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	<link rel="modulepreload" href="/docs/ml-for-3d-course/main/en/_app/immutable/chunks/CodeBlock.3130f36f.js"><!-- HEAD_svelte-u9bgzb_START --><meta name="hf:doc:metadata" content="{"title":"What is it?","local":"what-is-it","sections":[{"title":"Differentiable Rasterization","local":"differentiable-rasterization","sections":[],"depth":2},{"title":"Gaussian Splatting","local":"gaussian-splatting","sections":[],"depth":2},{"title":"Inference","local":"inference","sections":[],"depth":2},{"title":"Training","local":"training","sections":[],"depth":2},{"title":"Generative 3D","local":"generative-3d","sections":[],"depth":2}],"depth":1}"><!-- HEAD_svelte-u9bgzb_END --> <p></p> <div class="items-center shrink-0 min-w-[100px] max-sm:min-w-[50px] justify-end ml-auto flex" style="float: right; margin-left: 10px; display: inline-flex; position: relative; z-index: 10;"><div class="inline-flex rounded-md max-sm:rounded-sm"><button class="inline-flex items-center gap-1 h-7 max-sm:h-7 px-2 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disabled:pointer-events-none text-sm text-gray-500 hover:text-gray-700 dark:hover:text-white rounded-r-md max-sm:rounded-r-sm border border-l transition border-gray-200 bg-white hover:shadow-inner dark:border-gray-850 dark:bg-gray-950 dark:text-gray-200 dark:hover:bg-gray-800" aria-haspopup="menu" aria-expanded="false" aria-label="Open copy menu"><svg class="transition-transform text-gray-400 overflow-visible sm:size-3.5 size-3 rotate-0" width="1em" height="1em" viewBox="0 0 12 7" fill="none" xmlns="http://www.w3.org/2000/svg"><path d="M1 1L6 6L11 1" stroke="currentColor"></path></svg></button></div> </div> <h1 class="relative group"><a id="what-is-it" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#what-is-it"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>What is it?</span></h1> <p data-svelte-h="svelte-1l7u0lq">Gaussian Splatting is a <strong>differentiable rasterization technique</strong>.</p> <h2 class="relative group"><a id="differentiable-rasterization" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#differentiable-rasterization"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>Differentiable Rasterization</span></h2> <p data-svelte-h="svelte-7t4fq2">In simple terms:</p> <ul data-svelte-h="svelte-isap97"><li>Differentiable can be thought of as a fancy way to say “AI-compatible”</li> <li>Rasterization means taking data and drawing it on the screen</li></ul> <p data-svelte-h="svelte-yvwu9g">Rasterization is already really common. It usually takes the form of <a href="https://en.wikipedia.org/wiki/Rasterisation" rel="nofollow">triangle rasterization</a>, where 3D data is converted to 2D pixel data and drawn on the screen. That’s how meshes are usually rendered.</p> <p data-svelte-h="svelte-1xent91"><img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/ml-for-3d-course/mesh.png" alt="Mesh"></p> <p data-svelte-h="svelte-9ucodi">However, triangle rasterization isn’t very AI-compatible. This is because it includes discrete decisions like:</p> <ul data-svelte-h="svelte-19d9d9h"><li>Is this pixel inside the triangle?</li></ul> <p data-svelte-h="svelte-180fjqc">Neural networks don’t like discrete decisions. They want everything to be fuzzy and continous - or in other words, <em>differentiable</em>.</p> <h2 class="relative group"><a id="gaussian-splatting" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#gaussian-splatting"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>Gaussian Splatting</span></h2> <p data-svelte-h="svelte-2vaw9h">Gaussian Splatting is a differentiable rasterization technique. But how does it actually work?