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I have an image with width: 1980 and height: 1080.
Ultimately, I want to place various shapes within the image, but at random locations and in such a way that they do not overlap. The 0,0 coordinates of the image are in the center.
Before rendering the shapes into the image (I don't need help with this), I need to write an algorithm to generate the XY points/locations. I want to be able to specify the minimum distance any given point is allowed to get to any other points.
How can do this?
All I have been able to do, is to generate points at equally spaced locations and then add a bit of randomness to each point. But this is not ideal, because it means points just vary within some 'cell' within a grid, and if the randomness value is too high, they will appear outside of the rectangle. Here is my code:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
from random import randrange
def is_square(integer):
root = np.sqrt(integer)
return integer == int(root + 0.5) ** 2
def perfect_sqr(n):
nextN = np.floor(np.sqrt(n)) + 1
return int(nextN * nextN)
def generate_cells(width = 1920, height = 1080, n = 9, show_plot=False):
# If the number is not a perfect square, we need to find the next number which is
# so that we can get the root N, which will be used to determine the number of rows/columns
if not is_square(n):
n = perfect_sqr(n)
N = np.sqrt(n)
# generate x and y lists, where each represents an array of points evenly spaced between 0 and the width/height
x = np.array(list(range(0, width, int(width/N))))
y = np.array(list(range(0, height, int(height/N))))
# center the points within each 'cell'
x_centered = x+int(width/N)/2
y_centered = y+int(height/N)/2
x_centered = [a+randrange(50) for a in x_centered]
y_centered = [a+randrange(50) for a in y_centered]
# generate a grid with the points
xv, yv = np.meshgrid(x_centered, y_centered)
if(show_plot):
plt.scatter(xv,yv)
plt.gca().add_patch(Rectangle((0,0),width, height,edgecolor='red', facecolor='none', lw=1))
plt.show()
# convert the arrays to 1D
xx = xv.flatten()
yy = yv.flatten()
# Merge them side-by-side
zips = zip(xx, yy)
# convert to set of points/tuples and return
return set(zips)
coords = generate_cells(width=1920, height=1080, n=15, show_plot=True)
print(coords)
Assuming you simply want to randomly define non-overlapping coordinates within the confines of a maximum image size subject to not having images overlap, this might be a good solution.
import numpy as np
def locateImages(field_height: int, field_width: int, min_sep: int, points: int)-> np.array:
h_range = np.array(range(min_sep//2, field_height - (min_sep//2), min_sep))
w_range = np.array(range(min_sep//2, field_width-(min_sep//2), min_sep))
mx_len = max(len(h_range), len(w_range))
if len(h_range) < mx_len:
xtra = np.random.choice(h_range, mx_len - len(h_range))
h_range = np.append(h_range, xtra)
if len(w_range) < mx_len:
xtra = np.random.choice(w_range, mx_len - len(w_range))
w_range = np.append(w_range, xtra)
h_points = np.random.choice(h_range, points, replace=False)
w_points = np.random.choice(w_range, points, replace=False)
return np.concatenate((np.vstack(h_points), np.vstack(w_points)), axis= 1)
Then given:
field_height = the vertical coordinate of the Image space
field_width = the maximum horizontal coordinate of the Image space
min_sep = the minimum spacing between images
points = number of coordinates to be selected
Then:
locateImages(15, 8, 2, 5) will yield:
array([[13, 1],
[ 7, 3],
[ 1, 5],
[ 5, 5],
[11, 5]])
Render the output:
points = locateImages(1080, 1920, 100, 15)
x,y= zip(*points)
plt.scatter(x,x)
plt.gca().add_patch(Rectangle((0,0),1920, 1080,edgecolor='red', facecolor='none', lw=1))
