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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 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 <br>
Oak Ridge National Laboratory<br>
1/19/2017
Configure the notebook first
Step1:  Load the image that will be cleaned
Step2:  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
Step3:  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
Step4:  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
Step5:  Visualize the source image
Step6:  Extract the optimal window size from the image
Step7:  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.
Step8:  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
Step9:  Visualize the SVD results
S (variance)
Step10:  V (Eigenvectors or end-members)
The V dataset contains the end members for each component
Step11:  U (Abundance maps)
Step12:  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
Step13:  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
Step14:  Check the cleaned image now
Step15:  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.<br>
Here, we will be performing k-means clustering on a set of components in the U matrix from SVD.<br>
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.
Step16:  Visualize the hierarchical clustering
The vertical length of the branches indicates the relative separation between neighboring clusters.
Step17:  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.
Step18:  Visualize the motifs that were selected above
Step19:  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
Step20:  Visualize the matching scores
Note
Step21:  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
Step22:  Find the atom centers from the binary maps
The centers of the atoms will be inferred from the centroid of each of the blobs.
Step23:  Visualize the atom positions
Step24:  Save and close
Save the .h5 file that we are working on by closing it. <br>
Also, consider exporting this notebook as a notebook or an html file. <br> To do this, go to File >> Download as >> HTML
Finally consider saving this notebook if necessary
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Python Code:
# set up notebook to show plots within the notebook
% matplotlib inline
# Import necessary libraries:
# General utilities:
import os
import sys
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 
# 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
import ipywidgets as widgets
from mpl_toolkits.axes_grid1 import ImageGrid
# Finally, pycroscopy itself
import pycroscopy as px
Explanation: 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 <br>
Oak Ridge National Laboratory<br>
1/19/2017
Configure the notebook first
End of explanation
image_path = px.io.uiGetFile('*.png *PNG *TIFF * TIF *tif *tiff *BMP *bmp','Images')
#image_path = r"C:\Users\sjz\Desktop\MM workshop\Data\Image_Cleaning\16_55_31_256_256b.tif"
print('Working on: \n{}'.format(image_path))
folder_path, file_name = os.path.split(image_path)
base_name, _ = os.path.splitext(file_name)
Explanation: Load the image that will be cleaned:
End of explanation
# 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))
Explanation: 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.
End of explanation
print('Datasets and datagroups within the file:')
px.io.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]))
Explanation: 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
End of explanation
# Initialize the windowing class
iw = px.ImageWindow(h5_raw, max_RAM_mb=1024*4)
# grab position indices from the H5 file
h5_pos = h5_raw.parent[h5_raw.attrs['Position_Indices']]
# determine the image size:
num_x = len(np.unique(h5_pos[:,0]))
num_y = len(np.unique(h5_pos[:,1]))
# extract figure data and reshape to proper numpy array
raw_image_mat = np.reshape(h5_raw[()], [num_x,num_y]);
Explanation: 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
End of explanation
fig, axis = plt.subplots(figsize=(10,10))
img = axis.imshow(raw_image_mat,cmap=px.plot_utils.cmap_jet_white_center(), origin='lower');
divider = make_axes_locatable(axis)
cax = divider.append_axes("right", size="5%", pad=0.2)
plt.colorbar(img, cax=cax)
axis.set_title('Raw Image', fontsize=16);
Explanation: Visualize the source image:
Though the source file is actually grayscale image, we will visualize it using a color-scale
End of explanation
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 = 8
# plot a single window
row_offset = int(0.5*(num_x-win_size))
col_offset = int(0.5*(num_y-win_size))
plt.imshow(raw_image_mat[row_offset:row_offset+win_size,
                         col_offset:col_offset+win_size], 
           cmap=px.plot_utils.cmap_jet_white_center(),
          origin='lower');
# 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
Explanation: Extract the optimal window size from the image
End of explanation
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 is None:
    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 = h5_wins_grp['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']))
    
