То, что вы описываете, не совсем обработка изображения в традиционном смысле, но это довольно легко сделать с помощью NumPy и т. Д.
Вот довольно большой пример выполнения некоторых вещей, о которых вы упомянули, чтобы получитьВы указали в правильном направлении ... Обратите внимание, что на всех примерах изображения показывают результаты для источника в центре изображения, но функции принимают аргумент источника, поэтому вы должны иметь возможность напрямую адаптировать вещи для ваших целей.
import numpy as np
import scipy as sp
import scipy.ndimage
import Image
import matplotlib.pyplot as plt
def main():
im = Image.open('mri_demo.png')
im = im.convert('RGB')
data = np.array(im)
plot_polar_image(data, origin=None)
plot_directional_intensity(data, origin=None)
plt.show()
def plot_directional_intensity(data, origin=None):
"""Makes a cicular histogram showing average intensity binned by direction
from "origin" for each band in "data" (a 3D numpy array). "origin" defaults
to the center of the image."""
def intensity_rose(theta, band, color):
theta, band = theta.flatten(), band.flatten()
intensities, theta_bins = bin_by(band, theta)
mean_intensity = map(np.mean, intensities)
width = np.diff(theta_bins)[0]
plt.bar(theta_bins, mean_intensity, width=width, color=color)
plt.xlabel(color + ' Band')
plt.yticks([])
# Make cartesian coordinates for the pixel indicies
# (The origin defaults to the center of the image)
x, y = index_coords(data, origin)
# Convert the pixel indices into polar coords.
r, theta = cart2polar(x, y)
# Unpack bands of the image
red, green, blue = data.T
# Plot...
plt.figure()
plt.subplot(2,2,1, projection='polar')
intensity_rose(theta, red, 'Red')
plt.subplot(2,2,2, projection='polar')
intensity_rose(theta, green, 'Green')
plt.subplot(2,1,2, projection='polar')
intensity_rose(theta, blue, 'Blue')
plt.suptitle('Average intensity as a function of direction')
def plot_polar_image(data, origin=None):
"""Plots an image reprojected into polar coordinages with the origin
at "origin" (a tuple of (x0, y0), defaults to the center of the image)"""
polar_grid, r, theta = reproject_image_into_polar(data, origin)
plt.figure()
plt.imshow(polar_grid, extent=(theta.min(), theta.max(), r.max(), r.min()))
plt.axis('auto')
plt.ylim(plt.ylim()[::-1])
plt.xlabel('Theta Coordinate (radians)')
plt.ylabel('R Coordinate (pixels)')
plt.title('Image in Polar Coordinates')
def index_coords(data, origin=None):
"""Creates x & y coords for the indicies in a numpy array "data".
"origin" defaults to the center of the image. Specify origin=(0,0)
to set the origin to the lower left corner of the image."""
ny, nx = data.shape[:2]
if origin is None:
origin_x, origin_y = nx // 2, ny // 2
else:
origin_x, origin_y = origin
x, y = np.meshgrid(np.arange(nx), np.arange(ny))
x -= origin_x
y -= origin_y
return x, y
def cart2polar(x, y):
r = np.sqrt(x**2 + y**2)
theta = np.arctan2(y, x)
return r, theta
def polar2cart(r, theta):
x = r * np.cos(theta)
y = r * np.sin(theta)
return x, y
def bin_by(x, y, nbins=30):
"""Bin x by y, given paired observations of x & y.
Returns the binned "x" values and the left edges of the bins."""
bins = np.linspace(y.min(), y.max(), nbins+1)
# To avoid extra bin for the max value
bins[-1] += 1
indicies = np.digitize(y, bins)
output = []
for i in xrange(1, len(bins)):
output.append(x[indicies==i])
# Just return the left edges of the bins
bins = bins[:-1]
return output, bins
def reproject_image_into_polar(data, origin=None):
"""Reprojects a 3D numpy array ("data") into a polar coordinate system.
"origin" is a tuple of (x0, y0) and defaults to the center of the image."""
ny, nx = data.shape[:2]
if origin is None:
origin = (nx//2, ny//2)
# Determine that the min and max r and theta coords will be...
x, y = index_coords(data, origin=origin)
r, theta = cart2polar(x, y)
# Make a regular (in polar space) grid based on the min and max r & theta
r_i = np.linspace(r.min(), r.max(), nx)
theta_i = np.linspace(theta.min(), theta.max(), ny)
theta_grid, r_grid = np.meshgrid(theta_i, r_i)
# Project the r and theta grid back into pixel coordinates
xi, yi = polar2cart(r_grid, theta_grid)
xi += origin[0] # We need to shift the origin back to
yi += origin[1] # back to the lower-left corner...
xi, yi = xi.flatten(), yi.flatten()
coords = np.vstack((xi, yi)) # (map_coordinates requires a 2xn array)
# Reproject each band individually and the restack
# (uses less memory than reprojection the 3-dimensional array in one step)
bands = []
for band in data.T:
zi = sp.ndimage.map_coordinates(band, coords, order=1)
bands.append(zi.reshape((nx, ny)))
output = np.dstack(bands)
return output, r_i, theta_i
if __name__ == '__main__':
main()
Исходное изображение:
Проецируемое в полярные координаты:
Интенсивность как функциянаправление от центра изображения: 