Unpermutator.md

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()

scramble.svg

scramble2d.svg

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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