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Slicing a 3D image to create a 2D image

I have several 3D images of shape (32,32,32) and I want to create 2D images from them. I want to do that by getting each slice in the z-axis and putting each of them in a square array in order, something like this:
Because I want the 2D image to be square I need to fill the missing slices with zeros (Black in the example).
This is what I did:
# I created an array of the desired dimensions
grid = np.zeros((6*32,6*32))
# Then, I assigned to each section of the grid the values of every slice of the 3d_image:
grid[0:32, 0:32] = 3d_image[:,:,0]
grid[0:32, 32:64] = 3d_image[:,:,1]
grid[0:32, 64:96] = 3d_image[:,:,2]
grid[0:32, 96:128] = 3d_image[:,:,3]
grid[0:32, 128:160] = 3d_image[:,:,4]
grid[0:32, 160:192] = 3d_image[:,:,5]
grid[32:64, 0:32] = 3d_image[:,:,6]
grid[32:64, 32:64] = 3d_image[:,:,7]
grid[32:64, 64:96] = 3d_image[:,:,8]
grid[32:64, 96:128] = 3d_image[:,:,9]
grid[32:64, 128:160] = 3d_image[:,:,10]
grid[32:64, 160:192] = 3d_image[:,:,11]
grid[64:96, 0:32] = 3d_image[:,:,12]
grid[64:96, 32:64] = 3d_image[:,:,13]
...
grid[160:192, 160:192] = 3d_image[:,:,31]
And It worked!! But I want to automate it, so I tried this:
d = [0, 32, 64, 96, 128, 160]
for j in range(6):
for i in d:
grid[0:32, i:i+32] = 3d_image[:,:,j]
But it didn't work, the slice index for 3d_image (j) is not changing, and I don't know how to change the index range for grid after every 6th slice.
Could you help me?

Assuming that that img is an array of the shape (32,32,32), this should work:
N = 32
a = np.vstack([img, np.zeros((4, N, N), dtype=img.dtype)])
grid = a.transpose(1, 0, 2).reshape(N, -1, 6*N).transpose(1, 0, 2).reshape(6*N, -1)

Here's an automated way to do it. Let's say your array with shape (32, 32, 32) is called n. Note that this method relies on all 3 dimensions having the same size.
num_layers = n.shape[0]
# num_across = how many images will go in 1 row or column in the final array.
num_across = int(np.ceil(np.sqrt(num_layers)))
# new_shape = how many numbers go in a row in the final array.
new_shape = num_across * num_layers
final_im = np.zeros((new_shape**2)).reshape(new_shape, new_shape)
for i in range(num_layers):
# Get what number row and column the image goes in (e.g. in the example,
# the image labelled 28 is in the 4th (3rd with 0-indexing) column and 5th
# (4th with 0-indexing) row.
col_num = i % num_across
row_num = i // num_across
# Put the image in the appropriate part of the final image.
final_im[row_num*num_layers:row_num*num_layers + num_layers, col_num*num_layers:col_num*num_layers + num_layers] = n[i]
final_im now contains what you want. Below is a representation where each image is a different color and the "black" areas are purple because matplotlib colormaps are funny like that:
Anyway, you can tell that the images go where they're supposed to and you get your empty space along the bottom.

Storing pixel values of a greyscale video ,averaging them and then showing the resulting video

`n = 3
array = np.ones((n,n)) / (n*n)
n = array.shape[0] * array.shape1
while(True):
ret, frame = cap.read()
if ret is True:
print("newframe")
gframe = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
dst = cv2.copyMakeBorder(gframe, 1, 1, 1, 1, borderType, None, None)
blur = cv2.blur(dst,(3,3))
if k == 1 :
lastframe = gframe
curframe = gframe
nextframe = gframe
newFrame = gframe
k = 0
else :
lf = ndimage.convolve(lastframe, array, mode='constant', cval= 0.0)
cf = ndimage.convolve(curframe, array, mode='constant', cval= 0.0)
nf = ndimage.convolve(nextframe, array, mode='constant', cval= 0.0)
lastframe = curframe
curframe = nextframe
nextframe = gframe
b = np.zeros((3, 528, 720))
b[0] = lf
b[1] = cf
b[2] = nf
result = np.mean(b, axis=0)
cv2.imshow('frame',result)
cv2.imshow('frame2',gframe)
`enter image description here
I am trying to add all pixel values of a 3x3 pixel and then average them. I need to do that for every pixel and every frame and replace the primary pixel with the averaged one. However the way i am trying to do it makes it really slow and not really accurate.

