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superpixel_analysis.py
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superpixel_analysis.py
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import os
import sys
import mmap
import cv2
import time
import matplotlib.pyplot as plt
import pylab
import networkx as nx
import numpy as np
import scipy.io as sio
import scipy.stats as ss
import scipy.ndimage
import scipy.signal
import scipy.sparse
import scipy
import cvxpy as cvx
import cvxopt as cvxopt
from mpl_toolkits.axes_grid1 import make_axes_locatable
from sklearn.decomposition import NMF
from sklearn import linear_model
from scipy.ndimage.filters import convolve
from scipy.sparse import csc_matrix
from sklearn.decomposition import TruncatedSVD
from matplotlib.patches import Rectangle
from matplotlib import ticker
##################################### utility functions (to decimate data and estimate noise level) ###################################
#######################################################################################################################################
def resize(Y, size, interpolation=cv2.INTER_AREA):
"""faster and 3D compatible version of skimage.transform.resize"""
if Y.ndim == 2:
return cv2.resize(Y, tuple(size[::-1]), interpolation=interpolation)
elif Y.ndim == 3:
if np.isfortran(Y):
return (cv2.resize(np.array(
[cv2.resize(y, size[:2], interpolation=interpolation) for y in Y.T]).T
.reshape((-1, Y.shape[-1]), order='F'),
(size[-1], np.prod(size[:2])), interpolation=interpolation).reshape(size, order='F'))
else:
return np.array([cv2.resize(y, size[:0:-1], interpolation=interpolation) for y in
cv2.resize(Y.reshape((len(Y), -1), order='F'),
(np.prod(Y.shape[1:]), size[0]), interpolation=interpolation)
.reshape((size[0],) + Y.shape[1:], order='F')])
else: # TODO deal with ndim=4
raise NotImplementedError
def local_correlations_fft(Y, eight_neighbours=True, swap_dim=True, opencv=True):
"""Computes the correlation image for the input dataset Y using a faster FFT based method, adapt from caiman
Parameters:
-----------
Y: np.ndarray (3D or 4D)
Input movie data in 3D or 4D format
eight_neighbours: Boolean
Use 8 neighbors if true, and 4 if false for 3D data (default = True)
Use 6 neighbors for 4D data, irrespectively
swap_dim: Boolean
True indicates that time is listed in the last axis of Y (matlab format)
and moves it in the front
opencv: Boolean
If True process using open cv method
Returns:
--------
Cn: d1 x d2 [x d3] matrix, cross-correlation with adjacent pixels
"""
if swap_dim:
Y = np.transpose(
Y, tuple(np.hstack((Y.ndim - 1, list(range(Y.ndim))[:-1]))))
Y = Y.astype('float32')
Y -= np.mean(Y, axis=0)
Ystd = np.std(Y, axis=0)
Ystd[Ystd == 0] = np.inf
Y /= Ystd
if Y.ndim == 4:
if eight_neighbours:
sz = np.ones((3, 3, 3), dtype='float32')
sz[1, 1, 1] = 0
else:
sz = np.array([[[0, 0, 0], [0, 1, 0], [0, 0, 0]],
[[0, 1, 0], [1, 0, 1], [0, 1, 0]],
[[0, 0, 0], [0, 1, 0], [0, 0, 0]]], dtype='float32')
else:
if eight_neighbours:
sz = np.ones((3, 3), dtype='float32')
sz[1, 1] = 0
else:
sz = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]], dtype='float32')
if opencv and Y.ndim == 3:
Yconv = Y.copy()
for idx, img in enumerate(Yconv):
Yconv[idx] = cv2.filter2D(img, -1, sz, borderType=0)
MASK = cv2.filter2D(
np.ones(Y.shape[1:], dtype='float32'), -1, sz, borderType=0)
else:
Yconv = convolve(Y, sz[np.newaxis, :], mode='constant')
MASK = convolve(
np.ones(Y.shape[1:], dtype='float32'), sz, mode='constant')
Cn = np.mean(Yconv * Y, axis=0) / MASK
return Cn
def mean_psd(y, method='logmexp'):
"""
Averaging the PSD, adapt from caiman
Parameters:
----------
y: np.ndarray
PSD values
method: string
method of averaging the noise.
Choices:
'mean': Mean
'median': Median
'logmexp': Exponential of the mean of the logarithm of PSD (default)
Returns:
-------
mp: array
mean psd
"""
if method == 'mean':
mp = np.sqrt(np.mean(np.divide(y, 2), axis=-1))
elif method == 'median':
mp = np.sqrt(np.median(np.divide(y, 2), axis=-1))
else:
mp = np.log(np.divide((y + 1e-10), 2))
mp = np.mean(mp, axis=-1)
mp = np.exp(mp)
mp = np.sqrt(mp)
return mp
def noise_estimator(Y, noise_range=[0.25, 0.5], noise_method='logmexp', max_num_samples_fft=4000,
opencv=True):
"""Estimate the noise level for each pixel by averaging the power spectral density.
Inputs:
-------
Y: np.ndarray
Input movie data with time in the last axis
noise_range: np.ndarray [2 x 1] between 0 and 0.5
Range of frequencies compared to Nyquist rate over which the power spectrum is averaged
default: [0.25,0.5]
noise method: string
method of averaging the noise.