plt.show()
Here I have some code that can vertically and horizontally shift images so that a specific feature can align (credits to https://stackoverflow.com/a/24769222/15016884):
def cross_image(im1, im2):
im1_gray = np.sum(im1.astype('float'), axis=2)
im2_gray = np.sum(im2.astype('float'), axis=2)
im1_gray -= np.mean(im1_gray)
im2_gray -= np.mean(im2_gray)
return signal.fftconvolve(im1_gray, im2_gray[::-1,::-1], mode='same')
corr_img_null = cross_image(cloud1,cloud1)
corr_img = cross_image(cloud1,cloud2)
y0, x0 = np.unravel_index(np.argmax(corr_img_null), corr_img_null.shape)
y, x = np.unravel_index(np.argmax(corr_img), corr_img.shape)
ver_shift = y0-y
hor_shift = x0-x
print('horizontally shifted', hor_shift)
print('vertically shifted', ver_shift)
#defining the bounds of the part of the images I'm actually analyzing
xstart = 100
xstop = 310
ystart = 50
ystop = 200
crop_cloud1 = cloud1[ystart:ystop, xstart:xstop]
crop_cloud2 = cloud2[ystart:ystop, xstart:xstop]
crop_cloud2_shift = cloud2[ystart+ver_shift:ystop+ver_shift, xstart+hor_shift:xstop+hor_shift]
plot_pos = plt.figure(5)
plt.title('image 1')
plt.imshow(crop_cloud1)
plot_pos = plt.figure(6)
plt.title('image 2')
plt.imshow(crop_cloud2)
plot_pos = plt.figure(7)
plt.title('Shifted image 2 to align with image 1')
plt.imshow(crop_cloud2_shift)
Here are the results:
Now, I want to work with the example shown below, where rotations in addition to translations will be needed to align the features in my image.
Here is my code for that: The idea is to convolve each possible configuration of image 2 for every angle from -45 to 45 (for my application, this angle is not likely to be exceeded) and find at which coordinates and rotation angle the convolution is maximized.
import cv2
def rotate(img, theta):
(rows, cols) = img.shape[:2]
M = cv2.getRotationMatrix2D((cols / 2, rows / 2), theta, 1)
res = cv2.warpAffine(img, M, (cols, rows))
return res
#testing all rotations of image 2
corr_bucket = []
for i in range(-45,45):
rot_img = rotate(bolt2,i)
corr_img = cross_image(bolt1,rot_img)
corr_bucket.append(corr_img)
corr_arr = np.asarray(corr_bucket)
corr_img_null = cross_image(bolt1,bolt1)
y0, x0 = np.unravel_index(np.argmax(corr_img_null), corr_img_null.shape)
r_index, y1, x1 = np.unravel_index(np.argmax(corr_arr), corr_arr.shape)
r = -45+r_index
ver_shift = y0-y
hor_shift = x0-x
ver_shift_r = y0-y1
hor_shift_r = x0-x1
#What parts of the image do you want to analyze
xstart = 200
xstop = 300
ystart = 100
ystop = 200
crop_bolt1 = bolt1[ystart:ystop, xstart:xstop]
crop_bolt2 = bolt2[ystart:ystop, xstart:xstop]
rot_bolt2 = rotate(bolt2,r)
shift_rot_bolt2 = rot_bolt2[ystart+ver_shift_r:ystop+ver_shift_r, xstart+hor_shift_r:xstop+hor_shift_r]
plot_1 = plt.figure(9)
plt.title('image 1')
plt.imshow(crop_bolt1)
plot_2 = plt.figure(10)
plt.title('image 2')
plt.imshow(crop_bolt2)
plot_3 = plt.figure(11)
plt.title('Shifted and rotated image 2 to align with image 1')
plt.imshow(shift_rot_bolt2)
Unfortunately, from the very last line, I get the error ValueError: zero-size array to reduction operation minimum which has no identity. I'm kind of new to python so I don't really know what this means or why my approach isn't working. I have a feeling that my error is somewhere in unraveling corr_arr because the x, y and r values it returns I can already see, just by estimating, would not make the lightning bolts align. Any advice?
The issue came from feeding in the entire rotated image into scipy.signal.fftconvolve. Crop a part of image2 after rotating to use as a "probe image" (crop your unrotated image 1 in the same way), and the code I have written in my question works fine.
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.
