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It's all a blur

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Re: It's all a blur

#22
Sorry but this post is the blind leading the blind, pun intended. Allow me to explain, I have a DSP degree.

The reason the filters used in the post are easily reversible is because none of them are binomial (i.e. the discrete equivalent of a gaussian blur). A binomial blur uses the coefficients of a row of Pascal's triangle, and thus is what you get when you repeatedly average each pixel with its neighbor (in 1D).

When you do, the information at the Nyquist frequency is removed entirely, because a signal of the form "-1, +1, -1, +1, ..." ends up blurred _exactly_ into "0, 0, 0, 0...".

All the other blur filters, in particular the moving average, are just poorly conceived. They filter out the middle frequencies the most, not the highest ones. It's equivalent to doing a bandpass filter and then subtracting that from the original image.

Here's an interactive notebook that explains this in the context of time series. One important point is that the "look" that people associate with "scientific data series" is actually an artifact of moving averages. If a proper filter is used, the blurryness of the signal is evident. https://observablehq.com/d/a51954c61a72e1ef

Re: It's all a blur

#23
post #7

Can this be applied to camera shutter/motion blur, at low speeds the slight shake of the camera produces this type of blur. This is usually resolved with IBIS to stabilize the sensor.

The ability to reverse is very dependent on the transformation being well known, in this case it is deterministic and known with certainty. Any algorithm to reverse motion blur will depend on the translation and rotation of the camera in physical space, and the best the algorithm could do will be limited by the uncertainty in estimating those values. If you apply a fake motion blur like in photoshop or after effects…

Record gyro motion at time of shutter?

Re: It's all a blur

#24
post #7

Can this be applied to camera shutter/motion blur, at low speeds the slight shake of the camera produces this type of blur. This is usually resolved with IBIS to stabilize the sensor.

The missing piece of the puzzle is how to determine the blur kernel from the blurry image. There's a whole body of literature on that that's called blind deblurring.

For instance: https://deepinv.github.io/deepinv/auto_examples/blind-invers...

Re: It's all a blur

#25
What I find fascinating about blur is how computational photography has completely changed the game. Smartphone cameras now capture multiple exposures and computationally combine them, essentially solving the deblurring problem before it even happens. The irony is that we now have to add blur back artificially for portrait mode bokeh, which means we went from fighting blur to synthesizing it as a feature.

Re: It's all a blur

#26

Earlier quoted context omitted.

This was also my understanding. It's essentially like "cracking" a password when you have its hash and know the hashing algorithm. You don't have to know how to reverse the blur, you just need to know how to do it the normal way, you can then essentially brute force through all possible characters one at a time to see if it looks the same after applying the blur. Thinking about this, adding randomness to the blurring…

> just mask the sensitive data with a single color which is impossible to reverse (for rasterized images, this is not a good idea for PDFs Also not a good idea for masking already compressed images of text, like jpg, because some of the information might bleed out in uncovered areas.

Interesting - does a little extra coverage solve this or is it possible to use distant pixels to find the original?

Re: It's all a blur

#27

Captain Disillusion recently covered this subject in a more popular science format as well https://youtu.be/xDLxFGXuPEc

8 months ago, for those of us who got excited by the idea of a "recent" new video from CD.

Re: It's all a blur

#28
post #2

reminds me of the guy who used the photoshop swirl effect to mask his face in csam he produced, who was found out when someone just undid the swirl

Action Lab just did a video on physical swirling vs mixing. Swirling is reversible.

Re: It's all a blur

#29
post #4

Encode the image as a boundary condition of a laminar flow and you can recover the original image from an observation. If, however, you observe after turbulence has set in, then some of the information has been lost, it's in the entropy now. How much, that depends on the turbulent flow. Don't miss out on this video by smarter every day https://youtu.be/j2_dJY_mIys?si=ArMd0C5UzbA8pmzI Treat the dynamics and time of ev…

If you encode code your data directly in the fluid, then turbulence becomes the statistical TTL on the data.
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