Detecting rotation and line spacing of image of page of text using Radon transform

output.png

rotation_spacing.py

"""
Automatically detect rotation and line spacing of an image of text using
Radon transform

If image is rotated by the inverse of the output, the lines will be
horizontal (though they may be upside-down depending on the original image)

It doesn't work with black borders
"""

from skimage.transform import radon
from PIL import Image
from numpy import asarray, mean, array, blackman
import numpy as np
from numpy.fft import rfft
import matplotlib.pyplot as plt
try:
    # More accurate peak finding from
    # https://gist.github.com/endolith/255291#file-parabolic-py
    from parabolic import parabolic

    def argmax(x):
        return parabolic(x, np.argmax(x))[0]
except ImportError:
    from numpy import argmax


def rms_flat(a):
    """
    Return the root mean square of all the elements of *a*, flattened out.
    """
    return np.sqrt(np.mean(np.abs(a) ** 2))


filename = 'skew-linedetection.png'

# Load file, converting to grayscale
I = asarray(Image.open(filename).convert('L'))
I = I - mean(I)  # Demean; make the brightness extend above and below zero
plt.subplot(2, 2, 1)
plt.imshow(I)

# Do the radon transform and display the result
sinogram = radon(I)

plt.subplot(2, 2, 2)
plt.imshow(sinogram.T, aspect='auto')
plt.gray()

# Find the RMS value of each row and find "busiest" rotation,
# where the transform is lined up perfectly with the alternating dark
# text and white lines
r = array([rms_flat(line) for line in sinogram.transpose()])
rotation = argmax(r)
print('Rotation: {:.2f} degrees'.format(90 - rotation))
plt.axhline(rotation, color='r')

# Plot the busy row
row = sinogram[:, rotation]
N = len(row)
plt.subplot(2, 2, 3)
plt.plot(row)

# Take spectrum of busy row and find line spacing
window = blackman(N)
spectrum = rfft(row * window)
plt.plot(row * window)
frequency = argmax(abs(spectrum))
line_spacing = N / frequency  # pixels
print('Line spacing: {:.2f} pixels'.format(line_spacing))

plt.subplot(2, 2, 4)
plt.plot(abs(spectrum))
plt.axvline(frequency, color='r')
plt.yscale('log')
plt.show()

skew-linedetection.png

@endolith thanks !
1.
i see output on skew-linedetection.png:

Rotation: 5.00 degrees
Line spacing: 13.63 pixels

is it correct ?

and sometimes got this:

/home/pi/.local/lib/python3.9/site-packages/skimage/transform/radon_transform.py:75: UserWarning: Radon transform: image must be zero outside the reconstruction circle
  warn('Radon transform: image must be zero outside the '
Rotation: 3.00 degrees
/home/pi/Desktop/rotation_detection.py:69: RuntimeWarning: divide by zero encountered in long_scalars
  line_spacing = N / frequency  # pixels
Line spacing: inf pixels

i saw remark It doesn't work with black borders
what does it mean ? do you have an example image ?

@zoldaten That's what I get for the example image, yes:

Rotation: 5.00 degrees
Line spacing: 13.63 pixels

@endolith
if you dont mind i ll speed up a bit your code.
now i have time 0:00:01.228 sec (with skew-linedetection.png). on raspberry pi.
the bigger pic i use the more inference time. on 2MiB pic i have already 11 sec.
i used cprofile and found that sinogram = radon(I) eats all time.
to speed up it we need smaller image.

so. we need to replace:
I = asarray(Image.open(filename).convert('L'))
with this:

import sys
from PIL.Image import Resampling

I = Image.open(filename).convert('L')
I.thumbnail([sys.maxsize, 480], Resampling.LANCZOS)  #resize image keeping aspect ratio. 480 by example. it may be smaller i think.

now i have on skew-linedetection.png:
0:00:00.739

i didnt tested how the last code works as i need only rotation degrees. and it returns the result.