My question is if there is any way to smoothen 2D color map using matplotlib? My code:
def map():
# setup parameters
j = 0
N = 719
N2 = 35
x = np.linspace(190, 800, N)
y = np.linspace(10, 360, N2) # (1,2,3), 1 - start Temp, 2- end temp + 10K, 3 - how many steps to reach it
z = []
A = np.zeros([35,719]) # [1 2], 1 - number of spectras, 2 - delta wavelength
# run
for i in range(10,360,10):
Z = []
file_no = (str(0) + str(i))[-3:]
data = np.genfromtxt('C:\\Users\\micha_000\\Desktop\\Measure\\' + '160317_LaPONd_g500_%s_radio.txt'%file_no,skip_header = 12)
for line in data:
Z.append(line[1]-6000)
A[j,:] = Z
j = j+1
X, Y = np.meshgrid(x,y)
fig, ax = plt.subplots()
cs = ax.contourf(X, Y, A, cmap=cm.viridis)
norm = colors.Normalize(vmin = 0, vmax = 1)
plt.xlabel('wavelength [nm]')
plt.ylabel('temperature [K]')
plt.title('LaPONd_g500')
cbar = fig.colorbar(cs, norm = norm)
plt.savefig('C:\\Users\\micha_000\\Desktop\\Measure\\LaPONd_g500_radio_map.png')
plt.show()
plt.close()
And here is an example of what i receive:
Is there any way to make it look better by smoothening pixels transitions?
The problem is not the palette (which are all smooth in matplotlib), but that fact that you are using contourf(), which generates a finite set of countours, each with a single color, and is therefore not smooth. The default is something like 10 countours.
One quick solution:, increase the number of contour levels by specifying levels (you can also give an array of which levels to include):
cs = ax.contourf(X, Y, A, cmap=cm.viridis, levels=100)
Better yet, since it seems your data data is already on a grid (e.g. X,Y,Z values for each pixel), you should use pcolormesh(X,Y,A) instead of contour to plot it. That will plot with fully continuous values, rather than steps.
open the png as an array, and blur it with a mean value filter. search convolution filters to learn more. I've just used a 25 pixel square averaging filter, but you could use a gaussian distribution to make it look smoother..
import numpy as np
from scipy import ndimage, signal, misc
img = ndimage.imread('C:/.../Zrj50.png')
#I used msPaint to get coords... there's probably a better way
x0, y0, x1, y1 = 87,215,764,1270 #chart area (pixel coords)
#you could use a gaussian filter to get a rounder blur pattern
kernel = np.ones((5,5),)/25 #mean value convolution
#convolve roi with averaging filter
#red
img[x0:x1, y0:y1, 0] = signal.convolve2d(img[x0:x1, y0:y1, 0], kernel, mode='same', boundary='symm')
#green
img[x0:x1, y0:y1, 1] = signal.convolve2d(img[x0:x1, y0:y1, 1], kernel, mode='same', boundary='symm')
#blue
img[x0:x1, y0:y1, 2] = signal.convolve2d(img[x0:x1, y0:y1, 2], kernel, mode='same', boundary='symm')
#do it again for ledgend area
#...
misc.imsave('C:/.../Zrj50_blurred.png', img)
Using a gaussian instead is pretty easy:
#red
img[x0:x1, y0:y1, 0] = ndimage.gaussian_filter(img[x0:x1, y0:y1, 0], 4, mode='nearest')
There is an array containing 3D data of shape e.g. (64,64,64), how do you plot a plane given by a point and a normal (similar to hkl planes in crystallography), through this dataset?
Similar to what can be done in MayaVi by rotating a plane through the data.
The resulting plot will contain non-square planes in most cases.
Can those be done with matplotlib (some sort of non-rectangular patch)?
Edit: I almost solved this myself (see below) but still wonder how non-rectangular patches can be plotted in matplotlib...?
Edit: Due to discussions below I restated the question.
This is funny, a similar question I replied to just today. The way to go is: interpolation. You can use griddata from scipy.interpolate:
Griddata
This page features a very nice example, and the signature of the function is really close to your data.
