One thing that's interesting with this is that if we apply the reflection matrix again, we return to our original image. That's making me wonder - is there a way to design a matrix such that it obfuscates an image (sort of like a "secret key") and have it be the same decrypting key? Or what if we had a different matrix to decrypt?
NKJEW
@adityaramkumar Definitely an interesting thought! As far as I know, most linear transformations do have an "inverse" transformation if you wanted to "undo" the effect of some previous transformation to simulate "decryption" process. An exception to this might be a matrix which compresses all of 2D space onto the origin (i.e. a matrix of all 0s), at which point there's no way you can "decrypt" that transformation to bring back your original image.
However, I feel like a linear transformation (e.g. what you'd get via matrix multiplication) probably wouldn't do a great job of obfuscating an image, since - as a general property - straight lines will always remain straight lines if your transformation is linear. So at best you could maybe shear the image so much that it becomes super stretched out, but you'd probably still be able to tell what it was just based on the fact that the relative positions of things will stay the same.
x = -1, y = 1
One thing that's interesting with this is that if we apply the reflection matrix again, we return to our original image. That's making me wonder - is there a way to design a matrix such that it obfuscates an image (sort of like a "secret key") and have it be the same decrypting key? Or what if we had a different matrix to decrypt?
@adityaramkumar Definitely an interesting thought! As far as I know, most linear transformations do have an "inverse" transformation if you wanted to "undo" the effect of some previous transformation to simulate "decryption" process. An exception to this might be a matrix which compresses all of 2D space onto the origin (i.e. a matrix of all 0s), at which point there's no way you can "decrypt" that transformation to bring back your original image.
However, I feel like a linear transformation (e.g. what you'd get via matrix multiplication) probably wouldn't do a great job of obfuscating an image, since - as a general property - straight lines will always remain straight lines if your transformation is linear. So at best you could maybe shear the image so much that it becomes super stretched out, but you'd probably still be able to tell what it was just based on the fact that the relative positions of things will stay the same.