I want to loop over the pixels of a binary image in python and set the value of a pixel depending on a surrounding neighborhood of pixels. Similar to convolution but I want create a method that sets the value of the center pixel using a custom function rather than normal convolution that sets the center pixel to the arithmetic mean of the neighborhood.
In essence I would like to create a function that does the following:
def convolve(img, conv_function = lambda subImg: np.mean(subImg)):
newImage = emptyImage
for nxn_window in img:
newImage[center_pixel] = conv_function(nxn_window)
return newImage
At the moment I have a solution but it is very slow:
#B is the structuing array or convolution window/kernel
def convolve(func):
def wrapper(img, B):
#get dimensions of img
length, width = len(img), len(img[0])
#half width and length of dimensions
hw = (int)((len(B) - 1) / 2)
hh = (int)((len(B[0]) - 1) / 2)
#convert to npArray for fast operations
B = np.array(B)
#initialize empty return image
retVal = np.zeros([length, width])
#start loop over the values where the convolution window has a neighborhood
for row in range(hh, length - hh):
for pixel in range(hw, width - hw):
#window as subarray of pixels
window = [arr[pixel-hh:pixel+hh+1]
for arr in img[row-hw:row+hw+1]]
retVal[row][pixel] = func(window, B)
return retVal
return wrapper
with this function as a decorator I then do
# dilation
#convolve
def __add__(img, B):
return np.mean(np.logical_and(img, B)) > 0
# erosion
#convolve
def __sub__(img, B):
return np.mean(np.logical_and(img, B)) == 1
Is there a library that provides this type of function or is there a better way I can loop over the image?
Here's an idea: assign each pixel an array with its neighborhood and then simply apply your custom function to the extended image. It'll be fast BUT will consume more memory ( times more memory; if your B.shape is (3, 3) then you'll need 9 times more memory). Try this:
import numpy as np
def convolve2(func):
def conv(image, kernel):
""" Apply given filter on an image """
k = kernel.shape[0] # which is assumed equal to kernel.shape[1]
width = k//2 # note that width == 1 for k == 3 but also width == 1 for k == 2
a = framed(image, width) # create a frame around an image to compensate for kernel overlap when shifting
b = np.empty(image.shape + kernel.shape) # add two more dimensions for each pixel's neighbourhood
di, dj = image.shape[:2] # will be used as delta for slicing
# add the neighbourhood ('kernel size') to each pixel in preparation for the final step
# in other words: slide the image along the kernel rather than sliding the kernel along the image
for i in range(k):
for j in range(k):
b[..., i, j] = a[i:i+di, j:j+dj]
# apply the desired function
return func(b, kernel)
return conv
def framed(image, width):
a = np.zeros(np.array(image.shape) + [2 * width, 2 * width]) # only add the frame to the first two dimensions
a[width:-width, width:-width] = image # place the image centered inside the frame
return a
I've used a greyscale image 512x512 pixels and a filter 3x3 for testing:
embossing_kernel = np.array([
[-2, -1, 0],
[-1, 1, 1],
[0, 1, 2]
])
#convolve2
def filter2(img, B):
return np.sum(img * B, axis=(2,3))
#convolve2
def __add2__(img, B):
return np.mean(np.logical_and(img, B), axis=(2,3)) > 0
# image_gray is a 2D grayscale image (not color/RGB)
b = filter2(image_gray, embossing_kernel)
To compare with your convolve I've used:
#convolve
def filter(img, B):
return np.sum(img * B)
#convolve
def __add__(img, B):
return np.mean(np.logical_and(img, B)) > 0
b = filter2(image_gray, embossing_kernel)
The time for convolve was 4.3 s, for convolve2 0.05 s on my machine.
In my case the custom function needs to specify the axes over which to operate, i.e., the additional dimensions holding the neighborhood data. Perhaps the axes could be avoided too but I haven't tried.
Note: this works for 2D images (grayscale) (as you asked about binary images) but can be easily extended to 3D (color) images. In your case you could probably get rid of the frame (or fill it with zeros or ones e.g., in case of repeated application of the function).
In case memory was an issue you might want to adapt a fast implementation of convolve I've posted here: https://stackoverflow.com/a/74288118/20188124.