You still have to somehow define the points on you plane for which you want to interpolate the data. I will have a look at this, my linear algebra lessons where a couple of years ago
I have the penultimate solution for this problem. Partially solved by using the second answer to Plot a plane based on a normal vector and a point in Matlab or matplotlib :
# coding: utf-8
import numpy as np
from matplotlib.pyplot import imshow,show
A=np.empty((64,64,64)) #This is the data array
def f(x,y):
return np.sin(x/(2*np.pi))+np.cos(y/(2*np.pi))
xx,yy= np.meshgrid(range(64), range(64))
for x in range(64):
A[:,:,x]=f(xx,yy)*np.cos(x/np.pi)
N=np.zeros((64,64))
"""This is the plane we cut from A.
It should be larger than 64, due to diagonal planes being larger.
Will be fixed."""
normal=np.array([-1,-1,1]) #Define cut plane here. Normal vector components restricted to integers
point=np.array([0,0,0])
d = -np.sum(point*normal)
def plane(x,y): # Get plane's z values
return (-normal[0]*x-normal[1]*y-d)/normal[2]
def getZZ(x,y): #Get z for all values x,y. If z>64 it's out of range
for i in x:
for j in y:
if plane(i,j)<64:
N[i,j]=A[i,j,plane(i,j)]
getZZ(range(64),range(64))
imshow(N, interpolation="Nearest")
show()
It's not the ultimate solution since the plot is not restricted to points having a z value, planes larger than 64 * 64 are not accounted for and the planes have to be defined at (0,0,0).
For the reduced requirements, I prepared a simple example
import numpy as np
import pylab as plt
data = np.arange((64**3))
data.resize((64,64,64))
def get_slice(volume, orientation, index):
orientation2slicefunc = {
"x" : lambda ar:ar[index,:,:],
"y" : lambda ar:ar[:,index,:],
"z" : lambda ar:ar[:,:,index]
}
return orientation2slicefunc[orientation](volume)
plt.subplot(221)
plt.imshow(get_slice(data, "x", 10), vmin=0, vmax=64**3)
plt.subplot(222)
plt.imshow(get_slice(data, "x", 39), vmin=0, vmax=64**3)
plt.subplot(223)
plt.imshow(get_slice(data, "y", 15), vmin=0, vmax=64**3)
plt.subplot(224)
plt.imshow(get_slice(data, "z", 25), vmin=0, vmax=64**3)
plt.show()
This leads to the following plot:
The main trick is dictionary mapping orienations to lambda-methods, which saves us from writing annoying if-then-else-blocks. Of course you can decide to give different names,
e.g., numbers, for the orientations.
Maybe this helps you.
Thorsten
P.S.: I didn't care about "IndexOutOfRange", for me it's o.k. to let this exception pop out since it is perfectly understandable in this context.
I had to do something similar for a MRI data enhancement:
Probably the code can be optimized but it works as it is.
My data is 3 dimension numpy array representing an MRI scanner. It has size [128,128,128] but the code can be modified to accept any dimensions. Also when the plane is outside the cube boundary you have to give the default values to the variable fill in the main function, in my case I choose: data_cube[0:5,0:5,0:5].mean()
def create_normal_vector(x, y,z):
normal = np.asarray([x,y,z])
normal = normal/np.sqrt(sum(normal**2))
return normal
def get_plane_equation_parameters(normal,point):
a,b,c = normal
d = np.dot(normal,point)
return a,b,c,d #ax+by+cz=d
def get_point_plane_proximity(plane,point):
#just aproximation
return np.dot(plane[0:-1],point) - plane[-1]
def get_corner_interesections(plane, cube_dim = 128): #to reduce the search space
#dimension is 128,128,128
corners_list = []
only_x = np.zeros(4)
min_prox_x = 9999
min_prox_y = 9999
min_prox_z = 9999
min_prox_yz = 9999
for i in range(cube_dim):
temp_min_prox_x=abs(get_point_plane_proximity(plane,np.asarray([i,0,0])))
# print("pseudo distance x: {0}, point: [{1},0,0]".format(temp_min_prox_x,i))
if temp_min_prox_x < min_prox_x:
min_prox_x = temp_min_prox_x
corner_intersection_x = np.asarray([i,0,0])
only_x[0]= i
temp_min_prox_y=abs(get_point_plane_proximity(plane,np.asarray([i,cube_dim,0])))
# print("pseudo distance y: {0}, point: [{1},{2},0]".format(temp_min_prox_y,i,cube_dim))
if temp_min_prox_y < min_prox_y:
min_prox_y = temp_min_prox_y
corner_intersection_y = np.asarray([i,cube_dim,0])
only_x[1]= i
temp_min_prox_z=abs(get_point_plane_proximity(plane,np.asarray([i,0,cube_dim])))
#print("pseudo distance z: {0}, point: [{1},0,{2}]".format(temp_min_prox_z,i,cube_dim))
if temp_min_prox_z < min_prox_z:
min_prox_z = temp_min_prox_z
corner_intersection_z = np.asarray([i,0,cube_dim])
only_x[2]= i
temp_min_prox_yz=abs(get_point_plane_proximity(plane,np.asarray([i,cube_dim,cube_dim])))
#print("pseudo distance z: {0}, point: [{1},{2},{2}]".format(temp_min_prox_yz,i,cube_dim))
if temp_min_prox_yz < min_prox_yz:
min_prox_yz = temp_min_prox_yz
corner_intersection_yz = np.asarray([i,cube_dim,cube_dim])
only_x[3]= i
corners_list.append(corner_intersection_x)
corners_list.append(corner_intersection_y)
corners_list.append(corner_intersection_z)
corners_list.append(corner_intersection_yz)
corners_list.append(only_x.min())
corners_list.append(only_x.max())
return corners_list
def get_points_intersection(plane,min_x,max_x,data_cube,shape=128):
fill = data_cube[0:5,0:5,0:5].mean() #this can be a parameter
extended_data_cube = np.ones([shape+2,shape,shape])*fill
extended_data_cube[1:shape+1,:,:] = data_cube
diag_image = np.zeros([shape,shape])
min_x_value = 999999
for i in range(shape):
for j in range(shape):
for k in range(int(min_x),int(max_x)+1):
current_value = abs(get_point_plane_proximity(plane,np.asarray([k,i,j])))
#print("current_value:{0}, val: [{1},{2},{3}]".format(current_value,k,i,j))
if current_value < min_x_value:
diag_image[i,j] = extended_data_cube[k,i,j]
min_x_value = current_value
min_x_value = 999999
return diag_image
The way it works is the following:
you create a normal vector:
for example [5,0,3]
normal1=create_normal_vector(5, 0,3) #this is only to normalize
then you create a point:
(my cube data shape is [128,128,128])
point = [64,64,64]
You calculate the plane equation parameters, [a,b,c,d] where ax+by+cz=d
plane1=get_plane_equation_parameters(normal1,point)
then to reduce the search space you can calculate the intersection of the plane with the cube:
corners1 = get_corner_interesections(plane1,128)
where corners1 = [intersection [x,0,0],intersection [x,128,0],intersection [x,0,128],intersection [x,128,128], min intersection [x,y,z], max intersection [x,y,z]]
With all these you can calculate the intersection between the cube and the plane:
image1 = get_points_intersection(plane1,corners1[-2],corners1[-1],data_cube)
Some examples:
normal is [1,0,0] point is [64,64,64]
normal is [5,1,0],[5,1,1],[5,0,1] point is [64,64,64]:
normal is [5,3,0],[5,3,3],[5,0,3] point is [64,64,64]:
normal is [5,-5,0],[5,-5,-5],[5,0,-5] point is [64,64,64]:
Thank you.
The other answers here do not appear to be very efficient with explicit loops over pixels or using scipy.interpolate.griddata, which is designed for unstructured input data. Here is an efficient (vectorized) and generic solution.
There is a pure numpy implementation (for nearest-neighbor "interpolation") and one for linear interpolation, which delegates the interpolation to scipy.ndimage.map_coordinates. (The latter function probably didn't exist in 2013, when this question was asked.)
import numpy as np
from scipy.ndimage import map_coordinates
def slice_datacube(cube, center, eXY, mXY, fill=np.nan, interp=True):
"""Get a 2D slice from a 3-D array.