px.plot_utils.plot_map_stack(example_wins, heading='Example Windows', cmap=px.plot_utils.cmap_jet_white_center(),
                             title=['Window # ' + str(win_pos) for win_pos in rand_positions]);
Explanation: 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.
End of explanation
# check to make sure number of components is correct:
num_comp = 1024
num_comp = min(num_comp, 
                min(h5_wins.shape)*len(h5_wins.dtype))
h5_svd = px.hdf_utils.check_for_old(h5_wins, 'SVD', {'num_components':num_comp})
if h5_svd is None:
    print('SVD was either not performed or was performed with different parameters')
    h5_svd = px.processing.doSVD(h5_wins, num_comps=num_comp)
else:
    print('Taking existing SVD results')
    
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))
Explanation: 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
End of explanation
fig_S, ax_S = px.plot_utils.plotScree(h5_S[()]);
Explanation: 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.
End of explanation
for field in V_map_stack.dtype.names:
    fig_V, ax_V = px.plot_utils.plot_map_stack(V_map_stack[:,:,:][field], heading='', title='Vector-'+field, num_comps=plot_comps, 
                                               color_bar_mode='each', cmap=px.plot_utils.cmap_jet_white_center())   
Explanation: V (Eigenvectors or end-members)
The V dataset contains the end members for each component
End of explanation
fig_U, ax_U = px.plot_utils.plot_map_stack(U_map_stack[:,:,:25], heading='', title='Component', num_comps=plot_comps, 
                                           color_bar_mode='each', cmap=px.plot_utils.cmap_jet_white_center())
Explanation: U (Abundance maps):
The plot below shows the spatial distribution of each component
End of explanation
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 old_comps.size == len(list(clean_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_U, ax_U = px.plot_utils.plot_map_stack(image_components[:,:,:25], heading='', evenly_spaced=False,
                                           title='Upto component', num_comps=plot_comps, color_bar_mode='single', 
                                           cmap=px.plot_utils.cmap_jet_white_center())
Explanation: 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
End of explanation
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)
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)
    display(fig)
    
widgets.interact(move_comp_line, num_comps=(1, image_components.shape[2]-1, 1));
Explanation: 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
End of explanation
num_comps = 28
fig, axis = plt.subplots(figsize=(7, 7))
clean_image_mat = image_components[:, :, num_comps]
img_clean = axis.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)
axis.get_yaxis().set_visible(False)
axis.get_xaxis().set_visible(False)
axis.set_title('Cleaned Image', fontsize=16);
Explanation: Check the cleaned image now:
End of explanation
clean_components = 64
num_clusters = 32
# Check for existing Clustering results
estimator = px.Cluster(h5_U, 'KMeans', num_comps=clean_components, n_clusters=num_clusters)
do_cluster = False
# See if there are existing cluster results
try:
    h5_kmeans = h5_svd['U-Cluster_000']
    print( 'Clustering results loaded.  Will now check parameters')
except:
    print( 'Could not load Clustering results.')
    do_cluster = True
# Check that the same components are used
if not do_cluster:
    new_clean = estimator.data_slice[1]
    if isinstance(new_clean, np.ndarray):
        new_clean = new_clean.tolist()
    else:
        # print(new_clean)
        if new_clean.step is None:
            new_clean = range(new_clean.start, new_clean.stop)
        else:
            new_clean = range(new_clean.start, new_clean.stop, new_clean.step)
    
    if all(h5_kmeans.attrs['components_used']==new_clean):
        print( 'Clustering results used the same components as those requested.')
    else:
        do_cluster = True
        print( 'Clustering results used the different components from those requested.')
# Check that the same number of clusters were used
if not do_cluster:
    old_clusters = len(np.unique(h5_kmeans['Cluster_Indices']))
    