Choices:
'mean': Mean
'median': Median
'logmexp': Exponential of the mean of the logarithm of PSD (default)
Output:
------
sn: np.ndarray
Noise level for each pixel
"""
T = Y.shape[-1]
# Y=np.array(Y,dtype=np.float64)
if T > max_num_samples_fft:
Y = np.concatenate((Y[..., 1:max_num_samples_fft // 3 + 1],
Y[..., np.int(T // 2 - max_num_samples_fft / 3 / 2):np.int(T // 2 + max_num_samples_fft / 3 / 2)],
Y[..., -max_num_samples_fft // 3:]), axis=-1)
T = np.shape(Y)[-1]
# we create a map of what is the noise on the FFT space
ff = np.arange(0, 0.5 + 1. / T, 1. / T)
ind1 = ff > noise_range[0]
ind2 = ff <= noise_range[1]
ind = np.logical_and(ind1, ind2)
# we compute the mean of the noise spectral density s
if Y.ndim > 1:
if opencv:
import cv2
psdx = []
for y in Y.reshape(-1, T):
dft = cv2.dft(y, flags=cv2.DFT_COMPLEX_OUTPUT).squeeze()[
:len(ind)][ind]
psdx.append(np.sum(1. / T * dft * dft, 1))
psdx = np.reshape(psdx, Y.shape[:-1] + (-1,))
else:
xdft = np.fft.rfft(Y, axis=-1)
xdft = xdft[..., ind[:xdft.shape[-1]]]
psdx = 1. / T * abs(xdft)**2
psdx *= 2
sn = mean_psd(psdx, method=noise_method)
else:
xdft = np.fliplr(np.fft.rfft(Y))
psdx = 1. / T * (xdft**2)
psdx[1:] *= 2
sn = mean_psd(psdx[ind[:psdx.shape[0]]], method=noise_method)
return sn
################################################# begin functions for superpixel analysis ##################################################
############################################################################################################################################
def threshold_data(Yd, th=2):
"""
Threshold data: in each pixel, compute the median and median absolute deviation (MAD),
then zero all bins (x,t) such that Yd(x,t) < med(x) + th * MAD(x). Default value of th is 2.
Parameters:
----------------
Yd: 3d np.darray: dimension d1 x d2 x T
denoised data
Return:
----------------
Yt: 3d np.darray: dimension d1 x d2 x T
cleaned, thresholded data
"""
dims = Yd.shape;
Yt = np.zeros(dims);
ii=0;
for array in [Yd]:
Yd_median = np.median(array, axis=2, keepdims=True)
Yd_mad = np.median(abs(array - Yd_median), axis=2, keepdims=True)
for i in range(dims[2]):
Yt[:,:,i] = np.clip(array[:,:,i], a_min = (Yd_median + th*Yd_mad)[:,:,0], a_max = None) - (Yd_median + th*Yd_mad)[:,:,0]
return Yt
def find_superpixel(Yt, cut_off_point, length_cut, eight_neighbours=True):
"""
Find superpixels in Yt. For each pixel, calculate its correlation with neighborhood pixels.
If it's larger than threshold, we connect them together. In this way, we form a lot of connected components.
If its length is larger than threshold, we keep it as a superpixel.
Parameters:
----------------
Yt: 3d np.darray, dimension d1 x d2 x T
thresholded data
cut_off_point: double scalar
correlation threshold
length_cut: double scalar
length threshold
eight_neighbours: Boolean
Use 8 neighbors if true. Defalut value is True.
Return:
----------------
connect_mat_1: 2d np.darray, d1 x d2
illustrate position of each superpixel.
Each superpixel has a random number "indicator". Same number means same superpixel.
idx: double scalar
number of superpixels
comps: list, length = number of superpixels
comp on comps is also list, its value is position of each superpixel in Yt_r = Yt.reshape(np.prod(dims[:2]),-1,order="F")
permute_col: list, length = number of superpixels
all the random numbers used to idicate superpixels in connect_mat_1
"""
dims = Yt.shape;
ref_mat = np.arange(np.prod(dims[:-1])).reshape(dims[:-1],order='F')
######### calculate correlation ############
w_mov = (Yt.transpose(2,0,1) - np.mean(Yt, axis=2)) / np.std(Yt, axis=2);
w_mov[np.isnan(w_mov)] = 0;
rho_v = np.mean(np.multiply(w_mov[:, :-1, :], w_mov[:, 1:, :]), axis=0)
rho_h = np.mean(np.multiply(w_mov[:, :, :-1], w_mov[:, :, 1:]), axis=0)
if eight_neighbours:
rho_l = np.mean(np.multiply(w_mov[:, 1:, :-1], w_mov[:, :-1, 1:]), axis=0)
rho_r = np.mean(np.multiply(w_mov[:, :-1, :-1], w_mov[:, 1:, 1:]), axis=0)
rho_v = np.concatenate([rho_v, np.zeros([1, rho_v.shape[1]])], axis=0)
rho_h = np.concatenate([rho_h, np.zeros([rho_h.shape[0],1])], axis=1)