Copyright: Han-Kwang Nienhuys, 2020.
License: any of CC-BY-SA, CC-BY, BSD, GPL, LGPL
Reference: https://stackoverflow.com/a/62733930/6228891
Parameters:
- cube: 3D array, assumed shape (nx, ny, nz).
- center: shape (3,) with coordinates of center.
can be float.
- eXY: unit vectors, shape (2, 3) - for X and Y axes of the slice.
(unit vectors must be orthogonal; normalization is optional).
- mXY: size tuple of output array (mX, mY) - int.
- fill: value to use for out-of-range points.
- interp: whether to interpolate (rather than using 'nearest')
Return:
- slice: array, shape (mX, mY).
"""
center = np.array(center, dtype=float)
assert center.shape == (3,)
eXY = np.array(eXY)/np.linalg.norm(eXY, axis=1)[:, np.newaxis]
if not np.isclose(eXY[0] # eXY[1], 0, atol=1e-6):
raise ValueError(f'eX and eY not orthogonal.')
# R: rotation matrix: data_coords = center + R # slice_coords
eZ = np.cross(eXY[0], eXY[1])
R = np.array([eXY[0], eXY[1], eZ], dtype=np.float32).T
# setup slice points P with coordinates (X, Y, 0)
mX, mY = int(mXY[0]), int(mXY[1])
Xs = np.arange(0.5-mX/2, 0.5+mX/2)
Ys = np.arange(0.5-mY/2, 0.5+mY/2)
PP = np.zeros((3, mX, mY), dtype=np.float32)
PP[0, :, :] = Xs.reshape(mX, 1)
PP[1, :, :] = Ys.reshape(1, mY)
# Transform to data coordinates (x, y, z) - idx.shape == (3, mX, mY)
if interp:
idx = np.einsum('il,ljk->ijk', R, PP) + center.reshape(3, 1, 1)
slice = map_coordinates(cube, idx, order=1, mode='constant', cval=fill)
else:
idx = np.einsum('il,ljk->ijk', R, PP) + (0.5 + center.reshape(3, 1, 1))
idx = idx.astype(np.int16)
# Find out which coordinates are out of range - shape (mX, mY)
badpoints = np.any([
idx[0, :, :] < 0,
idx[0, :, :] >= cube.shape[0],
idx[1, :, :] < 0,
idx[1, :, :] >= cube.shape[1],
idx[2, :, :] < 0,
idx[2, :, :] >= cube.shape[2],
], axis=0)
idx[:, badpoints] = 0
slice = cube[idx[0], idx[1], idx[2]]
slice[badpoints] = fill
return slice
# Demonstration
nx, ny, nz = 50, 70, 100
cube = np.full((nx, ny, nz), np.float32(1))
cube[nx//4:nx*3//4, :, :] += 1
cube[:, ny//2:ny*3//4, :] += 3
cube[:, :, nz//4:nz//2] += 7
cube[nx//3-2:nx//3+2, ny//2-2:ny//2+2, :] = 0 # black dot
Rz, Rx = np.pi/6, np.pi/4 # rotation angles around z and x
cz, sz = np.cos(Rz), np.sin(Rz)
cx, sx = np.cos(Rx), np.sin(Rx)
Rmz = np.array([[cz, -sz, 0], [sz, cz, 0], [0, 0, 1]])
Rmx = np.array([[1, 0, 0], [0, cx, -sx], [0, sx, cx]])
eXY = (Rmx # Rmz).T[:2]
slice = slice_datacube(
cube,
center=[nx/3, ny/2, nz*0.7],
eXY=eXY,
mXY=[80, 90],
fill=np.nan,
interp=False
)
import matplotlib.pyplot as plt
plt.close('all')
plt.imshow(slice.T) # imshow expects shape (mY, mX)
plt.colorbar()
Output (for interp=False):
For this test case (50x70x100 datacube, 80x90 slice size) the run time is 376 µs (interp=False) and 550 µs (interp=True) on my laptop.