This sounds like a convolution.
import numpy as np
from scipy import ndimage
a = np.random.random((5, 5))
a
[[0.14742615 0.83548453 0.67433445 0.59162829 0.21160044]
[0.1700598 0.89074466 0.84155171 0.65092969 0.3842437 ]
[0.22662423 0.2266929 0.47757456 0.34480112 0.06261333]
[0.89402116 0.00101947 0.90503461 0.93112109 0.44817247]
[0.21788789 0.3338606 0.07323461 0.28944439 0.91217591]]
Convolution operation with window size 3x3
n = 3
k = np.ones((n, n)) / (n * n)
n = k.shape[0] * k.shape[1]
b = ndimage.convolve(a, k, mode='constant', cval=0.0)
b
[[0.22707946 0.39551126 0.49829704 0.3726987 0.2042669 ]
[0.27744803 0.49894366 0.61486021 0.47103081 0.24953517]
[0.26768469 0.51481368 0.58549664 0.56067136 0.31354238]
[0.21112292 0.37288334 0.39808704 0.4937969 0.33203648]
[0.16075435 0.26945093 0.28152386 0.39546479 0.28676821]]
Now you just have to do it for the current frame, and the two prior frames.
-------- EDIT: For three frames -----------
For 3D you could write a convolution function like in this post, but its quite complex as it uses FFTs
If you just want to average across three frames, you could do:
f1 = np.random.random((5, 5)) # Frame1
f2 = np.random.random((5, 5)) # Frame2
f3 = np.random.random((5, 5)) # Frame3
n = 3
k = np.ones((n, n)) / (n * n)
n = k.shape[0] * k.shape[1]
b0 = ndimage.convolve(f1, k, mode='constant', cval=0.0)
b1 = ndimage.convolve(f2, k, mode='constant', cval=0.0)
b2 = ndimage.convolve(f3, k, mode='constant', cval=0.0)
# Create a 3D Matrix, with each fame placed along the first dimension
b = np.zeros((3, 5, 5))
b[0] = b0
b[1] = b1
b[2] = b2
# Take the average across the first dimension (across frames)
result = np.mean(b, axis=0)
There probably is a more elegant solution than this, but it gets the job done.
-------- EDIT: For Movies -----------
Based on all the questions in the comments I've decided to attempt to add some more code to help with implementation.
Firstly I'm starting out with these 7 consecutive stills from a movie:
I have not verified that the following code is bug proof or actually returns the correct result.
import cv2
import numpy as np
from scipy import ndimage
# this is a function to do previous code
def mean_frames(frames, kernel):
b = np.zeros(frames.shape)
for i in range(frames.shape[0]):
b[i] = ndimage.convolve(frames[i], k, mode='constant', cval=0.0)
b = np.mean(b, axis=0) / frames.shape[0]
return b
mean_N = 3 # frames to average
# read in 1 file to get dimenions
im = cv2.imread(f'{root}1.png', cv2.IMREAD_GRAYSCALE)
# setup numpy matrix that will hold mean_N frames at a time
frames = np.zeros((mean_N, im.shape[0], im.shape[1]))
avg_frames = [] # list to store our 3 averaged frames
count = 0 # counter to position frames in 1st dim of 3D matrix for avg
k = np.ones((3, 3)) / (3 * 3) # kernel for 2D convolution
for j in range(1, 7): # 7 images
file_name = root + str(j) + '.png'
im = cv2.imread(file_name, cv2.IMREAD_GRAYSCALE)
frames[count, ::] = im # store in 3D matrix
# if loaded more than min req. for avg, we average
if j >= mean_N:
# average and store to list
avg_frames.append(mean_frames(frames, k))
# if the count is mean_N - 1, that means we need to replace
# the 0th matrix in frames so that we are doing a 'moving avg'
if count == (mean_N - 1):
count = 0
else:
count += 1 #increase position in 0th dim for 3D matrix storage
# ouput averaged frames
for i, f in enumerate(avg_frames):
cv2.imwrite(f'{path}output{i}.jpg', f)
Then looking at the folder, there are 5 files (as expected if we did a moving average of 3 frames over 7 stills:
looking at before and after:
Image 3:
and averaged image #1:
The image not only is in gray scale (as expected) but seems quite dark. Perhaps some brightening would make things look better/more apparent.

