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How and why to take a logarithm of an image [video]

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Re: How and why to take a logarithm of an image [video]

#51

Post by daedrdev »

ahns wrote: post #48
ahns wrote: post #13

Earlier quoted context omitted.

One of Dutch artist M.C. Escher's works is a man is admiring a piece of art that itself depicts the building the (very same) man is in [0]. Escher left out the middle bit of the painting, probably since it's fairly complicated, putting his signature there instead. The video itself is about the complex analysis used to fill in that missing middle, based on a paper ~20 years ago. [0] https://en.wikipedia.org/wiki/Print…

Hm, since I can't edit my comment: link to paper [0] [0] https://pub.math.leidenuniv.nl/~smitbde/papers/2003-de_smit-...

HN only allows editing comments for a short time

Re: How and why to take a logarithm of an image [video]

#52

Post by UltraSane »

3b1b wrote: post #40
close04 wrote: post #31

Earlier quoted context omitted.

> How (and why) to take a logarithm of an image I watched it a few days ago and this descriptive title was part of the reason I clicked. I generally trust 3B1B anyway but normally a title like "This picture broke my brain" would put me off.

In case you're curious, when I ran that title/thumbnail AB test, the option "This picture broke my brain" did end up winning. I was a bit disappointed, because I didn't really _want_ it to win, but I did include it out of curiosity. Ultimately, I changed it to the other title, mostly because I like it better, and the margin was small. I was genuinely torn about how to title this, because one of my aims is that it sta…

You should be able to have different titles for different ages and education levels of users

Re: How and why to take a logarithm of an image [video]

#54

Post by griffzhowl »

marginalia_nu wrote: post #47
griffzhowl wrote: post #45

Earlier quoted context omitted.

Answers that are only comprehensible to those who already know the answer:

Well he wanted video boiled down to the punchline. Ask a silly question, get a silly answer.

Well, maybe, but that seems like a deliberately uncharitable interpretation of the question, which I interpreted more as "Can you summarize the video in ~1 line?" - or at least closer to that than "Can you give me the answer the video comes to without specifying the question it asks?"

Even in those terms the answer given isn't really an answer because it just gives an expression with undefined variables.

Re: How and why to take a logarithm of an image [video]

#55

Post by rappatic »

Similarly, it's possible to take the derivative of a song. You can use a Fourier transform to express the song's waveform as a series of sin and cosine functions, then take the derivative.

Imagine, for the sake of simplicity, you could express the song's waveform with the function 13 * sin(41x).

The derivative of this function is 533 * cos(41x).

Cosine, of course, is just a phase shifted sine, and the constant coefficient inside the function stays the same. So you're not changing anything about the shape of the wave, just stretching it vertically.

This has the effect of mimicking a "high pass filter," amplifying the volume of the highs.

Re: How and why to take a logarithm of an image [video]

#56

Post by gowld »

3b1b wrote: post #40
close04 wrote: post #31

Earlier quoted context omitted.

> How (and why) to take a logarithm of an image I watched it a few days ago and this descriptive title was part of the reason I clicked. I generally trust 3B1B anyway but normally a title like "This picture broke my brain" would put me off.

In case you're curious, when I ran that title/thumbnail AB test, the option "This picture broke my brain" did end up winning. I was a bit disappointed, because I didn't really _want_ it to win, but I did include it out of curiosity. Ultimately, I changed it to the other title, mostly because I like it better, and the margin was small. I was genuinely torn about how to title this, because one of my aims is that it sta…

As annoying as those titles are, the work that you (and few others, like Veritasium) do makes it well worth the tradeoff. Just keep reminding everyone that the annoying title gets the video into the brain of thousands of other people who aren't subscribed yet. It's a tiny price to pay for astounding value.

Everyone who watches your videos loves them and wants everyone else to watch them.

Re: How and why to take a logarithm of an image [video]

#57

Post by toxik »

rappatic wrote: post #55

Similarly, it's possible to take the derivative of a song. You can use a Fourier transform to express the song's waveform as a series of sin and cosine functions, then take the derivative. Imagine, for the sake of simplicity, you could express the song's waveform with the function 13 * sin(41x). The derivative of this function is 533 * cos(41x). Cosine, of course, is just a phase shifted sine, and the constant coeffi…

Well, you get the frequency domain derivative. This is the same as scaling the time domain by a linear ramp. Not exactly hugely useful, unless you happen to be in radar.

You can take the finite difference with eg np.diff(waveform) though.

Re: How and why to take a logarithm of an image [video]

#59

Post by gowld »

OscarCunningham wrote: post #29

I've been wondering if you could do a similar thing for a Droste effect image containing two copies of itself. Packs of Laughing Cow cheese show a cow with two earrings, each of which is a pack of the cheese.

What "similar thing" are you asking for? The Laughing Cow image exists. The Print Gallery is an object itself existing at 2 zoom levels in the same place, but the cheese exists in different places. You can't have two copies of the same image in the same place - that's not a copy; it's just itself.

Re: How and why to take a logarithm of an image [video]

#60

Post by ant6n »

pdpi wrote: post #21
Jeff_Brown wrote: post #7

I love 3B1B but generally don't have time to watch long videos. Can anyone sum up the punchline?

The punchline is that you can fill in the centre of Escher's piece by using complex analysis, and it produces a very satisfying, "obviously correct", solution. But, as with all jokes, the punchline isn't funny at all without the setup.

The joke is that if you fill in the center, it shows the Droste effect of the image and kind of diminishes the magic of it.
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