if eight_neighbours:
rho_r = np.concatenate([rho_r, np.zeros([rho_r.shape[0],1])], axis=1)
rho_r = np.concatenate([rho_r, np.zeros([1, rho_r.shape[1]])], axis=0)
rho_l = np.concatenate([np.zeros([rho_l.shape[0],1]), rho_l], axis=1)
rho_l = np.concatenate([rho_l, np.zeros([1, rho_l.shape[1]])], axis=0)
################## find pairs where correlation above threshold
temp_v = np.where(rho_v > cut_off_point);
A_v = ref_mat[temp_v];
B_v = ref_mat[(temp_v[0] + 1, temp_v[1])]
temp_h = np.where(rho_h > cut_off_point);
A_h = ref_mat[temp_h];
B_h = ref_mat[(temp_h[0], temp_h[1] + 1)]
if eight_neighbours:
temp_l = np.where(rho_l > cut_off_point);
A_l = ref_mat[temp_l];
B_l = ref_mat[(temp_l[0] + 1, temp_l[1] - 1)]
temp_r = np.where(rho_r > cut_off_point);
A_r = ref_mat[temp_r];
B_r = ref_mat[(temp_r[0] + 1, temp_r[1] + 1)]
A = np.concatenate([A_v,A_h,A_l,A_r])
B = np.concatenate([B_v,B_h,B_l,B_r])
else:
A = np.concatenate([A_v,A_h])
B = np.concatenate([B_v,B_h])
########### form connected componnents #########
G = nx.Graph();
G.add_edges_from(list(zip(A, B)))
comps=list(nx.connected_components(G))
connect_mat=np.zeros(np.prod(dims[:2]));
idx=0;
for comp in comps:
if(len(comp) > length_cut):
idx = idx+1;
permute_col = np.random.permutation(idx)+1;
ii=0;
for comp in comps:
if(len(comp) > length_cut):
connect_mat[list(comp)] = permute_col[ii];
ii = ii+1;
connect_mat_1 = connect_mat.reshape(dims[0],dims[1],order='F');
return connect_mat_1, idx, comps, permute_col
def find_superpixel_3d(Yt, num_plane, cut_off_point, length_cut, eight_neighbours=True):
"""
Find 3d supervoxels in Yt. For each pixel, calculate its correlation with neighborhood pixels.
If it's larger than threshold, we connect them together. In this way, we form a lot of connected components.
If its length is larger than threshold, we keep it as a superpixel.
Parameters:
----------------
Yt: 3d np.darray, dimension d1 x (d2*num_plane) x T
thresholded data
cut_off_point: double scalar
correlation threshold
length_cut: double scalar
length threshold
eight_neighbours: Boolean
Use 8 neighbors in same plane if true. Defalut value is True.
Return:
----------------
connect_mat_1: 2d np.darray, d1 x (d2*num_plane)
illustrate position of each superpixel.
Each superpixel has a random number "indicator". Same number means same superpixel.
idx: double scalar
number of superpixels
comps: list, length = number of superpixels
comp on comps is also list, its value is position of each superpixel in Yt_r = Yt.reshape(np.prod(dims[:2]),-1,order="F")
permute_col: list, length = number of superpixels
all the random numbers used to idicate superpixels in connect_mat_1
"""
dims = Yt.shape;
Yt_3d = Yt.reshape(dims[0],int(dims[1]/num_plane),num_plane,dims[2],order="F");
dims = Yt_3d.shape;
ref_mat = np.arange(np.prod(dims[:-1])).reshape(dims[:-1],order='F');
######### calculate correlation ############
w_mov = (Yt_3d.transpose(3,0,1,2) - np.mean(Yt_3d, axis=3)) / np.std(Yt_3d, axis=3);
w_mov[np.isnan(w_mov)] = 0;
rho_v = np.mean(np.multiply(w_mov[:, :-1, :], w_mov[:, 1:, :]), axis=0)
rho_h = np.mean(np.multiply(w_mov[:, :, :-1], w_mov[:, :, 1:]), axis=0)
if eight_neighbours:
rho_l = np.mean(np.multiply(w_mov[:, 1:, :-1], w_mov[:, :-1, 1:]), axis=0)
rho_r = np.mean(np.multiply(w_mov[:, :-1, :-1], w_mov[:, 1:, 1:]), axis=0)
rho_u = np.mean(np.multiply(w_mov[:, :, :, :-1], w_mov[:, :, :, 1:]), axis=0)
rho_v = np.concatenate([rho_v, np.zeros([1, rho_v.shape[1],num_plane])], axis=0)
rho_h = np.concatenate([rho_h, np.zeros([rho_h.shape[0],1,num_plane])], axis=1)
if eight_neighbours:
rho_r = np.concatenate([rho_r, np.zeros([rho_r.shape[0],1,num_plane])], axis=1)
rho_r = np.concatenate([rho_r, np.zeros([1, rho_r.shape[1],num_plane])], axis=0)
rho_l = np.concatenate([np.zeros([rho_l.shape[0],1,num_plane]), rho_l], axis=1)
rho_l = np.concatenate([rho_l, np.zeros([1, rho_l.shape[1],num_plane])], axis=0)
rho_u = np.concatenate([rho_u, np.zeros([rho_u.shape[0], rho_u.shape[1],1])], axis=2)
################## find pairs where correlation above threshold
temp_v = np.where(rho_v > cut_off_point);