Your question is very interesting.
I saw that you use many loops for activating this function. Let's process analysis.
Just for a frame.
You want to add all pixel values of a 3x3 pixel neighborhood. So I think Image interpolation is very suitable for this case. In OpenCV, we use resize() to interpolate pixel for image. So the INTER_NEAREST is best for this situation.
This is the formula for INTER_NEAREST.
Now you get the pixel added image.
Then you want to do that for every pixel and every frame and replace the primary pixel with the average one. And I think the Average filtering is a better solution.
The filter will work every pixel.
The code of a temporary example.
Interpolation
img = cv2.resize(img, (img.size[0]*3, img.size[1]*3), cv2.INTER_NEAREST)
Filter
img = cv2.blur(img, (3, 3))

Check the parity of the Green and Blue values into an image

I have an array ver of shape (9,8,2) which I extracted from an image.
What I'm searching to do is to iterate over the pixels of this array, check if Green and Blue values have a different parity, if so, put the result True in a list, and do the same for each lines.
ver = im_arr[:9,:8,1:3]
Here I took the first 9 lines of the image, the 8 first pixels, and I've extracted the columns to have only the Green and Blue values.
I now know how to with a 2D array like that :
cf = cf[:,1:3]
jou = (cf.sum(1)%2).astype(bool)
But in this case, with a 3D array, I really don't know how to do, I tried with three for loop, but it doesn't work :
for i in range(ver.shape[0]):
for y in range(ver.shape[1]):
for z in range(ver.shape[2]):
juju[i,y,z] = (ver.sum(1)%2).astype(bool)

import numpy as np
image = np.random.randint(0, 255, (100, 100, 3))
subset = image[:9, :8, 1:]
mask = ~np.all(np.remainder(subset, 2) == 0, axis=-1)
This code generates a random image and extracts the subset. Then it checks that the remainder of all numbers in the array are divisible by 2. The np.all call checks if across the last dimension, all values are True and returns True if so, False otherwise. To get the mask you want I just negate the result with ~
Edit to add a solution that checks whether both values across dimensions are either equal or odd.
import numpy as np
image = np.random.randint(0, 255, (100, 100, 3))
subset = image[:9, :8, 1:]
even = np.remainder(subset, 2) == 0
mask = ~np.equal(even[..., 0], even[..., 1])

If you mask the LSB of the Green and Blue channels and add them, you can only get:
0 + 0 = 0
0 + 1 = 1 <--- THIS
1 + 0 = 1 <--- THIS
1 + 1 = 2
So, you want to identify where they add up to 1, i.e. they are different:
mask = np.sum((ver & 1), axis=-1) == 1

Image texture with skimage

I'm trying to get texture properties from a GLCM I created using greycomatrix from skimage.feature. My input data is an image with multiple bands and I want the texture properties for each pixel (resulting in an image with the dimensions cols x rows x (properties *bands)), as it can be achieved using ENVI. But I'm too new to this to come to grips with greycomatrix and greycoprops. This is what I tried:
import numpy as np
from skimage import io
from skimage.feature import greycomatrix, greycoprops
array = io.imread('MYFILE.tif')
array = array.astype(np.int64)
props = ['contrast', 'dissimilarity', 'homogeneity', 'energy', 'correlation', 'ASM']
textures = np.zeros((array.shape[0], array.shape[1], array.shape[2] * len(props)), np.float32)
angles = [0, np.pi / 4, np.pi / 2, 3 * np.pi / 4]
bands = array.shape[2]
for b in range(bands):
glcm = greycomatrix(array[:, :, b], [1], angles, np.nanmax(array) + 1,
symmetric=True, normed=True)
for p, prop in enumerate(props):
textures[:, :, b] = greycoprops(glcm, prop)
Unfortunately, this gives me a 1 x 4 matrix per prop, which I guess is one value per angle FOR THE WHOLE IMAGE, but this is not what I want. I need it per pixel, like contrast for each single pixel, computed from its respective surroundings. What am I missing?

