realazthat/Unpermutator.md Secret

## scramble.py
"""
Scramble/permute a frame of a video, requires numpy and opencv.

Licensed under CC0 (https://creativecommons.org/publicdomain/zero/1.0/)
"""


import argparse


import cv2
import numpy as np

def main():

    parser = argparse.ArgumentParser(description='Extract and permute a frame.')


    parser.add_argument('invideo', type=argparse.FileType('rb'),
                       help='A video to add to the MI frame')
    parser.add_argument('--out', dest='outfile', type=argparse.FileType('wb'),
                        help='path to output frame')
    parser.add_argument('--frame', type=int, default=0,
                       help='Frame number to extract (defaults to 0)')
    parser.add_argument('--permute', action='store_true', default=False,
                       help='Should the output frame be permuted')
    parser.add_argument('--gray', action='store_true', default=False,
                       help='Should the output frame be gray scale')
    parser.add_argument('--binary', action='store_true', default=False,
                       help='Should the output frame be binary')


    args = parser.parse_args()
    cap = cv2.VideoCapture(args.invideo.name)
    expected_frames = int(cap.get(cv2.CAP_PROP_FRAME_COUNT))
    width0 = int(cap.get(cv2.CAP_PROP_FRAME_WIDTH))
    height0 = int(cap.get(cv2.CAP_PROP_FRAME_HEIGHT))
    n0 = width0*height0

    ret = True
    i = 0

    while(ret and cap.isOpened()):
        ret, frame0 = cap.read()

        if not ret:
            break


        if i < args.frame:
            i += 1
            continue

        frame = frame0
        depth = 3

        if args.gray or args.binary:
            frame = cv2.cvtColor(frame0, cv2.COLOR_BGR2GRAY)
            depth = 1

        print (frame.dtype)
        print (frame)
        if args.binary:
            frame >>= 7
            frame *= 255
        print (frame.dtype)
        print (frame)


        expected_size = n0*depth
        expected_shape = (height0,width0,depth)
        if depth == 1:
            expected_shape = (height0, width0)

        assert frame.size == expected_size
        assert frame.shape == expected_shape, (frame.shape, expected_shape, depth)

        permuted_frame = np.copy(frame)
        permuted_frame = permuted_frame.reshape((height0*width0,depth))
        print ('permuted_frame.shape:',permuted_frame.shape)
        np.random.shuffle(permuted_frame)
        permuted_frame = permuted_frame.reshape((height0,width0, depth))

        print (permuted_frame.shape)

        outframe = frame
        if args.permute:
            outframe = permuted_frame

        if args.outfile is not None:
            cv2.imwrite(args.outfile.name, img=outframe)
        return


if __name__ == '__main__':
    main()

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## Unpermutator.md

      
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              Unpermutator.md
            
          
    #Question
##Reconstructing a screen of permuted pixels
###Summary
Given a video with the pixel locations randomly permuted (once, for the entire video), can we (efficiently) reconstruct the original picture?
###Details

You are given an LCD screen with $n = w \times h$ pixels, that has been altered so that the pixel locations are permuted, once, in some random manner.
Watching a video on this LCD screen would obviously result in quite a garbled picture.
The permutation is mapped by some unknown function, we shall call $\text{permute}\left(x_0,y_0\right) \implies (x,y)$

Each pixel on the screen has a permuted location $(x,y)$ and some unknown original location $(x_0,y_0)$ (such that $\text{permute}\left(x_0,y_0\right)=(x,y)$).
You (and your computer) are given to watch a particular video of an average film of average length, with $m$ frames, and having the same resolution as the LCD screen; however for simplicity, assume the video will be in grayscale (for example, each pixel is a single color in the range $[0,256)$).
As a frame of reference, you are also informed which pixel is the lowest location in the original non-permuted screen (i.e you are given the values $x$ and $y$, such that $(x_0,y_0) =(0,0)$, and $\text{permute}\left(0,0\right)=(x,y)$).