Related
I am trying to horizontally stretch an image in a very specific way. Each x prime coordinate should follow a tangent path with respect to the original x coordinate. I believe there are two ways to do this:
Inverse the tangent function and map it normally
Map the tangent function and then inverse the mapping
Using this answer for map inversion, Im trying to figure out why the two images are not the same. I know that the first method gives me the correct image that I'm looking for, so why doesnt the second method work? Is it because of the "limited precision" that #ChristophRackwitz commented on the answer?
import cv2
import glob
import numpy as np
import math
A = -1010
B = -3.931
C = 5.258
D = 978.3
M = -193.8
N = 1740
def get_tan_func_value(x):
return A * math.tan((((x-N)/M)+B)/C) + D
def get_inverse_tan_func_value(x):
return M * (C*math.atan((x-D)/A) - B) + N
# answer from linked post
def invert_map(F, shape):
I = np.zeros_like(F)
I[:,:,1], I[:,:,0] = np.indices(shape)
P = np.copy(I)
for i in range(10):
P += I - cv2.remap(F, P, None, interpolation=cv2.INTER_LINEAR)
return P
# import image
images = glob.glob('*.jpg')
img = cv2.imread(images[0])
h, w = img.shape[:2]
map_x_tan = np.zeros((img.shape[0], img.shape[1]), dtype=np.float32)
map_x_inverse_tan = np.zeros((img.shape[0], img.shape[1]), dtype=np.float32)
map_y = np.zeros((img.shape[0], img.shape[1]), dtype=np.float32)
# x tan function map
for i in range(map_x_tan.shape[0]):
map_x_tan[i,:] = [get_tan_func_value(x) for x in range(map_x_tan.shape[1])]
# x inverse tan function map
for i in range(map_x_inverse_tan.shape[0]):
map_x_inverse_tan[i,:] = [get_inverse_tan_func_value(x) for x in range(map_x_inverse_tan.shape[1])]
# default y map
for j in range(map_y.shape[1]):
map_y[:,j] = [y for y in range(map_y.shape[0])]
# convert x tan map to 2 channel (x,y) map
(xymap_tan, _) = cv2.convertMaps(map1=map_x_tan, map2=map_y, dstmap1type=cv2.CV_32FC2)
# invert the 2 channel x tan map
xymap_inverted = invert_map(xymap_tan, (h,w))
# remap and write the target image (inverse tan function with normal map)
target = cv2.remap(img, map_x_inverse_tan, map_y, cv2.INTER_LINEAR)
cv2.imwrite("target.jpg", target)
# remap and write the attempted image (normal tan function with inverted map)
attempt = cv2.remap(img, xymap_inverted, None, cv2.INTER_LINEAR)
cv2.imwrite("attempt.jpg", attempt)
Method 1: Target Image
Method 2: Attempt Image
The results show that the attempt (normal tan function with inverted map) has less stretching near the edges of the image than expected. Almost everywhere else on the images are identical except the edges. I did not post the original picture to save space.
I've played around with that invert_map procedure. It seems slightly susceptible to oscillation.
use this instead:
def invert_map(F):
(h, w) = F.shape[:2] # (h, w, 2), "xymap"
I = np.zeros_like(F)
I[:,:,1], I[:,:,0] = np.indices((h,w)) # identity map
P = np.copy(I)
for i in range(10):
correction = I - cv2.remap(F, P, None, interpolation=cv2.INTER_LINEAR)
P += correction * 0.5
return P
I simply damped the correction by 0.5, which makes the fixed point iteration tamer, converging a lot faster too.
In my experiments with your tan map, I've found that 5-10 iterations are good enough already, and there's no further progress in further iterations.
Entire notebook of my explorations: https://gist.github.com/crackwitz/67f76f8a9eff21476b080c06d20660d0
Feature request: https://github.com/opencv/opencv/issues/22120
I am reading an image, getting objects that have a certain brightness value, and then plotting the X and Y coords to the image.
But, there is a huge group of outliers, which are all located in a rectangular part of the image, Its X and Y coords are 1110-1977 (width) and 1069-1905 (height). From here, I'm looping through this little square portion of the image, and from my pre-created x and y arrays any values that have the same coords as shown there are removed.
However, this removes a lot more coords, which, for example, have X in the range 1110-1977. So the end result is a cross pattern filtering when I only want the square in the center to be filtered. How would I do this?