A_v = ref_mat[temp_v];
B_v = ref_mat[(temp_v[0] + 1, temp_v[1], temp_v[2])]
temp_h = np.where(rho_h > cut_off_point);
A_h = ref_mat[temp_h];
B_h = ref_mat[(temp_h[0], temp_h[1] + 1, temp_h[2])]
temp_u = np.where(rho_u > cut_off_point);
A_u = ref_mat[temp_u];
B_u = ref_mat[(temp_u[0], temp_u[1], temp_u[2]+1)]
if eight_neighbours:
temp_l = np.where(rho_l > cut_off_point);
A_l = ref_mat[temp_l];
B_l = ref_mat[(temp_l[0] + 1, temp_l[1] - 1, temp_l[2])]
temp_r = np.where(rho_r > cut_off_point);
A_r = ref_mat[temp_r];
B_r = ref_mat[(temp_r[0] + 1, temp_r[1] + 1, temp_r[2])]
A = np.concatenate([A_v,A_h,A_l,A_r,A_u])
B = np.concatenate([B_v,B_h,B_l,B_r,B_u])
else:
A = np.concatenate([A_v,A_h,A_u])
B = np.concatenate([B_v,B_h,B_u])
########### form connected componnents #########
G = nx.Graph()
G.add_edges_from(list(zip(A, B)))
comps=list(nx.connected_components(G))
connect_mat=np.zeros(np.prod(dims[:-1]));
idx=0;
for comp in comps:
if(len(comp) > length_cut):
idx = idx+1;
permute_col = np.random.permutation(idx)+1;
ii=0;
for comp in comps:
if(len(comp) > length_cut):
connect_mat[list(comp)] = permute_col[ii];
ii = ii+1;
connect_mat_1 = connect_mat.reshape(Yt.shape[:-1],order='F');
return connect_mat_1, idx, comps, permute_col
def spatial_temporal_ini(Yt, comps, idx, length_cut, bg=False):
"""
Apply rank 1 NMF to find spatial and temporal initialization for each superpixel in Yt.
"""
dims = Yt.shape;
T = dims[2];
Yt_r= Yt.reshape(np.prod(dims[:2]),T,order = "F");
ii = 0;
U_mat = np.zeros([np.prod(dims[:2]),idx]);
V_mat = np.zeros([T,idx]);
for comp in comps:
if(len(comp) > length_cut):
y_temp = Yt_r[list(comp),:];
#nmf = nimfa.Nmf(y_temp, seed="nndsvd", rank=1)
#nmf_fit = nmf();
#U_mat[list(comp),ii] = np.array(nmf.W)[:,0];
#V_mat[:,[ii]] = nmf.H.T;
model = NMF(n_components=1, init='custom');
U_mat[list(comp),ii] = model.fit_transform(y_temp, W=y_temp.mean(axis=1,keepdims=True),
H = y_temp.mean(axis=0,keepdims=True))[:,0];
#U_mat[list(comp),ii] = model.fit_transform(y_temp)[:,0];
V_mat[:,ii] = model.components_;
ii = ii+1;
if bg:
bg_comp_pos = np.where(U_mat.sum(axis=1) == 0)[0];
y_temp = Yt_r[bg_comp_pos,:];
bg_u = np.zeros([Yt_r.shape[0],bg]);
y_temp = y_temp - y_temp.mean(axis=1,keepdims=True);
svd = TruncatedSVD(n_components=bg, n_iter=7, random_state=0);
bg_u[bg_comp_pos,:] = svd.fit_transform(y_temp);
bg_v = svd.components_.T;
bg_v = bg_v - bg_v.mean(axis=0,keepdims=True);
else:
bg_v = None;
bg_u = None;
return V_mat, U_mat, bg_v, bg_u
def vcorrcoef(U, V, c):
"""
fast way to calculate correlation between c and Y(UV).
"""
temp = (c - c.mean(axis=0,keepdims=True));
return np.matmul(U, np.matmul(V - V.mean(axis=1,keepdims=True), temp/np.std(temp, axis=0, keepdims=True)));
def vcorrcoef2(X,y):
"""
calculate correlation between vector y and matrix X.
"""
Xm = np.reshape(np.mean(X,axis=1),(X.shape[0],1))
ym = np.mean(y)
r_num = np.sum((X-Xm)*(y-ym),axis=1)
r_den = np.sqrt(np.sum((X-Xm)**2,axis=1)*np.sum((y-ym)**2))
r = r_num/r_den
return r
def search_superpixel_in_range(connect_mat, permute_col, V_mat):
"""
Search all the superpixels within connect_mat
Parameters:
----------------
connect_mat_1: 2d np.darray, d1 x d2
illustrate position of each superpixel, same value means same superpixel
permute_col: list, length = number of superpixels
random number used to idicate superpixels in connect_mat_1
V_mat: 2d np.darray, dimension T x number of superpixel
temporal initilization
Return:
----------------
unique_pix: list, length idx (number of superpixels)
random numbers for superpixels in this patch
M: 2d np.array, dimension T x idx
temporal components for superpixels in this patch
"""
unique_pix = np.asarray(np.sort(np.unique(connect_mat)),dtype="int");
unique_pix = unique_pix[np.nonzero(unique_pix)];
#unique_pix = list(unique_pix);
M = np.zeros([V_mat.shape[0], len(unique_pix)]);
for ii in range(len(unique_pix)):
M[:,ii] = V_mat[:,int(np.where(permute_col==unique_pix[ii])[0])];
return unique_pix, M
def fast_sep_nmf(M, r, th, normalize=1):
"""
Find pure superpixels. solve nmf problem M = M(:,K)H, K is a subset of M's columns.
