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>you will get the same results using a simple matmul, because euclidean distance over normalized vectors is a linear transform of the cosine distance.

Squared euclidean distance of normalized vectors is an affine transform of their cosine similarity (the cosine of the angle between them).

  EuclideanDistance(x, y) = sqrt(dot(x - y, x - y)) = sqrt(dot(x, x) - 2dot(x, y) + dot(y, y)) = sqrt(2 - 2dot(x, y))

yes, you are right. I realized my mistake afterwards but it was after the edit window.

1. Create a point cloud from a scene (either via lidar, or via photogrammetry from multiple images)

2. Replace each point of the point cloud with a fuzzy ellipsoid, that has a bunch of parameters for its position + size + orientation + view-dependent color (via spherical harmonics up to some low order)

3. If you render these ellipsoids using a differentiable renderer, then you can subtract the resulting image from the ground truth (i.e. your original photos), and calculate the partial derivatives of the error with respect to each of the millions of ellipsoid parameters that you fed into the renderer.

4. Now you can run gradient descent using the differentiable renderer, which makes your fuzzy ellipsoids converge to something closely reproducing the ground truth images (from multiple angles).

5. Since the ellipsoids started at the 3D point cloud's positions, the 3D structure of the scene will likely be preserved during gradient descent, thus the resulting scene will support novel camera angles with plausible-looking results.


You... you must have been quite some 5 year old.

ELI5 has meant friendly simplified explanations (not responses aimed at literal five-year-olds) since forever, at least on the subreddit where the concept originated.

Now, perhaps referring to differentiability isn't layperson-accessible, but this is HN after all. I found it to be the perfect degree of simplification personally.


Some things would be literally impossible to properly explain to a 5 year old.

If one actually tried to explain to a five year old, they can use things like analogy, simile, metaphor, and other forms of rhetoric. This was just a straight-up technical explanation.

Lol. Def not for 5 year olds but it's about exactly what I needed

How about this:

Take a lot of pictures of a scene from different angles, do some crazy math, and then you can later pretend to zoom and pan the camera around however you want


sure, but does that explanation really help anyone. Imo it might scare people off actually diving into things, the math isn't too crazy.

And what about the "mature enough" part? How has it changed / progressed recently?

The field is advancing rapidly. New research papers are being published daily for a few years now. The best news feed I've found on the topic is

https://radiancefields.com/

https://x.com/RadianceFields alt: https://xcancel.com/RadianceFields


Thanks.

How hard is it to handle cases where the starting positions of ellipsoids in 3D is not correct (being too off). How common is such a scenario with the state of the art? E.g., if having only a stereoscopic image pair, the correspondences are often not accurate.

Thanks.


I assume that the differentiable renderer is only given its position and viewing angle at any one time (in order to be able to generalize to new viewing angles)?

Is it a fully connected NN?


No. There are no neural networks here. The renderer is just a function that takes a bunch of ellipsoid parameters and outputs a bunch of pixels. You render the scene, then subtract the ground truth pixels from the result, and sum the squared differences to get the total error. Then you ask the question "how would the error change if the X position of ellipsoid #1 was changed slightly?" (then repeat for all ellipsoid parameters, not just the X position, and all ellipsoids, not just ellipsoid #1). In other words, compute the partial derivative of the error with respect to each ellipsoid parameter. This gives you a gradient, that you can use to adjust the ellipsoids to decrease the error (i.e. get closer to the ground truth image).

Thanks for the explanation!

Great explanation/simplification. Top quality contribution.

Or: Matrix bullet time with more viewpoints and less quality.


And especially the ulimit command mentioned, which is mostly unknown to folks nowadays, it seems.

Lol, no. When you buy "barrels" of oil on a commodity market, the barrel is a unit of volume (42 US gallons).

>4,000 tons is almost four million kilograms

It is exactly four million kilograms. (Germany uses the SI metric ton)


TIL there are two units of measurement that are both called ton but confusingly are not the same as a ton. One is a tiny bit more than a ton (1.016 tons) and one is a bit less (0.907 tons). Apparently people use the prefixes long and short to differentiate them, at least that part is intuitive.

Well, three, the two you mentioned and the metric ton (1000 kg)

We already have a term for this: muzak.

https://en.wikipedia.org/wiki/Muzak


>I've spent many hours learning to play guitar and ukulele but I'm really not very good, and probably never will be - but I can hear the music in my head I want to create. I'm not interested in monetary gain at all, just being able to hear it for real and maybe share it with some people.

Luckily there are hundreds of MIDI editor DAWs available. Open the piano roll, and write down the music note by note. Surely, it's not that hard if you can hear it in your head.


If you are very good at music theory and have good pitch recognition absolutely, but that is a skill that takes quite a bit of effort to train.

If you just want to do a one off track for a party or something with AI sure go for it, but don't expect others to call you an artist.

Just like we don't call anyone who can use a microwave a chef. The chef may use a microwave, but they don't use it exclusively and they've spent the time to learn other tools and techniques.


Good decision. Bandcamp makes money from people who consciously avoided the streaming shitfest in favor of directly supporting the artists. Hardly surprising that their have a strong aversion to AI slop.

This might be evidence that the gravitational constant G is changing (increasing) over time! Could this be the explanation for dark matter and dark energy?

This would also explain why my bathroom scale has been showing larger and larger numbers to me! Genius. I'd say you're onto something, but I can't tell if you're also joking.

Occam's razor says it's less likely that the gravitational constant is increasing and more likely that the ability to withstand the pull of gravity decreases with age.

Article says age-adjusted fall rates are up substantially, so it's not just older population.

People rollerblade less.

I read that fall injuries in the elderly are a significant contributor to both death and drops in quality of life.

When it comes to proprioception and balance one group of people over 60 seem to have equivalent balance to younger people and that is certain kinds of rollerbladers.

So as a person who was relatively active (40mi+ per week biking and other things) I started rollerblading and it's been unbelievable, I'm older and certain types of movements that take 8yr olds a couple weeks to learn took me nearly a year, it's absolutely amazing though, pain and soreness in parts of my leg and feet all related to stabilization, significantly strengthened stabilization muscles and improved reaction times at speed. I figure if I can rollerblade on one foot at 15 miles an hour, walking with both feet at 3 should be no problem.

I put rollerblading and bouldering as my top two 'puzzle' based activities.


Yoga has balance poses and is much more accessible than rollerblading.

Yoga is a great idea but many who find it boring are getting the same poses at 15mph and with more dynamic load and interruption (due to rocks and other high speed road defects.) There is quite a bit of overlap but unless you are doing acro yoga there is also quite a bit that doesn't overlap.

Well of course old people fall more, but the article is about changes over the last 20 years.

...Oh wait, are you saying there are more old people now? That's interesting.


Which was specifically addressed early in the article.

Not only are there more falls among the elderly, there are more falls even fully accounting for changes in age composition of the population.

>>But an aging population only partially explains the rise in these deaths. Deaths by falls have risen 2.4-fold on an age-adjusted basis. While they have fallen among younger people and only risen slightly among the middle aged, they have risen substantially within every age bracket of the elderly.


It's back end of the post-war boom.

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