Code
from PIL import Image, ImageDraw
import numpy as np
from math import sqrt
imag = Image.open("Centaurus_A-DeNoiseAI-denoise.jpg")
imag = imag.convert ('RGB')
x=[]
y=[]
imag2=Image.open("Cen_A_cropped.jpg")
imag2=imag2.convert('RGB')
r=[]
g=[]
b=[]
width2, height2=imag2.size
for count2 in range(width2):
for i2 in range(height2):
X,Y=count2,i2
(R,G,B)=imag2.getpixel((X,Y))
r.append(R)
g.append(G)
b.append(B)
average_r=sum(r)/len(r)
average_g=sum(g)/len(g)
average_b=sum(b)/len(b)
brightness_average=sqrt(0.299*(average_r**2) + 0.587*(average_g**2) + 0.114*(average_b**2))
print("Avg. brightness "+str(brightness_average))
def calculate_brightness(galaxy,ref_clus,clus_mag):
delta_b=(galaxy/ref_clus)
bright=delta_b**2
mag=np.log(bright)/np.log(2.512)
return mag+clus_mag
count=0
X,Y = 1556,1568
(R,G,B) = imag.getpixel((X,Y))
width, height=imag.size
brightness = sqrt(0.299*(R**2) + 0.587*(G**2) + 0.114*(B**2))
print("Magnitude: "+str((calculate_brightness(13050, 15.79,3.7))))
reference=brightness_average/(calculate_brightness(13050, 15.79,3.7)/6.84)
print("Reference: "+str(reference))
for count in range(width):
for i in range(height):
X,Y = count,i
(R,G,B) = imag.getpixel((X,Y))
brightness = sqrt(0.299*(R**2) + 0.587*(G**2) + 0.114*(B**2))
if(reference<=brightness<=reference+3):
x.append(X)
y.append(Y)
#post processing----------------------------------------------------------------------------------------------------
for x2 in range(1110, 1977):
for y2 in range(1069, 1905):
X,Y=x2,y2
if(X in x and Y in y):
x.remove(X)
y.remove(Y)
#-------------------------------------------------------------------------------------------------------------------
with imag as im:
delta = 19
draw = ImageDraw.Draw(im)
for i in range(len(x)):
draw.rectangle([x[i-delta],y[i-delta],x[i-delta],y[i-delta]], fill=(0,255,0))
im.save("your_image.png")
Centaurus_A-DeNoiseAI-denoise.jpg
Cen_A_cropped.jpg
Your post-processing logic is flawed. You remove a bunch of X values in the range 1110-1977, without checking whether its corresponding Y value is also in the range of the box. Remove this code section instead and add that logic the first time you loop to gather your x and y coords.
for count in range(width):
for i in range(height):
X,Y = count,i
if 1110 <= X < 1977 and 1069 <= Y < 1905: # add these
continue # two lines
(R,G,B) = imag.getpixel((X,Y))
However, there is a better way of doing the exact same thing by using numpy arrays. Instead of writing explicit loops, you can vectorise a lot of your computations.
import numpy as np
from PIL import Image, ImageDraw
image = Image.open('Centaurus_A-DeNoiseAI-denoise.jpg').convert('RGB')
img1 = np.array(image)
img2 = np.array(Image.open('Cen_A_cropped.jpg').convert('RGB'))
coeffs = np.array([.299, .587, .114])
average = img2.mean(axis=(0, 1))
brightness_average = np.sqrt(np.sum(average**2 * coeffs))
reference = brightness_average / (calculate_brightness(13050, 15.79,3.7) / 6.84)
print(f'Avg. brightness: {brightness_average}')
print(f'Reference: {reference}')
brightness = np.sqrt(np.sum(img1.astype(int)**2 * coeffs, axis=-1))
accepted_brightness = (brightness >= reference) * (brightness <= reference + 3)
pixels_used = np.ones((img1.shape[:2]), dtype=bool)
pixels_used[1069:1905,1110:1977] = False
rows, cols = np.where(accepted_brightness * pixels_used)
with image as im:
draw = ImageDraw.Draw(im)
draw.point(list(zip(cols, rows)), fill=(0, 255, 0))
image.save('out.png')
The main trick used here is in the line
rows, cols = np.where(accepted_brightness * pixels_used)
accepted_brightess is a 2d array of each pixel with a boolean value whether its brightness is within your preferred range. pixels_used is another 2d boolean array, where every pixel is True, except from the pixels in the box near the centre you want to ignore. The combination of those two gives you the pixel coordinates that have the correct brightness and are not in the square in the centre.
I am trying to do texture analysis in a satellite imagery using GLCM algorithm. The scikit-image documentation is very helpful on that but for GLCM calculation we need a window size looping over the image. This is too slow in Python. I found many posts on stackoverflow about sliding windows but the computation takes for ever. I have an example shown below, it works but takes forever. I guess this must be a a naive way of doing it
image = np.pad(image, int(win/2), mode='reflect')
row, cols = image.shape
feature_map = np.zeros((M, N))
for m in xrange(0, row):
for n in xrange(0, cols):
window = image[m:m+win, n:n+win]
glcm = greycomatrix(window, d, theta, levels)
contrast = greycoprops(glcm, 'contrast')
feature_map[m,n] = contrast
I came across with skimage.util.view_as_windows method which might be good solution for me. My problem is that, when I try to calculate the GLCM I get an error which says:
ValueError: The parameter image must be a 2-dimensional array
This is because the result of the GLCM image has 4d dimensions and scikit-image view_as_windows method accepts only 2d arrays. Here is my attempt
win_w=40
win_h=40
features = np.zeros(image.shape, dtype='uint8')
target = features[win_h//2:-win_h//2+1, win_w//2:-win_w//2+1]
windowed = view_as_windows(image, (win_h, win_w))
GLCM = greycomatrix(windowed, [1], [0, np.pi/4, np.pi/2, 3*np.pi/4], symmetric=True, normed=True)
haralick = greycoprops(GLCM, 'ASM')
Does anyone have an idea on how I can calculate the GLCM using skimage.util.view_as_windows method?
The feature extraction you are trying to perform is a computer-intensive task. I have speeded up your method by computing the co-occurrence map only once for the whole image, rather than computing the co-occurrence map over and over on overlapping positions of the sliding window.
The co-occurrence map is a stack of images of the same size as the original image, in which - for each pixel - intensity levels are replaced by integer numbers that encode the co-occurrence of two intensities, namely Ii at that pixel and Ij at an offset pixel. The co-occurrence map has as many layers as we considered offsets (i.e. all the possible distance-angle pairs). By retaining the co-occurrence map you don't need to compute the GLCM at each position of the sliding window from the scratch, as you can reuse the previously computed co-occurrence maps to obtain the adjacency matrices (the GLCMs) for each distance-angle pair. This approach provides you with a significant speed gain.
The solution I came up with relies on the functions below:
import numpy as np
from skimage import io
from scipy import stats
from skimage.feature import greycoprops
def offset(length, angle):
"""Return the offset in pixels for a given length and angle"""
dv = length * np.sign(-np.sin(angle)).astype(np.int32)
dh = length * np.sign(np.cos(angle)).astype(np.int32)
return dv, dh
def crop(img, center, win):
"""Return a square crop of img centered at center (side = 2*win + 1)"""
row, col = center
side = 2*win + 1
first_row = row - win
first_col = col - win
last_row = first_row + side
last_col = first_col + side
return img[first_row: last_row, first_col: last_col]
def cooc_maps(img, center, win, d=[1], theta=[0], levels=256):
"""
Return a set of co-occurrence maps for different d and theta in a square
crop centered at center (side = 2*w + 1)
"""
shape = (2*win + 1, 2*win + 1, len(d), len(theta))
cooc = np.zeros(shape=shape, dtype=np.int32)
row, col = center
Ii = crop(img, (row, col), win)
for d_index, length in enumerate(d):
for a_index, angle in enumerate(theta):
dv, dh = offset(length, angle)
Ij = crop(img, center=(row + dv, col + dh), win=win)
cooc[:, :, d_index, a_index] = encode_cooccurrence(Ii, Ij, levels)
return cooc
def encode_cooccurrence(x, y, levels=256):
"""Return the code corresponding to co-occurrence of intensities x and y"""
return x*levels + y
def decode_cooccurrence(code, levels=256):
"""Return the intensities x, y corresponding to code"""
return code//levels, np.mod(code, levels)
def compute_glcms(cooccurrence_maps, levels=256):
"""Compute the cooccurrence frequencies of the cooccurrence maps"""
Nr, Na = cooccurrence_maps.shape[2:]
glcms = np.zeros(shape=(levels, levels, Nr, Na), dtype=np.float64)
for r in range(Nr):
for a in range(Na):
table = stats.itemfreq(cooccurrence_maps[:, :, r, a])
codes = table[:, 0]
freqs = table[:, 1]/float(table[:, 1].sum())
i, j = decode_cooccurrence(codes, levels=levels)
glcms[i, j, r, a] = freqs
return glcms
def compute_props(glcms, props=('contrast',)):
"""Return a feature vector corresponding to a set of GLCM"""
Nr, Na = glcms.shape[2:]
features = np.zeros(shape=(Nr, Na, len(props)))
for index, prop_name in enumerate(props):
features[:, :, index] = greycoprops(glcms, prop_name)
return features.ravel()
def haralick_features(img, win, d, theta, levels, props):
"""Return a map of Haralick features (one feature vector per pixel)"""
rows, cols = img.shape
margin = win + max(d)
arr = np.pad(img, margin, mode='reflect')
n_features = len(d) * len(theta) * len(props)
feature_map = np.zeros(shape=(rows, cols, n_features), dtype=np.float64)
for m in xrange(rows):
for n in xrange(cols):
coocs = cooc_maps(arr, (m + margin, n + margin), win, d, theta, levels)
glcms = compute_glcms(coocs, levels)
feature_map[m, n, :] = compute_props(glcms, props)
return feature_map
DEMO
The following results correspond to a (250, 200) pixels crop from a Landsat image. I have considered two distances, four angles, and two GLCM properties. This results in a 16-dimensional feature vector for each pixel. Notice that the sliding window is squared and its side is 2*win + 1 pixels (in this test a value of win = 19 was used). This sample run took around 6 minutes, which is fairly shorter than "forever" ;-)
In [331]: img.shape
Out[331]: (250L, 200L)
In [332]: img.dtype
Out[332]: dtype('uint8')
In [333]: d = (1, 2)
In [334]: theta = (0, np.pi/4, np.pi/2, 3*np.pi/4)
In [335]: props = ('contrast', 'homogeneity')
In [336]: levels = 256
In [337]: win = 19
In [338]: %time feature_map = haralick_features(img, win, d, theta, levels, props)
Wall time: 5min 53s
In [339]: feature_map.shape
Out[339]: (250L, 200L, 16L)
In [340]: feature_map[0, 0, :]
Out[340]:
array([ 10.3314, 0.3477, 25.1499, 0.2738, 25.1499, 0.2738,
25.1499, 0.2738, 23.5043, 0.2755, 43.5523, 0.1882,
43.5523, 0.1882, 43.5523, 0.1882])
In [341]: io.imshow(img)
Out[341]: <matplotlib.image.AxesImage at 0xce4d160>
Goal: To input an image (2d numpy array) and a window size, and output the same array with the local maxima remaining, but 0 elsewhere.
What I am struggling with: I think I made a stupid mistake in my code, maybe a few typos in my loop but I am not sure (the local maxima are only on the left side of the image, which is not true). As I note below I would also welcome any easy tricks with OpenCV or numpy to make this solution shorter.
similar questions: Finding Local Maxima in an Image
and Find local maxima in grayscale image using OpenCV
Mine is different because: I am looking to surpress all but local maxima. I don't have to use my code below, I haven't been able to find a built in function of opencv or numpy to do what I need to (harris corners in cv will implicitly do this as one of the steps, but I need something to perform the sole operation I need). I read a little bit on dilate and wasn't sure if that would be useful here as well.
What I have tried so far.
def nonMaximalSupress(image,NHoodSize):
#For
for x in range(0,image.shape[0]-1):
if x+NHoodSize[0]<image.shape[0]:
#while we can still take a square
#print "AHH ", image.shape
startWindow=0
for y in range(startWindow,image.shape[1]-NHoodSize[1]):
#try:
if np.sum(image[x:x+NHoodSize[0]][y:y+NHoodSize[1]])==0:
localMax=0
else:
localMax = np.amax(image[x:x+NHoodSize[0]][y:y+NHoodSize[1]])
#except ValueError:
#localMax=0
#print "local max is ", localMax
maxCoord=np.unravel_index(np.argmax((image[x:x+NHoodSize[0],y:y+NHoodSize[1]])),
image.shape)+np.array((x,y))
#print "X is %r, Y is %r, max coord is %r \n y+nhood is %r" %(x,y,maxCoord,y+NHoodSize[1])
#suppress everything
image[x:x+NHoodSize[0]][y:y+NHoodSize[1]]=0
#reset only the max
#print maxCoord
if localMax > 0:
print localMax
print "max coord is ", maxCoord[0], maxCoord[1]
image[maxCoord[0]][maxCoord[1]]=localMax
#increment y
x+=NHoodSize[0]
return image
How about something like this:
# Use the max filter to make a mask
roi = 3
size = 2 * roi + 1
image_max = ndimage.maximum_filter(image, size=size, mode='constant')
mask = (image == image_max)
image *= mask
# Remove the image borders
image[:roi] = 0
image[-roi:] = 0
image[:, :roi] = 0
image[:, -roi:] = 0
# Optionally find peaks above some threshold
image_t = (image > peak_threshold) * 1
# get coordinates of peaks
f = np.transpose(image_t.nonzero())
This may not be entirely correct, but it works better on a small test case
def nonMaximalSupress1(image,NHoodSize):
#
dX, dY = NHoodSize
M, N = image.shape
for x in range(0,M-dX+1):
for y in range(0,N-dY+1):
window = image[x:x+dX, y:y+dY]
if np.sum(window)==0:
localMax=0
else:
localMax = np.amax(window)
maxCoord=np.unravel_index(np.argmax(window), window.shape) + np.array((x,y))
#suppress everything
image[x:x+dX, y:y+dY]=0
#reset only the max
if localMax > 0:
print localMax
print "max coord is ", maxCoord
image[tuple(maxCoord)] = localMax
return image
I've used local variables to make things easier to read, and tweaked the loop ranges. But the big change is in how I index image. Especially when indexing with slices, you must use one set of brackets.
image[x:x+dX, y:y+dY] is the correct way to select a window, not image[x:x+dX][y:y+dY].
It can be cleaned up a bit more by modifying the window. Since it is a view, changing it changes image.
def nonMaximalSupress2(image,NHoodSize):
#
dX, dY = NHoodSize
M, N = image.shape
for x in range(0,M-dX+1):
for y in range(0,N-dY+1):
window = image[x:x+dX, y:y+dY]
if np.sum(window)==0:
localMax=0
else:
localMax = np.amax(window)
maxCoord = np.argmax(window)
# zero all but the localMax in the window
window[:] = 0
window.flat[maxCoord] = localMax
return image
A different approach using peak_local_max from skimage.feature.peak and center_of_mass from scipy.ndimage.measurements for localizing the centers of the peaks if a peak may consist of multiple pixels with the same pixel intensity:
from skimage.feature.peak import peak_local_max
from scipy.ndimage.measurements import center_of_mass
from scipy.ndimage import label
from scipy.ndimage.morphology import generate_binary_structure
footprint = generate_binary_structure(3, 3)
peaks = peak_local_max(img, indices=False, footprint=footprint)
lbl, num_features = label(maxima)
centers = center_of_mass(maxima, lbl, range(1, num_features + 1))
values = img[tuple(np.int0(np.transpose(centers)))]
I have an image processing problem I'm currently solving in python, using numpy and scipy. Briefly, I have an image that I want to apply many local contractions to. My prototype code is working, and the final images look great. However, processing time has become a serious bottleneck in our application. Can you help me speed up my image processing code?
I've tried to boil down our code to the 'cartoon' version below. Profiling suggests that I'm spending most of my time on interpolation. Are there obvious ways to speed up execution?
import cProfile, pstats
import numpy
from scipy.ndimage import interpolation
def get_centered_subimage(
center_point, window_size, image):
x, y = numpy.round(center_point).astype(int)
xSl = slice(max(x-window_size-1, 0), x+window_size+2)
ySl = slice(max(y-window_size-1, 0), y+window_size+2)
subimage = image[xSl, ySl]
interpolation.shift(
subimage, shift=(x, y)-center_point, output=subimage)
return subimage[1:-1, 1:-1]
"""In real life, this is experimental data"""
im = numpy.zeros((1000, 1000), dtype=float)
"""In real life, this mask is a non-zero pattern"""
window_radius = 10
mask = numpy.zeros((2*window_radius+1, 2*window_radius+1), dtype=float)
"""The x, y coordinates in the output image"""
new_grid_x = numpy.linspace(0, im.shape[0]-1, 2*im.shape[0])
new_grid_y = numpy.linspace(0, im.shape[1]-1, 2*im.shape[1])
"""The grid we'll end up interpolating onto"""
grid_step_x = new_grid_x[1] - new_grid_x[0]
grid_step_y = new_grid_y[1] - new_grid_y[0]
subgrid_radius = numpy.floor(
(-1 + window_radius * 0.5 / grid_step_x,
-1 + window_radius * 0.5 / grid_step_y))
subgrid = (
window_radius + 2 * grid_step_x * numpy.arange(
-subgrid_radius[0], subgrid_radius[0] + 1),
window_radius + 2 * grid_step_y * numpy.arange(
-subgrid_radius[1], subgrid_radius[1] + 1))
subgrid_points = ((2*subgrid_radius[0] + 1) *
(2*subgrid_radius[1] + 1))
"""The coordinates of the set of spots we we want to contract. In real
life, this set is non-random:"""
numpy.random.seed(0)
num_points = 10000
center_points = numpy.random.random(2*num_points).reshape(num_points, 2)
center_points[:, 0] *= im.shape[0]
center_points[:, 1] *= im.shape[1]
"""The output image"""
final_image = numpy.zeros(
(new_grid_x.shape[0], new_grid_y.shape[0]), dtype=numpy.float)
def profile_me():
for m, cp in enumerate(center_points):
"""Take an image centered on each illumination point"""
spot_image = get_centered_subimage(
center_point=cp, window_size=window_radius, image=im)
if spot_image.shape != (2*window_radius+1, 2*window_radius+1):
continue #Skip to the next spot
"""Mask the image"""
masked_image = mask * spot_image
"""Resample the image"""
nearest_grid_index = numpy.round(
(cp - (new_grid_x[0], new_grid_y[0])) /
(grid_step_x, grid_step_y))
nearest_grid_point = (
(new_grid_x[0], new_grid_y[0]) +
(grid_step_x, grid_step_y) * nearest_grid_index)
new_coordinates = numpy.meshgrid(
subgrid[0] + 2 * (nearest_grid_point[0] - cp[0]),
subgrid[1] + 2 * (nearest_grid_point[1] - cp[1]))
resampled_image = interpolation.map_coordinates(
masked_image,
(new_coordinates[0].reshape(subgrid_points),
new_coordinates[1].reshape(subgrid_points))
).reshape(2*subgrid_radius[1]+1,
2*subgrid_radius[0]+1).T
"""Add the recentered image back to the scan grid"""
final_image[
nearest_grid_index[0]-subgrid_radius[0]:
nearest_grid_index[0]+subgrid_radius[0]+1,
nearest_grid_index[1]-subgrid_radius[1]:
nearest_grid_index[1]+subgrid_radius[1]+1,
] += resampled_image
cProfile.run('profile_me()', 'profile_results')
p = pstats.Stats('profile_results')
p.strip_dirs().sort_stats('cumulative').print_stats(10)
Vague explanation of what the code does:
We start with a pixellated 2D image, and a set of arbitrary (x, y) points in our image that don't generally fall on an integer grid. For each (x, y) point, I want to multiply the image by a small mask centered precisely on that point. Next we contract/expand the masked region by a finite amount, before finally adding this processed sub-image to a final image, which may not have the same pixel size as the original image. (Not my finest explanation. Ah well).
I'm pretty sure that, as you said, the bulk of the calculation time happens in interpolate.map_coordinates(…), which gets called once for every iteration on center_points, here 10,000 times. Generally, working with the numpy/scipy stack, you want the repetitive task over a large array to happen in native Numpy/Scipy functions -- i.e. in a C loop over homogeneous data -- as opposed to explicitely in Python.
One strategy that might speed up the interpolation, but that will also increase the amount of memory used, is :
First, fetch all the subimages (here named masked_image) in a 3-dimensional array (window_radius x window_radius x center_points.size)
Make a ufunc (read that, it's useful) that wraps the work that has to be done on each subimage, using numpy.frompyfunc, which should return another 3-dimensional array (subgrid_radius[0] x subgrid_radius[1] x center_points.size). In short, this creates a vectorized version of the python function, that can be broadcast element-wise on an array.
Build the final image by summing over the third dimension.
Hope that gets you closer to your goals!