Parameters:
----------------
M: 2d np.array, dimension T x idx
temporal components of superpixels.
r: int scalar
maximum number of pure superpixels you want to find. Usually it's set to idx, which is number of superpixels.
th: double scalar, correlation threshold
Won't pick up two pure superpixels, which have correlation higher than th.
normalize: Boolean.
Normalize L1 norm of each column to 1 if True. Default is True.
Return:
----------------
pure_pixels: 1d np.darray, dimension d x 1. (d is number of pure superpixels)
pure superpixels for these superpixels, actually column indices of M.
"""
pure_pixels = [];
if normalize == 1:
M = M/np.sum(M, axis=0,keepdims=True);
normM = np.sum(M**2, axis=0,keepdims=True);
normM_orig = normM.copy();
normM_sqrt = np.sqrt(normM);
nM = np.sqrt(normM);
ii = 0;
U = np.zeros([M.shape[0], r]);
while ii < r and (normM_sqrt/nM).max() > th:
## select the column of M with largest relative l2-norm
temp = normM/normM_orig;
pos = np.where(temp == temp.max())[1][0];
## check ties up to 1e-6 precision
pos_ties = np.where((temp.max() - temp)/temp.max() <= 1e-6)[1];
if len(pos_ties) > 1:
pos = pos_ties[np.where(normM_orig[0,pos_ties] == (normM_orig[0,pos_ties]).max())[0][0]];
## update the index set, and extracted column
pure_pixels.append(pos);
U[:,ii] = M[:,pos].copy();
for jj in range(ii):
U[:,ii] = U[:,ii] - U[:,jj]*sum(U[:,jj]*U[:,ii])
U[:,ii] = U[:,ii]/np.sqrt(sum(U[:,ii]**2));
normM = np.maximum(0, normM - np.matmul(U[:,[ii]].T, M)**2);
normM_sqrt = np.sqrt(normM);
ii = ii+1;
#coef = np.matmul(np.matmul(np.linalg.inv(np.matmul(M[:,pure_pixels].T, M[:,pure_pixels])), M[:,pure_pixels].T), M);
pure_pixels = np.array(pure_pixels);
#coef_rank = coef.copy(); ##### from large to small
#for ii in range(len(pure_pixels)):
# coef_rank[:,ii] = [x for _,x in sorted(zip(len(pure_pixels) - ss.rankdata(coef[:,ii]), pure_pixels))];
return pure_pixels #, coef, coef_rank
def prepare_iteration(Yd, connect_mat_1, permute_col, pure_pix, U_mat, V_mat, more=False):
"""
Get some needed variables for the successive nmf iterations.
Parameters:
----------------
Yt: 3d np.darray, dimension d1 x d2 x T
thresholded data
connect_mat_1: 2d np.darray, d1 x d2
illustrate position of each superpixel, same value means same superpixel
permute_col: list, length = number of superpixels
random number used to idicate superpixels in connect_mat_1
pure_pix: 1d np.darray, dimension d x 1. (d is number of pure superpixels)
pure superpixels for these superpixels, actually column indices of M.
V_mat: 2d np.darray, dimension T x number of superpixel
temporal initilization
U_mat: 2d np.darray, dimension (d1*d2) x number of superpixel
spatial initilization
Return:
----------------
U_mat: 2d np.darray, number pixels x number of pure superpixels
initialization of spatial components
V_mat: 2d np.darray, T x number of pure superpixels
initialization of temporal components
brightness_rank: 2d np.darray, dimension d x 1
brightness rank for pure superpixels in this patch. Rank 1 means the brightest.
B_mat: 2d np.darray
initialization of constant background
normalize_factor: std of Y
"""
dims = Yd.shape;
T = dims[2];
Yd = Yd.reshape(np.prod(dims[:-1]),-1, order="F");
####################### pull out all the pure superpixels ################################
permute_col = list(permute_col);
pos = [permute_col.index(x) for x in pure_pix];
U_mat = U_mat[:,pos];
V_mat = V_mat[:,pos];
####################### order pure superpixel according to brightness ############################
brightness = np.zeros(len(pure_pix));
u_max = U_mat.max(axis=0);
v_max = V_mat.max(axis=0);
brightness = u_max * v_max;
brightness_arg = np.argsort(-brightness); #
brightness_rank = U_mat.shape[1] - ss.rankdata(brightness,method="ordinal");
U_mat = U_mat[:,brightness_arg];
V_mat = V_mat[:,brightness_arg];
temp = np.sqrt((U_mat**2).sum(axis=0,keepdims=True));
V_mat = V_mat*temp
U_mat = U_mat/temp;
if more:
start = time.time();
normalize_factor = np.std(Yd, axis=1, keepdims=True)*T;
print(time.time()-start);
B_mat = np.median(Yd, axis=1, keepdims=True);
return U_mat, V_mat, B_mat, normalize_factor, brightness_rank
else:
return U_mat, V_mat, brightness_rank
def ls_solve_ac(X, U, V, mask=None, beta_LS=None):
"""
fast hals solution to update a, c
Parameters:
----------------
X: 2d np.darray
U: 2d np.darray (low rank decomposition of Y)
V: 2d np.darray
mask: 2d np.darray
support constraint of coefficient beta
ind: 2d binary np.darray
indication matrix of whether this data is used (=1) or not (=0).
