π3: PERMUTATION-EQUIVARIANT VISUAL GEOMETRY LEARNING

<h1 id="technical" Technical Analysis</h1 Jump to Section: Motivation motivation | Results summary-of-results | Conclusions final-conclusions <figure class="my-6" <video controls playsinline style="display: block; margin: 0 auto; max-width: 100%; height: auto;" src="$BUCKET URL/pi3/videos/video in post 012cb5fe-b289-4588-83c3-b08b11fb4b46.mp4" </video </figure "π3" https://yyfz.github.io/pi3/ is a feed-forward neural network that offers a novel approach to visual geometry reconstruction, breaking the reliance on a conventional fixed reference view. π3 employs a fully permutation-equivariant architecture to predict affine-invariant camera poses and scale-invariant local point maps without any reference frames. High-level Analogy : Imagine you and your friends are trying to build a 3D model of a new building, but none of you have a master blueprint or a single 'official' measuring stick. Instead, each of you takes pictures and notes down measurements from your own perspective, using your own rulers. The trick is, you all agree on how your rulers relate to each other e.g., 'my ruler is twice as long as yours for this particular wall' , and you can figure out the exact position of each friend relative to the others. This new system, π3 , is like everyone sharing their individual measurements and relative positions, without ever needing to pick one person's ruler or viewpoint as the 'master' one. This way, if someone's camera is shaky or their initial measurements are off, it does