This snippet should get the job done:
import numpy as np
from skimage import io, util
from skimage.feature.texture import greycomatrix, greycoprops
img = io.imread('fourbandimg.tif')
rows, cols, bands = img.shape
radius = 5
side = 2*radius + 1
distances = [1]
angles = [0, np.pi/2]
props = ['contrast', 'dissimilarity', 'homogeneity']
dim = len(distances)*len(angles)*len(props)*bands
padded = np.pad(img, radius, mode='reflect')
windows = [util.view_as_windows(padded[:, :, band].copy(), (side, side))
for band in range(bands)]
feats = np.zeros(shape=(rows, cols, dim))
for row in range(rows):
for col in range(cols):
pixel_feats = []
for band in range(bands):
glcm = greycomatrix(windows[band][row, col, :, :],
distances=distances,
angles=angles)
pixel_feats.extend([greycoprops(glcm, prop).ravel()
for prop in props])
feats[row, col, :] = np.concatenate(pixel_feats)
The sample image has 128 rows, 128 columns and 4 bands (click here to download). At each image pixel a square local neighbourhood of size 11 is used to compute the grayscale matrices corresponding to the pixel to the right and the pixel above for each band. Then, contrast, dissimilarity and homogeneity are computed for those matrices. Thus we have 4 bands, 1 distance, 2 angles and 3 properties. Hence for each pixel the feature vector has 4 × 1 × 2 × 3 = 24 components.
Notice that in order to preserve the number of rows and columns the image has been padded using the image itself mirrored along the edge of the array. It this approach does not fit your needs you could simply ignore the outer frame of the image.
As a final caveat, the code could take a while to run.
Demo
In [193]: img.shape
Out[193]: (128, 128, 4)
In [194]: feats.shape
Out[194]: (128, 128, 24)
In [195]: feats[64, 64, :]
Out[195]:
array([ 1.51690000e+04, 9.50100000e+03, 1.02300000e+03,
8.53000000e+02, 1.25203577e+01, 9.38930575e+00,
2.54300000e+03, 1.47800000e+03, 3.89000000e+02,
3.10000000e+02, 2.95064854e+01, 3.38267222e+01,
2.18970000e+04, 1.71690000e+04, 1.21900000e+03,
1.06700000e+03, 1.09729371e+01, 1.11741654e+01,
2.54300000e+03, 1.47800000e+03, 3.89000000e+02,
3.10000000e+02, 2.95064854e+01, 3.38267222e+01])
In [196]: io.imshow(img)
Out[196]: <matplotlib.image.AxesImage at 0x2a74bc728d0>
Edit
You could cast your data to the type required by greycomatrix through NumPy's uint8 or scikit-images's img_as_ubyte.