Return:
----------------
beta_LS: 2d np.darray
least square solution
"""
K = X.shape[1];
if beta_LS is None:
beta_LS = np.zeros([K,V.shape[0]]);
UK = np.matmul(np.matmul(X.T, U), V.T);
VK = np.matmul(X.T, X);
aa = np.diag(VK);
beta_LS = beta_LS.T;
for ii in range(K):
if mask is None: ## for update temporal component c
beta_LS[[ii],:] = np.maximum(0, beta_LS[[ii],:] + ((UK[[ii],:] - np.matmul(VK[[ii],:],beta_LS))/aa[ii]));
else:
ind = (mask[ii,:]>0); ## for update spatial component a
beta_LS[[ii],ind] = np.maximum(0, beta_LS[[ii],ind] + ((UK[[ii],ind] - np.matmul(VK[[ii],:],beta_LS[:,ind]))/aa[ii]));
return beta_LS
def ls_solve_acc(X, U, V, mask=None, hals=False, beta_LS=None):
"""
fast hals solution to update temporal component and temporal background component
Parameters:
----------------
X: 2d np.darray
U: 2d np.darray (low rank decomposition of Y)
V: 2d np.darray
mask: 2d np.darray
support constraint of coefficient beta
ind: 2d binary np.darray
indication matrix of whether this data is used (=1) or not (=0).
Return:
----------------
beta_LS: 2d np.darray
least square solution
"""
K = X.shape[1];
if beta_LS is None:
beta_LS = np.zeros([K,V.shape[0]]);
UK = np.matmul(np.matmul(X.T, U), V.T);
VK = np.matmul(X.T, X);
aa = np.diag(VK);
beta_LS = beta_LS.T;
for ii in range(K):
if ii<K-1:
beta_LS[[ii],:] = np.maximum(0, beta_LS[[ii],:] + ((UK[[ii],:] - np.matmul(VK[[ii],:],beta_LS))/aa[ii]));
else:
beta_LS[[ii],:] = beta_LS[[ii],:] + ((UK[[ii],:] - np.matmul(VK[[ii],:],beta_LS))/aa[ii]);
return beta_LS
def make_mask(corr_img_all_r, corr, mask_a, num_plane=1,times=10,max_allow_neuron_size=0.2):
"""
update the spatial support: connected region in corr_img(corr(Y,c)) which is connected with previous spatial support
"""
s = np.ones([3,3]);
unit_length = int(mask_a.shape[0]/num_plane);
dims = corr_img_all_r.shape;
corr_img_all_r = corr_img_all_r.reshape(dims[0],int(dims[1]/num_plane),num_plane,-1,order="F");
mask_a = mask_a.reshape(corr_img_all_r.shape,order="F");
corr_ini = corr;
for ii in range(mask_a.shape[-1]):
for kk in range(num_plane):
jj=0;
corr = corr_ini;
if mask_a[:,:,kk,ii].sum()>0:
while jj<=times:
labeled_array, num_features = scipy.ndimage.measurements.label(corr_img_all_r[:,:,kk,ii] > corr,structure=s);
u, indices, counts = np.unique(labeled_array*mask_a[:,:,kk,ii], return_inverse=True, return_counts=True);
#print(u);
if len(u)==1:
labeled_array = np.zeros(labeled_array.shape);
if corr == 0 or corr == 1:
break;
else:
print("corr too high!")
corr = np.maximum(0, corr - 0.1);
jj = jj+1;
else:
if num_features>1:
c = u[1:][np.argmax(counts[1:])];
#print(c);
labeled_array = (labeled_array==c);
del(c);
if labeled_array.sum()/unit_length < max_allow_neuron_size or corr==1 or corr==0:
break;
else:
print("corr too low!")
corr = np.minimum(1, corr + 0.1);
jj = jj+1;
mask_a[:,:,kk,ii] = labeled_array;
mask_a = (mask_a*1).reshape(unit_length*num_plane,-1,order="F");
return mask_a
def merge_components(a,c,corr_img_all_r,U,V,normalize_factor,num_list,patch_size,merge_corr_thr=0.6,merge_overlap_thr=0.6,plot_en=False):
""" want to merge components whose correlation images are highly overlapped,
and update a and c after merge with region constrain
Parameters:
-----------
a: np.ndarray
matrix of spatial components (d x K)
c: np.ndarray
matrix of temporal components (T x K)
corr_img_all_r: np.ndarray
corr image
U, V: low rank decomposition of Y
normalize_factor: std of
num_list: indices of components
patch_size: dimensions for data
merge_corr_thr: scalar between 0 and 1
temporal correlation threshold for truncating corr image (corr(Y,c)) (default 0.6)
merge_overlap_thr: scalar between 0 and 1
overlap ratio threshold for two corr images (default 0.6)
Returns:
--------
a_pri: np.ndarray
matrix of merged spatial components (d x K')
c_pri: np.ndarray
matrix of merged temporal components (T x K')
corr_pri: np.ndarray
matrix of correlation images for the merged components (d x K')
flag: merge or not
"""
f = np.ones([c.shape[0],1]);
############ calculate overlap area ###########
a = csc_matrix(a);
a_corr = scipy.sparse.triu(a.T.dot(a),k=1);
cor = csc_matrix((corr_img_all_r>merge_corr_thr)*1);
temp = cor.sum(axis=0);
cor_corr = scipy.sparse.triu(cor.T.dot(cor),k=1);
cri = np.asarray((cor_corr/(temp.T)) > merge_overlap_thr)*np.asarray((cor_corr/temp) > merge_overlap_thr)*((a_corr>0).toarray());
a = a.toarray();
connect_comps = np.where(cri > 0);
if len(connect_comps[0]) > 0:
flag = 1;
a_pri = a.copy();
c_pri = c.copy();
G = nx.Graph();
G.add_edges_from(list(zip(connect_comps[0], connect_comps[1])))
comps=list(nx.connected_components(G))
merge_idx = np.unique(np.concatenate([connect_comps[0], connect_comps[1]],axis=0));
a_pri = np.delete(a_pri, merge_idx, axis=1);
c_pri = np.delete(c_pri, merge_idx, axis=1);
corr_pri = np.delete(corr_img_all_r, merge_idx, axis=1);
num_pri = np.delete(num_list,merge_idx);
for comp in comps:
comp=list(comp);
print("merge" + str(num_list[comp]+1));
a_zero = np.zeros([a.shape[0],1]);
a_temp = a[:,comp];
if plot_en:
spatial_comp_plot(a_temp, corr_img_all_r[:,comp].reshape(patch_size[0],patch_size[1],-1,order="F"),num_list[comp],ini=False);
mask_temp = np.where(a_temp.sum(axis=1,keepdims=True) > 0)[0];
a_temp = a_temp[mask_temp,:];
y_temp = np.matmul(a_temp, c[:,comp].T);
a_temp = a_temp.mean(axis=1,keepdims=True);
c_temp = c[:,comp].mean(axis=1,keepdims=True);
model = NMF(n_components=1, init='custom')
a_temp = model.fit_transform(y_temp, W=a_temp, H = (c_temp.T));
a_zero[mask_temp] = a_temp;
c_temp = model.components_.T;
corr_temp = vcorrcoef(U/normalize_factor, V.T, c_temp);
a_pri = np.hstack((a_pri,a_zero));
c_pri = np.hstack((c_pri,c_temp));
corr_pri = np.hstack((corr_pri,corr_temp));
num_pri = np.hstack((num_pri,num_list[comp[0]]));
return flag, a_pri, c_pri, corr_pri, num_pri
else:
flag = 0;
return flag
def delete_comp(a, c, corr_img_all_r, mask_a, num_list, temp, word, plot_en):
"""
delete those zero components
"""
print(word);
pos = np.where(temp)[0];
print("delete components" + str(num_list[pos]+1));
if plot_en:
spatial_comp_plot(a[:,pos], corr_img_all_r[:,:,pos], num_list=num_list[pos], ini=False);
corr_img_all_r = np.delete(corr_img_all_r, pos, axis=2);
mask_a = np.delete(mask_a, pos, axis=1);
a = np.delete(a, pos, axis=1);
c = np.delete(c, pos, axis=1);
num_list = np.delete(num_list, pos);
return a, c, corr_img_all_r, mask_a, num_list
def update_AC_l2(U, V, normalize_factor, a, c, b, patch_size, corr_th_fix,
maxiter=50, tol=1e-8, update_after=None, merge_corr_thr=0.5,
merge_overlap_thr=0.7, num_plane=1, plot_en=False, max_allow_neuron_size=0.2):
"""
update spatial, temporal and constant background
"""
K = c.shape[1];
res = np.zeros(maxiter);
uv_mean = (U*(V.mean(axis=0,keepdims=True))).sum(axis=1,keepdims=True);
## initialize spatial support ##
mask_a = (a>0)*1;
corr_img_all = vcorrcoef(U/normalize_factor, V.T, c);
corr_img_all_r = corr_img_all.reshape(patch_size[0],patch_size[1],-1,order="F");
f = np.ones([c.shape[0],1]);
num_list = np.arange(K);
for iters in range(maxiter):
start = time.time();
## update spatial ##
a = ls_solve_ac(c, np.hstack((V,-1*f)), np.hstack((U,b)), mask=mask_a.T, beta_LS=a).T;
temp = (a.sum(axis=0) == 0);
if sum(temp):
a, c, corr_img_all_r, mask_a, num_list = delete_comp(a, c, corr_img_all_r, mask_a, num_list, temp, "zero a!", plot_en);
b = np.maximum(0, uv_mean-((a*(c.mean(axis=0,keepdims=True))).sum(axis=1,keepdims=True)));
## update temporal ##
c = ls_solve_ac(a, np.hstack((U,b)), np.hstack((V,-1*f)), mask=None, beta_LS=c).T;
temp = (c.sum(axis=0) == 0);
if sum(temp):
a, c, corr_img_all_r, mask_a, num_list = delete_comp(a, c, corr_img_all_r, mask_a, num_list, temp, "zero c!", plot_en);
b = np.maximum(0, uv_mean-(a*(c.mean(axis=0,keepdims=True))).sum(axis=1,keepdims=True));
## merge and update spatial support ##
if update_after and ((iters+1) % update_after == 0):
corr_img_all = vcorrcoef(U/normalize_factor, V.T, c);
rlt = merge_components(a,c,corr_img_all,U, V, normalize_factor,num_list,patch_size,merge_corr_thr=merge_corr_thr,merge_overlap_thr=merge_overlap_thr,plot_en=plot_en);
flag = isinstance(rlt, int);
if ~np.array(flag):
a = rlt[1];
c = rlt[2];
corr_img_all = rlt[3];
num_list = rlt[4];
else:
print("no merge!");
mask_a = (a>0)*1;
corr_img_all_r = corr_img_all.reshape(patch_size[0],patch_size[1],-1,order="F");
mask_a = make_mask(corr_img_all_r, corr_th_fix, mask_a, num_plane, max_allow_neuron_size=max_allow_neuron_size);
temp = (mask_a.sum(axis=0) == 0);
if sum(temp):
a, c, corr_img_all_r, mask_a, num_list = delete_comp(a, c, corr_img_all_r, mask_a, num_list, temp, "zero mask!", plot_en);
a = a*mask_a;
#residual = (np.matmul(U, V.T) - np.matmul(a, c.T) - b);
#res[iters] = np.linalg.norm(residual, "fro");
#print(res[iters]);
print("time: " + str(time.time()-start));
#if iters > 0:
#if abs(res[iters] - res[iters-1])/res[iters-1] <= tol:
#break;
temp = np.sqrt((a**2).sum(axis=0,keepdims=True));
c = c*temp;
a = a/temp;
brightness = np.zeros(a.shape[1]);
a_max = a.max(axis=0);
c_max = c.max(axis=0);
brightness = a_max * c_max;
brightness_rank = np.argsort(-brightness);
a = a[:,brightness_rank];
c = c[:,brightness_rank];
corr_img_all_r = corr_img_all_r[:,:,brightness_rank];
num_list = num_list[brightness_rank];
ff = None;
fb = None;
#if iters > 0:
#print("residual relative change: " + str(abs(res[iters] - res[iters-1])/res[iters-1]));
return a, c, b, fb, ff, res, corr_img_all_r, num_list
def update_AC_bg_l2(U, V, normalize_factor, a, c, b, ff, fb, patch_size, corr_th_fix,
maxiter=50, tol=1e-8, update_after=None,merge_corr_thr=0.5,
merge_overlap_thr=0.7, num_plane=1, plot_en=False,
max_allow_neuron_size=0.2):
"""
update spatial, temporal, fluctuate background and constant background
"""
K = c.shape[1];
res = np.zeros(maxiter);
uv_mean = (U*(V.mean(axis=0,keepdims=True))).sum(axis=1,keepdims=True);
num_list = np.arange(K);
num_bg = ff.shape[1];
f = np.ones([c.shape[0],1]);
fg = np.ones([a.shape[0],num_bg]);
## initialize spatial support ##
mask_a = (a>0)*1;
corr_img_all = vcorrcoef(U/normalize_factor, V.T, c);
corr_img_all_r = corr_img_all.reshape(patch_size[0],patch_size[1],-1,order="F");
mask_ab = np.hstack((mask_a,fg));
for iters in range(maxiter):
start = time.time();
## update spatial and spatial background ##
temp = ls_solve_ac(np.hstack((c,ff)), np.hstack((V,-1*f)), np.hstack((U,b)), mask=mask_ab.T, beta_LS=np.hstack((a,fb))).T;
a = temp[:,:-num_bg];
fb = temp[:,-num_bg:];
temp = (a.sum(axis=0) == 0);
if sum(temp):
a, c, corr_img_all_r, mask_a, num_list = delete_comp(a, c, corr_img_all_r, mask_a, num_list, temp, "zero a!", plot_en);
b = np.maximum(0, uv_mean-(a*(c.mean(axis=0,keepdims=True))).sum(axis=1,keepdims=True));
## update temporal and temporal background ##
temp = ls_solve_acc(np.hstack((a,fb)), np.hstack((U,b)), np.hstack((V,-1*f)), mask=None, beta_LS=np.hstack((c,ff))).T;
c = temp[:,:-num_bg];
ff = temp[:,-num_bg:];
ff = ff - ff.mean(axis=0,keepdims=True);
temp = (c.sum(axis=0) == 0);
if sum(temp):
a, c, corr_img_all_r, mask_a, num_list = delete_comp(a, c, corr_img_all_r, mask_a, num_list, temp, "zero c!", plot_en);
b = np.maximum(0, uv_mean-(a*(c.mean(axis=0,keepdims=True))).sum(axis=1,keepdims=True));
## merge and update spatial support ##
if update_after and ((iters+1) % update_after == 0):
corr_img_all = vcorrcoef(U/normalize_factor, V.T, c);
rlt = merge_components(a,c,corr_img_all,U, V, normalize_factor,num_list,patch_size,merge_corr_thr=merge_corr_thr,merge_overlap_thr=merge_overlap_thr,plot_en=plot_en);
flag = isinstance(rlt, int);
if ~np.array(flag):
a = rlt[1];
c = rlt[2];
corr_img_all = rlt[3];
num_list = rlt[4];
else:
print("no merge!");
mask_a = (a>0)*1;
corr_img_all_r = corr_img_all.reshape(patch_size[0],patch_size[1],-1,order="F");
mask_a = make_mask(corr_img_all_r, corr_th_fix, mask_a, num_plane, max_allow_neuron_size=max_allow_neuron_size);
temp = (mask_a.sum(axis=0) == 0);
if sum(temp):
a, c, corr_img_all_r, mask_a, num_list = delete_comp(a, c, corr_img_all_r, mask_a, num_list, temp, "zero mask!", plot_en);
a = a*mask_a;
mask_ab = np.hstack((mask_a,fg));
#residual = (np.matmul(U, V.T) - np.matmul(a, c.T) - b - np.matmul(fb,ff.T));