###Goal

Algorithm to (efficiently) compute the mapping of the pixels to their original locations.
Can this be done in $o\left(n^2\right)$ space (i.e in better than $\mathcal O\left(n^2\right)$ space?)
Can this be done in $o\left(n^2f(m)\right)$ time?

I'm not sure how to ask this question correctly, but I am mostly wondering about reducing the $n^2$ factor.


Is this a known problem, or similar to any known problems?

PS. What about same question but for the case of binary images for each frame instead of grayscale.
###Appendix

 
^{Figure 1 Example permuted "LCD screen", side view}
^{Figure 2 Example permuted "LCD screen", front view}

 
^{Figure 3 Example video frame (color)}
^{Figure 4 Example permuted video frame (color)}

 
^{Figure 5 Example video frame (grayscale)}
^{Figure 6 Example permuted video frame (grayscale)}

 
^{Figure 7 Example video frame (binary, using most-significant-bitplane)}
^{Figure 8 Example permuted video frame (binary)}
###Related source codes are on gist.github.com
###Credits:

Images courtesy of NASA (NASA GoPro footage from EVA 30).

More info on archive.org.
Licensed under the Creative Commons Public Domain Mark 1.0 license


tags: reference-request, information-theory, algorithms, data-structures, probability
	"""
	Scramble/permute a frame of a video, requires numpy and opencv.

	Licensed under CC0 (https://creativecommons.org/publicdomain/zero/1.0/)
	"""


	import argparse


	import cv2
	import numpy as np

	def main():

	parser = argparse.ArgumentParser(description='Extract and permute a frame.')





	parser.add_argument('invideo', type=argparse.FileType('rb'),
	help='A video to add to the MI frame')
	parser.add_argument('--out', dest='outfile', type=argparse.FileType('wb'),
	help='path to output frame')
	parser.add_argument('--frame', type=int, default=0,
	help='Frame number to extract (defaults to 0)')
	parser.add_argument('--permute', action='store_true', default=False,
	help='Should the output frame be permuted')
	parser.add_argument('--gray', action='store_true', default=False,
	help='Should the output frame be gray scale')
	parser.add_argument('--binary', action='store_true', default=False,
	help='Should the output frame be binary')




	args = parser.parse_args()
	cap = cv2.VideoCapture(args.invideo.name)
	expected_frames = int(cap.get(cv2.CAP_PROP_FRAME_COUNT))
	width0 = int(cap.get(cv2.CAP_PROP_FRAME_WIDTH))
	height0 = int(cap.get(cv2.CAP_PROP_FRAME_HEIGHT))
	n0 = width0*height0

	ret = True
	i = 0

	while(ret and cap.isOpened()):
	ret, frame0 = cap.read()

	if not ret:
	break


	if i < args.frame:
	i += 1
	continue

	frame = frame0
	depth = 3

	if args.gray or args.binary:
	frame = cv2.cvtColor(frame0, cv2.COLOR_BGR2GRAY)
	depth = 1

	print (frame.dtype)
	print (frame)
	if args.binary:
	frame >>= 7
	frame *= 255
	print (frame.dtype)
	print (frame)


	expected_size = n0*depth
	expected_shape = (height0,width0,depth)
	if depth == 1:
	expected_shape = (height0, width0)

	assert frame.size == expected_size
	assert frame.shape == expected_shape, (frame.shape, expected_shape, depth)

	permuted_frame = np.copy(frame)
	permuted_frame = permuted_frame.reshape((height0*width0,depth))
	print ('permuted_frame.shape:',permuted_frame.shape)
	np.random.shuffle(permuted_frame)
	permuted_frame = permuted_frame.reshape((height0,width0, depth))

	print (permuted_frame.shape)

	outframe = frame
	if args.permute:
	outframe = permuted_frame

	if args.outfile is not None:
	cv2.imwrite(args.outfile.name, img=outframe)
	return


	if __name__ == '__main__':
	main()
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