Interpolate between two images

I'm trying to interpolate between two images in Python.
Images are of shapes (188, 188)
I wish to interpolate the image 'in-between' these two images. Say Image_1 is at location z=0 and Image_2 is at location z=2. I want the interpolated image at location z=1.
I believe this answer (MATLAB) contains a similar problem and solution.
Creating intermediate slices in a 3D MRI volume with MATLAB
I've tried to convert this code to Python as follows:
from scipy.interpolate import interpn
from scipy.interpolate import griddata
# Construct 3D volume from images
# arr.shape = (2, 182, 182)
arr = np.r_['0,3', image_1, image_2]
slices,rows,cols = arr.shape
# Construct meshgrids
[X,Y,Z] = np.meshgrid(np.arange(cols), np.arange(rows), np.arange(slices));
[X2,Y2,Z2] = np.meshgrid(np.arange(cols), np.arange(rows), np.arange(slices*2));
# Run n-dim interpolation
Vi = interpn([X,Y,Z], arr, np.array([X1,Y1,Z1]).T)
However, this produces an error:
ValueError: The points in dimension 0 must be strictly ascending
I suspect I am not constructing my meshgrid(s) properly but am kind of lost on whether or not this approach is correct.
Any ideas?
---------- Edit -----------
Found some MATLAB code that appears to solve this problem:
Interpolating Between Two Planes in 3d space
I attempted to convert this to Python:
from scipy.ndimage.morphology import distance_transform_edt
from scipy.interpolate import interpn
def ndgrid(*args,**kwargs):
"""
Same as calling ``meshgrid`` with *indexing* = ``'ij'`` (see
``meshgrid`` for documentation).
"""
kwargs['indexing'] = 'ij'
return np.meshgrid(*args,**kwargs)
def bwperim(bw, n=4):
"""
perim = bwperim(bw, n=4)
Find the perimeter of objects in binary images.
A pixel is part of an object perimeter if its value is one and there
is at least one zero-valued pixel in its neighborhood.
By default the neighborhood of a pixel is 4 nearest pixels, but
if `n` is set to 8 the 8 nearest pixels will be considered.
Parameters
----------
bw : A black-and-white image
n : Connectivity. Must be 4 or 8 (default: 8)
Returns
-------
perim : A boolean image
From Mahotas: http://nullege.com/codes/search/mahotas.bwperim
"""
if n not in (4,8):
raise ValueError('mahotas.bwperim: n must be 4 or 8')
rows,cols = bw.shape
# Translate image by one pixel in all directions
north = np.zeros((rows,cols))
south = np.zeros((rows,cols))
west = np.zeros((rows,cols))
east = np.zeros((rows,cols))
north[:-1,:] = bw[1:,:]
south[1:,:] = bw[:-1,:]
west[:,:-1] = bw[:,1:]
east[:,1:] = bw[:,:-1]
idx = (north == bw) & \
(south == bw) & \
(west == bw) & \
(east == bw)
if n == 8:
north_east = np.zeros((rows, cols))
north_west = np.zeros((rows, cols))
south_east = np.zeros((rows, cols))
south_west = np.zeros((rows, cols))
north_east[:-1, 1:] = bw[1:, :-1]
north_west[:-1, :-1] = bw[1:, 1:]
south_east[1:, 1:] = bw[:-1, :-1]
south_west[1:, :-1] = bw[:-1, 1:]
idx &= (north_east == bw) & \
(south_east == bw) & \
(south_west == bw) & \
(north_west == bw)
return ~idx * bw
def signed_bwdist(im):
'''
Find perim and return masked image (signed/reversed)
'''
im = -bwdist(bwperim(im))*np.logical_not(im) + bwdist(bwperim(im))*im
return im
def bwdist(im):
'''
Find distance map of image
'''
dist_im = distance_transform_edt(1-im)
return dist_im
def interp_shape(top, bottom, num):
if num<0 and round(num) == num:
print("Error: number of slices to be interpolated must be integer>0")
top = signed_bwdist(top)
bottom = signed_bwdist(bottom)
r, c = top.shape
t = num+2
print("Rows - Cols - Slices")
print(r, c, t)
print("")
# rejoin top, bottom into a single array of shape (2, r, c)
# MATLAB: cat(3,bottom,top)
top_and_bottom = np.r_['0,3', top, bottom]
#top_and_bottom = np.rollaxis(top_and_bottom, 0, 3)
# create ndgrids
x,y,z = np.mgrid[0:r, 0:c, 0:t-1] # existing data
x1,y1,z1 = np.mgrid[0:r, 0:c, 0:t] # including new slice
print("Shape x y z:", x.shape, y.shape, z.shape)
print("Shape x1 y1 z1:", x1.shape, y1.shape, z1.shape)
print(top_and_bottom.shape, len(x), len(y), len(z))
# Do interpolation
out = interpn((x,y,z), top_and_bottom, (x1,y1,z1))
# MATLAB: out = out(:,:,2:end-1)>=0;
array_lim = out[-1]-1
out[out[:,:,2:out] >= 0] = 1
return out
I call this as follows:
new_image = interp_shape(image_1,image_2, 1)
Im pretty sure this is 80% of the way there but I still get this error when running:
ValueError: The points in dimension 0 must be strictly ascending
Again, I am probably not constructing my meshes correctly. I believe np.mgrid should produce the same result as MATLABs ndgrid though.
Is there a better way to construct the ndgrid equivalents?

I figured this out. Or at least a method that produces desirable results.
Based on: Interpolating Between Two Planes in 3d space
def signed_bwdist(im):
'''
Find perim and return masked image (signed/reversed)
'''
im = -bwdist(bwperim(im))*np.logical_not(im) + bwdist(bwperim(im))*im
return im
def bwdist(im):
'''
Find distance map of image
'''
dist_im = distance_transform_edt(1-im)
return dist_im
def interp_shape(top, bottom, precision):
'''
Interpolate between two contours
Input: top
[X,Y] - Image of top contour (mask)
bottom
[X,Y] - Image of bottom contour (mask)
precision
float - % between the images to interpolate
Ex: num=0.5 - Interpolate the middle image between top and bottom image
Output: out
[X,Y] - Interpolated image at num (%) between top and bottom
'''
if precision>2:
print("Error: Precision must be between 0 and 1 (float)")
top = signed_bwdist(top)
bottom = signed_bwdist(bottom)
# row,cols definition
r, c = top.shape
# Reverse % indexing
precision = 1+precision
# rejoin top, bottom into a single array of shape (2, r, c)
top_and_bottom = np.stack((top, bottom))
# create ndgrids
points = (np.r_[0, 2], np.arange(r), np.arange(c))
xi = np.rollaxis(np.mgrid[:r, :c], 0, 3).reshape((r**2, 2))
xi = np.c_[np.full((r**2),precision), xi]
# Interpolate for new plane
out = interpn(points, top_and_bottom, xi)
out = out.reshape((r, c))
# Threshold distmap to values above 0
out = out > 0
return out
# Run interpolation
out = interp_shape(image_1,image_2, 0.5)
Example output:

I came across a similar problem where I needed to interpolate the shift between frames where the change did not merely constitute a translation but also changes to the shape itself . I solved this problem by :
Using center_of_mass from scipy.ndimage.measurements to calculate the center of the object we want to move in each frame
Defining a continuous parameter t where t=0 first and t=1 last frame
Interpolate the motion between two nearest frames (with regard to a specific t value) by shifting the image back/forward via shift from scipy.ndimage.interpolation and overlaying them.
Here is the code:
def inter(images,t):
#input:
# images: list of arrays/frames ordered according to motion
# t: parameter ranging from 0 to 1 corresponding to first and last frame
#returns: interpolated image
#direction of movement, assumed to be approx. linear
a=np.array(center_of_mass(images[0]))
b=np.array(center_of_mass(images[-1]))
#find index of two nearest frames
arr=np.array([center_of_mass(images[i]) for i in range(len(images))])
v=a+t*(b-a) #convert t into vector
idx1 = (np.linalg.norm((arr - v),axis=1)).argmin()
arr[idx1]=np.array([0,0]) #this is sloppy, should be changed if relevant values are near [0,0]
idx2 = (np.linalg.norm((arr - v),axis=1)).argmin()
if idx1>idx2:
b=np.array(center_of_mass(images[idx1])) #center of mass of nearest contour
a=np.array(center_of_mass(images[idx2])) #center of mass of second nearest contour
tstar=np.linalg.norm(v-a)/np.linalg.norm(b-a) #define parameter ranging from 0 to 1 for interpolation between two nearest frames
im1_shift=shift(images[idx2],(b-a)*tstar) #shift frame 1
im2_shift=shift(images[idx1],-(b-a)*(1-tstar)) #shift frame 2
return im1_shift+im2_shift #return average
if idx1<idx2:
b=np.array(center_of_mass(images[idx2]))
a=np.array(center_of_mass(images[idx1]))
tstar=np.linalg.norm(v-a)/np.linalg.norm(b-a)
im1_shift=shift(images[idx2],-(b-a)*(1-tstar))
im2_shift=shift(images[idx1],(b-a)*(tstar))
return im1_shift+im2_shift
Result example

I don't know the solution to your problem, but I don't think it's possible to do this with interpn.
I corrected the code that you tried, and used the following input images:
But the result is:
Here's the corrected code:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from scipy import interpolate
n = 8
img1 = np.zeros((n, n))
img2 = np.zeros((n, n))
img1[2:4, 2:4] = 1
img2[4:6, 4:6] = 1
plt.figure()
plt.imshow(img1, cmap=cm.Greys)
plt.figure()
plt.imshow(img2, cmap=cm.Greys)
points = (np.r_[0, 2], np.arange(n), np.arange(n))
values = np.stack((img1, img2))
xi = np.rollaxis(np.mgrid[:n, :n], 0, 3).reshape((n**2, 2))
xi = np.c_[np.ones(n**2), xi]
values_x = interpolate.interpn(points, values, xi, method='linear')
values_x = values_x.reshape((n, n))
print(values_x)
plt.figure()
plt.imshow(values_x, cmap=cm.Greys)
plt.clim((0, 1))
plt.show()
I think the main difference between your code and mine is in the specification of xi. interpn tends to be somewhat confusing to use, and I've explained it in greater detail in an older answer. If you're curious about the mechanics of how I've specified xi, see this answer of mine explaining what I've done.
This result is not entirely surprising, because interpn just linearly interpolated between the two images: so the parts which had 1 in one image and 0 in the other simply became 0.5.
Over here, since one image is the translation of the other, it's clear that we want an image that's translated "in-between". But how would interpn interpolate two general images? If you had one small circle and one big circle, is it in any way clear that there should be a circle of intermediate size "between" them? What about interpolating between a dog and a cat? Or a dog and a building?
I think you are essentially trying to "draw lines" connecting the edges of the two images and then trying to figure out the image in between. This is similar to sampling a moving video at a half-frame. You might want to check out something like optical flow, which connects adjacent frames using vectors. I'm not aware if and what python packages/implementations are available though.