    if old_clusters==num_clusters:
        print( 'Clustering results used the same number of clusters as requested.')
    else:
        do_cluster = True
        print( 'Clustering results used a different number of clusters from those requested.')
# Perform k-means clustering on the U matrix now using the list of components only if needed:
if do_cluster:
    t0 = time()
    h5_kmeans = estimator.do_cluster()
    print( 'kMeans took {} seconds.'.format(round(time()-t0, 2)))
else:
    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)
Explanation: 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.<br>
Here, we will be performing k-means clustering on a set of components in the U matrix from SVD.<br>
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.
End of explanation
# 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)
Explanation: Visualize the hierarchical clustering
The vertical length of the branches indicates the relative separation between neighboring clusters.
End of explanation
motif_win_size = win_size
half_wind = int(motif_win_size*0.5)
current_center = [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))
axes[0].hold(True)
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=current_center[1], color='k')
hor_line = axes[0].axhline(y=current_center[0], color='k')
motif_box = axes[0].add_patch(patches.Rectangle((current_center[1] - half_wind, current_center[0] - half_wind),
                                          motif_win_size, motif_win_size, fill=False,
                                         color='black', linewidth=2))
add_motif_button = widgets.Button(description="Set as motif")
display(add_motif_button)
def move_zoom_box(coarse_row, coarse_col, fine_row, fine_col):
    row = coarse_row + fine_row
    col = coarse_col + fine_col
    vert_line.set_xdata((col, col))
    hor_line.set_ydata((row, row))
    current_center[0] = row
    current_center[1] = 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)
    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')
    display(fig)
    
motif_win_centers = list()
def add_motif(butt):
    #print("Setting motif with coordinates ({}, {})".format(current_center[0], current_center[1]))
    axes[0].add_patch(patches.Rectangle((current_center[1] - int(0.5*motif_win_size), 
                                           current_center[0] - int(0.5*motif_win_size)),
                                          motif_win_size, motif_win_size, fill=False,
                                         color='black', linewidth=2))
    motif_win_centers.append((current_center[0], current_center[1]))
    # print motif_win_centers
    
widgets.interact(move_zoom_box, coarse_row=(motif_win_size, cropped_clean_image.shape[0] - motif_win_size, 1), 
                 coarse_col=(motif_win_size, cropped_clean_image.shape[1] - motif_win_size, 1),
                 fine_row=(-half_wind,half_wind,1), fine_col=(-half_wind,half_wind,1));
add_motif_button.on_click(add_motif)
Explanation: 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.
End of explanation
# select motifs from the cluster labels using the component list:
# motif_win_centers = [(135, 128), (106, 125), (62, 204), (33, 206)]
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');
Explanation: Visualize the motifs that were selected above
End of explanation
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)
Explanation: 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
End of explanation
show_legend = True
base_color_map = plt.cm.get_cmap('jet')
fig = plt.figure(figsize=(8, 8))
im = 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)
    im = 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()
Explanation: 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
End of explanation
thresholds = [0.25 for x in range(num_motifs)]
thresholded_maps = list()
motif_imgs = list()
base_color_map = plt.cm.jet
fig, axis = plt.subplots(figsize=(10, 10))
axis.hold(True)
axis.imshow(double_cropped_image, cmap="gray")
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(axis.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.)
plt.hold(False)
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)
    display(fig)
    
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);
Explanation: 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
End of explanation
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)
Explanation: Find the atom centers from the binary maps
The centers of the atoms will be inferred from the centroid of each of the blobs.
End of explanation
# overlay atom positions on original image
fig, axis = plt.subplots(figsize=(8,8))
axis.hold(True)
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()
#plt.show()
Explanation: Visualize the atom positions
End of explanation
h5_file.close()
Explanation: Save and close
Save the .h5 file that we are working on by closing it. <br>
Also, consider exporting this notebook as a notebook or an html file. <br> To do this, go to File >> Download as >> HTML
Finally consider saving this notebook if necessary
End of explanation
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