Configure the notebook first¶
In [1]:
# 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
sys.path.append('../../../')
import pycroscopy as px
Load the image that will be cleaned:¶
In [2]:
image_path = px.io.uiGetFile('*.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)
Make the image file pycrscopy 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 [3]:
# 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
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 [4]:
# define a small function called 'print_tree' to look at the folder tree stucture
def print_tree(parent):
print(parent.name)
if isinstance(parent, h5py.Group):
for child in parent:
print_tree(parent[child])
print('Datasets and datagroups within the file:')
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 [5]:
iw = px.ImageWindow(h5_raw, max_RAM_mb=1024*4)
# create a handle for the h5 file
file_handle = h5py.File(h5_file.filename, mode='r+')
# 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]);
Visualize the source image:¶
Though the source file is actually grayscale image, we will visualize it using a color-scale
In [6]:
fig, axis = plt.subplots(figsize=(10,10))
img = axis.imshow(raw_image_mat,cmap=px.plot_utils.cmap_jet_white_center());
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);
Extract the optimal window size from the image¶
In [7]:
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))
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 [8]:
# This creates a 4D data set that associates each pixel with a window
fft_mode = None # Options are None, 'abs', 'data+abs', or 'complex'
t0 = time()
h5_wins = iw.do_windowing(win_x=win_size,
win_y=win_size,
save_plots=False,
show_plots=False,
win_fft=fft_mode)
print('Windowing took {} seconds.'.format(round(time()-t0, 2)))
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')
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 [9]:
# Do SVD on all of the windows
h5_svd = px.processing.doSVD(h5_wins)
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
U_map_stack = np.reshape(h5_U[:, :25], [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 [10]:
# Visualizing the variance or importance of the components via a scree plot:
fig_S, ax_S = px.plot_utils.plotScree(h5_S[()]);
V (Eigenvectors)¶
The V dataset contains the eigenvectors for each component
In [11]:
# Plot eigenvectors
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=25,
color_bar_mode='each', cmap=px.plot_utils.cmap_jet_white_center())
U (Eigenvalues or loading maps):¶
The plot below shows the spatial distribution of each component
In [12]:
# Plot loading maps
fig_U, ax_U = px.plot_utils.plot_map_stack(U_map_stack[:,:,:], heading='', title='Component', num_comps=25,
color_bar_mode='each', cmap=px.plot_utils.cmap_jet_white_center())
# keeping the axis direction consistent with plots above
for axis in fig_U.axes:
axis.invert_yaxis()
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 [13]:
# Rebuild the image with up to a 100 components:
clean_components = range(100)
num_components=len(clean_components)
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))
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 [15]:
fig_U, ax_U = px.plot_utils.plot_map_stack(image_components, heading='', evenly_spaced=False,
title='Upto component', num_comps=25, color_bar_mode='single',
cmap=px.plot_utils.cmap_jet_white_center())
# keeping the axis direction consistent with plots above
for axis in ax_U:
axis.invert_yaxis()
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 [19]:
num_comps = min(16, image_components.shape[2])
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())
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)
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)
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)
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))
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 [21]:
clean_components = range(32)
num_clusters = 48
t0 = time()
estimator = px.Cluster(h5_U, 'KMeans', num_comps=clean_components, n_clusters=num_clusters)
h5_kmeans = estimator.do_cluster()
print 'kMeans took {} seconds.'.format(round(time()-t0, 2))
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())
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())
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)
Visualize the hierarchical clustering¶
The vertical length of the branches indicates the relative separation between neighboring clusters.
In [22]:
# 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)
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 [23]:
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())
axes[0].set_title('Cleaned Image', fontsize=16)
main_vert_line = axes[0].axvline(x=current_center[1], color='k')
main_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))
indices = (slice(current_center[0] - half_wind, current_center[0] + half_wind),
slice(current_center[1] - half_wind, current_center[1] + half_wind))
img_zoom = 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))
axes[1].axvline(x=half_wind, color='k')
axes[1].axhline(y=half_wind, color='k')
axes[1].set_title('Zoomed area', fontsize=16)
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
main_vert_line.set_xdata((col, col))
main_hor_line.set_ydata((row, row))
current_center[0] = row
current_center[1] = col
motif_box.set_x(col - half_wind)
motif_box.set_y(row - half_wind)
indices = (slice(row - half_wind, row + half_wind),
slice(col - half_wind, col + half_wind))
img_zoom.set_data(cropped_clean_image[indices])
img_zoom.set_clim(vmin=np.min(cropped_clean_image), vmax=np.max(cropped_clean_image))
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)
Visualize the motifs that were selected above¶
In [35]:
# select motifs from the cluster labels using the component list:
# motif_win_centers = [(182,82), (171,75), (44,199), (38,188)]
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())
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))
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)
ax_row[2].set_title('Motif from K-means labels');
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 [36]:
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 [37]:
show_legend = True
base_color_map = plt.cm.jet
fig = plt.figure(figsize=(8, 8))
im = plt.imshow(double_cropped_image, cmap="gray", vmin=0, vmax=1)
#fig.suptitle('Pattern matching coefficients', fontsize=16)
plt.hold(True)
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);
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)
plt.hold(False)
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)
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 [39]:
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", vmin=0, vmax=1)
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);
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 [42]:
print(thresholds)
# find the centers of the patches in the binarized images above
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 [45]:
# 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(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()
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 [ ]:
file_handle.close()
In [ ]: