resize a 2D numpy array excluding NaN
I'm trying to resize a 2D numpy array of a given factor, obtaining a smaller array in output.
The array is read from an image file and some of the values should be NaN (Not a Number, np.nan from numpy): it is the result of remote sensing measurements from satellite and simply some pixels weren't measured.
The suitable package I found for this is scypy.misc.imresize, but each pixel in the output array containing a NaN is set to NaN, even if there are some valid data in the original pixels interpolated together.
My solution is appended here, what I've done is essentially :
I'm planning to add keyword to choice between different output (average, median, standard deviation of the input pixels and so on).
It is working as expected, but on a ~1Mpx image it takes around 3 seconds. Due to my lack of experience in python I'm searching for improvements.
Do anyone have suggestion how to do it better and more efficiently?
Do anyone know a library that already implements all that stuff?
Thanks.
Here you have an example output for random pixel input generated with the code here below:
import numpy as np
import pylab as plt
from scipy import misc
def resize_2d_nonan(array,factor):
"""
Resize a 2D array by different factor on two axis sipping NaN values.
If a new pixel contains only NaN, it will be set to NaN
Parameters
----------
array : 2D np array
factor : int or tuple. If int x and y factor wil be the same
Returns
-------
array : 2D np array scaled by factor
Created on Mon Jan 27 15:21:25 2014
@author: damo_ma
"""
xsize, ysize = array.shape
if isinstance(factor,int):
factor_x = factor
factor_y = factor
elif isinstance(factor,tuple):
factor_x , factor_y = factor[0], factor[1]
else:
raise NameError('Factor must be a tuple (x,y) or an integer')
if not (xsize %factor_x == 0 or ysize % factor_y == 0) :
raise NameError('Factors must be intger multiple of array shape')
new_xsize, new_ysize = xsize/factor_x, ysize/factor_y
new_array = np.empty([new_xsize, new_ysize])
new_array[:] = np.nan # this saves us an assignment in the loop below
# submatrix indexes : is the average box on the original matrix
subrow, subcol = np.indices((factor_x, factor_y))
# new matrix indexs
row, col = np.indices((new_xsize, new_ysize))
# some output for testing
#for i, j, ind in zip(row.reshape(-1), col.reshape(-1),range(row.size)) :
# print '----------------------------------------------'
# print 'i: %i, j: %i, ind: %i ' % (i, j, ind)
# print 'subrow+i*new_ysize, subcol+j*new_xsize :'
# print i,'*',new_xsize,'=',i*factor_x
# print j,'*',new_ysize,'=',j*factor_y
# print subrow+i*factor_x,subcol+j*factor_y
# print '---'
# print 'array[subrow+i*factor_x,subcol+j*factor_y] : '
# print array[subrow+i*factor_x,subcol+j*factor_y]
for i, j, ind in zip(row.reshape(-1), col.reshape(-1),range(row.size)) :
# define the small sub_matrix as view of input matrix subset
sub_matrix = array[subrow+i*factor_x,subcol+j*factor_y]
# modified from any(a) and all(a) to a.any() and a.all()
# see https://stackoverflow.com/a/10063039/1435167
if not (np.isnan(sub_matrix)).all(): # if we haven't all NaN
if (np.isnan(sub_matrix)).any(): # if we haven no NaN at all
msub_matrix = np.ma.masked_array(sub_matrix,np.isnan(sub_matrix))
(new_array.reshape(-1))[ind] = np.mean(msub_matrix)
else: # if we haven some NaN
(new_array.reshape(-1))[ind] = np.mean(sub_matrix)
# the case assign NaN if we have all NaN is missing due
# to the standard values of new_array
return new_array
row , cols = 6, 4
a = 10*np.random.random_sample((row , cols))
a[0:3,0:2] = np.nan
a[0,2] = np.nan
factor_x = 2
factor_y = 2
a_misc = misc.imresize(a, .5, interp='nearest', mode='F')
a_2d_nonan = resize_2d_nonan(a,(factor_x,factor_y))
print a
print
print a_misc
print
print a_2d_nonan
plt.subplot(131)
plt.imshow(a,interpolation='nearest')
plt.title('original')
plt.xticks(arange(a.shape[1]))
plt.yticks(arange(a.shape[0]))
plt.subplot(132)
plt.imshow(a_misc,interpolation='nearest')
plt.title('scipy.misc')
plt.xticks(arange(a_misc.shape[1]))
plt.yticks(arange(a_misc.shape[0]))
plt.subplot(133)
plt.imshow(a_2d_nonan,interpolation='nearest')
plt.title('my.func')
plt.xticks(arange(a_2d_nonan.shape[1]))
plt.yticks(arange(a_2d_nonan.shape[0]))
EDIT
I add some modification to address ChrisProsser comment.
