising in electron and scanning probe microscopy imaging"
  • Dataset used here is available via OSTI / OLCF

About the Notebook:

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.

notebook_rules.png

Image courtesy of Jean Bilheux from the neutron imaging GitHub repository.

A note about software versions:

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

Configure the notebook first

In [ ]:
# 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
In [ ]:
# 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>
"""))
In [ ]:
# set up notebook to show plots within the notebook
% matplotlib notebook

Set some basic parameters for computation

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.

In [ ]:
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.

Load the image that will be cleaned:

In [ ]:
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)

Make the image file pycroscopy compatible

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

H5 files:

  • are like smart containers that can store matrices with data, folders to organize these datasets, images, metadata like experimental parameters, links or shortcuts to datasets, etc.
  • are readily compatible with high-performance computing facilities
  • scale very efficiently from few kilobytes to several terabytes
  • can be read and modified using any language including Python, Matlab, C/C++, Java, Fortran, Igor Pro, etc.
In [ ]:
# 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))

Inspect the contents of this h5 data file

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

In [ ]:
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 an object that will perform image windowing on the .h5 file

  • Note that after you run this, the H5 file is opened. If you want to re-run this cell, close the H5 file first
In [ ]:
# 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]);

Visualize the source image:

Though the source file is actually grayscale image, we will visualize it using a color-scale

In [ ]:
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')

Extract the optimal window size from the image

In [ ]:
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))
In [ ]:
# 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')

Now break the image into a sequence of small windows

We do this by sliding a small window across the image. This artificially baloons the size of the data.

In [ ]:
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')
In [ ]:
# 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')

Performing Singular Value Decompostion (SVD) on the windowed data

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

In [ ]:
# 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))

Visualize the SVD results

S (variance):

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.

In [ ]:
fig_S, ax_S = px.plot_utils.plot_scree(h5_S[()]);
usid.jupyter_utils.save_fig_filebox_button(fig_S, 'Scree_of_Windows.png')

V (Eigenvectors or end-members)

The V dataset contains the end members for each component

In [ ]:
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)))

U (Abundance maps):

The plot below shows the spatial distribution of each component

In [ ]:
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')

Reconstruct image (while removing noise)

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.

The key is to select the appropriate (number of) components to reconstruct the image without the noise
In [ ]:
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)))
In [ ]:
# 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)
In [ ]:
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')

Reconstruct the image with the first N components

slide the bar to pick the the number of components such that the noise is removed while maintaining the integrity of the image

In [ ]:
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')

Check the cleaned image now:

In [ ]:
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')

Atom Finding

We will attempt to find the positions and the identities of atoms in the image now

Perform clustering on the dataset

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.

In [ ]:
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')

Visualize the hierarchical clustering

The vertical length of the branches indicates the relative separation between neighboring clusters.

In [ ]:
# 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')

Identifiying the principal patterns

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.

In [ ]:
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')

Visualize the motifs that were selected above

In [ ]:
# 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')

Calculate matching scores for each motif

We do this by sliding each motif across the cluster labels image to find how the motif matches with the image

In [ ]:
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)

Visualize the matching scores

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:

  • clustering again with a different set of SVD components
  • increasing the number of clusters
  • Choosing a different fft mode ('data+fft' for better identify subtle but important variations) before performing windowing on the data
In [ ]:
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')

Convert matching scores to binary

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

In [ ]:
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')

Find the atom centers from the binary maps

The centers of the atoms will be inferred from the centroid of each of the blobs.

In [ ]:
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)

Visualize the atom positions

In [ ]:
# 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')

Save and close

  • Save the .h5 file that we are working on by closing it.
  • Also, consider exporting this notebook as a notebook or an html file.
    To do this, go to File >> Download as >> HTML
  • Finally consider saving this notebook if necessary
In [ ]:
h5_file.close()
In [ ]: