removes a perspective projection from a region of an image.

deproyector.py

#!/usr/bin/python

import Image
import math

# calculates simple two-line intersection. be warned: fails miserably with
# vertical lines and parallelograms.
def intersection(p0, p1, p2, p3):
	m0 = (p1[1] - p0[1]) / float(p1[0] - p0[0])
	m2 = (p3[1] - p2[1]) / float(p3[0] - p2[0])
	
	return intersection2(p0, m0, p2, m2)

# gets the intersection between two point-slope lines
def intersection2(p0, m0, p2, m2):
	x = (p2[1] - p0[1] + m0*p0[0] - m2*p2[0]) / (m0 - m2)
	y = m0 * (x - p0[0]) + p0[1]
	
	return x, y
	
img = Image.open('grid.jpg')
# sorry, you have to provide these yourself :P
corners = ((2018, 101), (143, 644), (188, 1699), (2227, 1678))

xf = intersection(*corners)
yf = intersection(*(corners[1:] + corners[:1]))

minx = math.atan2(corners[0][1] - xf[1], corners[0][0] - xf[0])
miny = math.atan2(corners[2][1] - yf[1], corners[2][0] - yf[0])
maxx = math.atan2(corners[2][1] - xf[1], corners[2][0] - xf[0])
maxy = math.atan2(corners[0][1] - yf[1], corners[0][0] - yf[0])

dx = maxx - minx
dy = maxy - miny

w = 1024
h = 600

out = Image.new('RGB', (w, h))

for y in xrange(h):
	for x in xrange(w):
		my = math.tan(miny + dy * (x / float(w)) ** 1.3) # don't ask, i don't know either
		mx = math.tan(minx + dx * (y / float(h)))
		
		xx, yy = intersection2(yf, my, xf, mx)
		
		try:
			out.putpixel((x, y), img.getpixel((xx, yy)))
		except:
			pass

out.save('output.jpg')