If I substitute the NaN with some other value, let say the average of the not-NaN pixels, it will affect all the subsequent calculation: the difference between the resampled original array and the resampled array with NaN substituted shows that 2 pixels changed their values.
My goal is simply skip all the NaN pixels.
# substitute NaN with the average value
ind_nonan , ind_nan = np.where(np.isnan(a) == False), np.where(np.isnan(a) == True)
a_substitute = np.copy(a)
a_substitute[ind_nan] = np.mean(a_substitute[ind_nonan]) # substitute the NaN with average on the not-Nan
a_substitute_misc = misc.imresize(a_substitute, .5, interp='nearest', mode='F')
a_substitute_2d_nonan = resize_2d_nonan(a_substitute,(factor_x,factor_y))
print a_2d_nonan-a_substitute_2d_nonan
[[ nan -0.02296697]
[ 0.23143208 0. ]
[ 0. 0. ]]
** 2nd EDIT**
To address the Hooked's answer I put some additional code. It is an iteresting idea, sadly it interpolates new values over pixels that should be "empty" (NaN) and for my small example generate more NaN than good values.
X , Y = np.indices((row , cols))
X_new , Y_new = np.indices((row/factor_x , cols/factor_y))
from scipy.interpolate import CloughTocher2DInterpolator as intp
C = intp((X[ind_nonan],Y[ind_nonan]),a[ind_nonan])
a_interp = C(X_new , Y_new)
print a
print
print a_interp
[[ nan, nan],
[ nan, nan],
[ nan, 6.32826577]])
You are operating on small windows of the array. Instead of looping through the array to make the windows, the array can be efficiently restructured by manipulating its strides. The numpy library provides the as_strided() function to help with that. An example is provided in the SciPy CookBook Stride tricks for the Game of Life.
The following will use a generalized sliding window function found at Efficient Overlapping Windows with Numpy - I will include it at the end.
Determine the shape of the new array:
rows, cols = a.shape
new_shape = rows / 2, cols / 2
Restructure the array into the windows you need, and create an indexing array identifying NaNs:
# 2x2 windows of the original array
windows = sliding_window(a, (2,2))
# make a windowed boolean array for indexing
notNan = sliding_window(np.logical_not(np.isnan(a)), (2,2))
The new array can be made using a list comprehension or a generator expression.
# using a list comprehension
# make a list of the means of the windows, disregarding the Nan's
means = [window[index].mean() for window, index in zip(windows, notNan)]
new_array = np.array(means).reshape(new_shape)
# generator expression
# produces the means of the windows, disregarding the Nan's
means = (window[index].mean() for window, index in zip(windows, notNan))
new_array = np.fromiter(means, dtype = np.float32).reshape(new_shape)
The generator expression should conserve memory. Using itertools.izip() instead of `zip should also help if memory is a problem. I just used the list comprehension for your solution.
Your function:
def resize_2d_nonan(array,factor):
"""
Resize a 2D array by different factor on two axis skipping NaN values.
If a new pixel contains only NaN, it will be set to NaN
Parameters
----------
array : 2D np array
factor : int or tuple. If int x and y factor wil be the same
Returns
-------
array : 2D np array scaled by factor
Created on Mon Jan 27 15:21:25 2014
@author: damo_ma
"""
xsize, ysize = array.shape
if isinstance(factor,int):
factor_x = factor
factor_y = factor
window_size = factor, factor
elif isinstance(factor,tuple):
factor_x , factor_y = factor
window_size = factor
else:
raise NameError('Factor must be a tuple (x,y) or an integer')
if (xsize % factor_x or ysize % factor_y) :
raise NameError('Factors must be integer multiple of array shape')
new_shape = xsize / factor_x, ysize / factor_y
# non-overlapping windows of the original array
windows = sliding_window(a, window_size)
# windowed boolean array for indexing
notNan = sliding_window(np.logical_not(np.isnan(a)), window_size)
#list of the means of the windows, disregarding the Nan's
means = [window[index].mean() for window, index in zip(windows, notNan)]
# new array
new_array = np.array(means).reshape(new_shape)
return new_array
I haven't done any time comparisons with your original function, but it should be faster.
Many solutions I've seen here on SO vectorize the operations to increase speed/efficiency - I don't quite have a handle on that and don't know if it can be applied to your problem. Searching SO for window, array, moving average, vectorize, and numpy should produce similar questions and answers for reference.
sliding_window() from Efficient Overlapping Windows with Numpy :
import numpy as np
from numpy.lib.stride_tricks import as_strided as ast
from itertools import product
def norm_shape(shape):
'''
Normalize numpy array shapes so they're always expressed as a tuple,
even for one-dimensional shapes.
Parameters
shape - an int, or a tuple of ints
Returns
a shape tuple
'''
try:
i = int(shape)
return (i,)
except TypeError:
# shape was not a number
pass
try:
t = tuple(shape)
return t
except TypeError:
# shape was not iterable
pass
raise TypeError('shape must be an int, or a tuple of ints')
def sliding_window(a,ws,ss = None,flatten = True):
'''
Return a sliding window over a in any number of dimensions
Parameters:
a - an n-dimensional numpy array
ws - an int (a is 1D) or tuple (a is 2D or greater) representing the size
of each dimension of the window
ss - an int (a is 1D) or tuple (a is 2D or greater) representing the
amount to slide the window in each dimension. If not specified, it
defaults to ws.
flatten - if True, all slices are flattened, otherwise, there is an
extra dimension for each dimension of the input.
Returns
an array containing each n-dimensional window from a
'''
if None is ss:
# ss was not provided. the windows will not overlap in any direction.
ss = ws
ws = norm_shape(ws)
ss = norm_shape(ss)
# convert ws, ss, and a.shape to numpy arrays so that we can do math in every
# dimension at once.
ws = np.array(ws)
ss = np.array(ss)
shape = np.array(a.shape)
# ensure that ws, ss, and a.shape all have the same number of dimensions
ls = [len(shape),len(ws),len(ss)]
if 1 != len(set(ls)):
raise ValueError(
'a.shape, ws and ss must all have the same length. They were %s' % str(ls))
# ensure that ws is smaller than a in every dimension
if np.any(ws > shape):
raise ValueError(
'ws cannot be larger than a in any dimension.
a.shape was %s and ws was %s' % (str(a.shape),str(ws)))
# how many slices will there be in each dimension?
newshape = norm_shape(((shape - ws) // ss) + 1)
# the shape of the strided array will be the number of slices in each dimension
# plus the shape of the window (tuple addition)
newshape += norm_shape(ws)
# the strides tuple will be the array's strides multiplied by step size, plus
# the array's strides (tuple addition)
newstrides = norm_shape(np.array(a.strides) * ss) + a.strides
strided = ast(a,shape = newshape,strides = newstrides)
if not flatten:
return strided
# Collapse strided so that it has one more dimension than the window. I.e.,
# the new array is a flat list of slices.
meat = len(ws) if ws.shape else 0
firstdim = (np.product(newshape[:-meat]),) if ws.shape else ()
dim = firstdim + (newshape[-meat:])
# remove any dimensions with size 1
dim = filter(lambda i : i != 1,dim)
return strided.reshape(dim)
Interpolate the points, using scipy.interpolate , on a different grid. Below I've shown a cubic interpolator, which is slower but probably more accurate. You'll notice that the corner pixels are missing with this function, you could then use a linear or nearest neighbor interpolation to handle those last values.
import numpy as np
import pylab as plt
# Test data
row = np.linspace(-3,3,50)
X,Y = np.meshgrid(row,row)
Z = np.sqrt(X**2+Y**2) + np.cos(Y)
# Make some dead pixels, favor an edge
dead = np.random.random(Z.shape)
dead = (dead*X>.7)
Z[dead] =np.nan
from scipy.interpolate import CloughTocher2DInterpolator as intp
C = intp((X[~dead],Y[~dead]),Z[~dead])
new_row = np.linspace(-3,3,25)
xi,yi = np.meshgrid(new_row,new_row)
zi = C(xi,yi)
plt.subplot(121)
plt.title("Original signal 50x50")
plt.imshow(Z,interpolation='nearest')
plt.subplot(122)
plt.title("Interpolated signal 25x25")
plt.imshow(zi,interpolation='nearest')
plt.show()
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