</p> <p data-svelte-h="svelte-w056v4">Splats are composed of millions of points, where each point is composed of four parameters:</p> <ul data-svelte-h="svelte-1pgaban"><li><strong>Position</strong>: where it’s located (XYZ)</li> <li><strong>Covariance</strong>: how it’s stretched (3x3 matrix)</li> <li><strong>Color</strong>: what color it is (RGB)</li> <li><strong>Alpha</strong>: how transparent it is (α)</li></ul> <p data-svelte-h="svelte-n6px5u">Then, to rasterize a splat, these points are projected into 2D. Then, for every pixel, contribute the contribution of every point. Or, in pseudocode:</p> <div class="code-block relative "><div class="absolute top-2.5 right-4"><button class="inline-flex items-center relative text-sm focus:text-green-500 cursor-pointer focus:outline-none transition duration-200 ease-in-out opacity-0 mx-0.5 text-gray-600 " title="code excerpt" type="button"><svg class="" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" fill="currentColor" focusable="false" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 32 32"><path d="M28,10V28H10V10H28m0-2H10a2,2,0,0,0-2,2V28a2,2,0,0,0,2,2H28a2,2,0,0,0,2-2V10a2,2,0,0,0-2-2Z" transform="translate(0)"></path><path d="M4,18H2V4A2,2,0,0,1,4,2H18V4H4Z" transform="translate(0)"></path><rect fill="none" width="32" height="32"></rect></svg> <div class="absolute pointer-events-none transition-opacity bg-black text-white py-1 px-2 leading-tight rounded font-normal shadow left-1/2 top-full transform -translate-x-1/2 translate-y-2 opacity-0"><div class="absolute bottom-full left-1/2 transform -translate-x-1/2 w-0 h-0 border-black border-4 border-t-0" style="border-left-color: transparent; border-right-color: transparent; "></div> Copied</div></button></div> <pre class=""><!-- HTML_TAG_START -->splat2d = splat.project_and_sort()
	<span class="hljs-keyword">for</span> point <span class="hljs-keyword">in</span> splat2d:
	<span class="hljs-keyword">for</span> pixel <span class="hljs-keyword">in</span> image:
	pixel += compute_contribution(point, pixel)<!-- HTML_TAG_END --></pre></div> <p data-svelte-h="svelte-dtphl0">The contribution of a point diminishes the further it is from the pixel. The points also need to be sorted, since they are blended back-to-front.</p> <p data-svelte-h="svelte-v7hqi9">In theory, every point contributes to every pixel, which is very inefficient. However, that’s okay, because it’s <em>differentiable</em>.</p> <p data-svelte-h="svelte-1wxfosp">In practice, this is optimized with a tile-based rasterization method, as detailed in the <a href="https://huggingface.co/papers/2308.04079" rel="nofollow">original paper</a>.</p> <h2 class="relative group"><a id="inference" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#inference"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>Inference</span></h2> <p data-svelte-h="svelte-tiuv9s">If you’re not training a model, then it doesn’t matter if it’s differentiable. You can just treat each point as an instanced quad, as in open-source web viewers like <a href="https://github.com/huggingface/gsplat.js" rel="nofollow">gsplat.js</a>.</p> <p data-svelte-h="svelte-nvtzrx">This can be seen in action <a href="https://huggingface.co/spaces/dylanebert/igf" rel="nofollow">here</a>.</p> <h2 class="relative group"><a id="training" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#training"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>Training</span></h2> <p data-svelte-h="svelte-1nuzef1">The <a href="https://huggingface.co/papers/2308.04079" rel="nofollow">original paper</a> intializes the points using <a href="https://en.wikipedia.org/wiki/Structure_from_motion" rel="nofollow">Structure-from-Motion</a>, a traditional algorithm for 3D reconstruction.</p> <p data-svelte-h="svelte-jnhg58"><img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/124_ml-for-games/gaussian/points.png" alt="Structure from Motion"></p> <p data-svelte-h="svelte-1xyf8kx">These points are then rasterized using the tile-based method, and the loss is computed by comparing the rasterized image to the ground truth. Gradient descent is applies to adjust the point parameters (position, covariance, color, alpha).</p> <p data-svelte-h="svelte-txetn1"><img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/124_ml-for-games/gaussian/ellipsoids.png" alt="Trained"></p> <p data-svelte-h="svelte-p9ikvl">The original paper also uses automated densification and pruning to automatically add and remove points as needed. More details can be found <a href="https://huggingface.co/blog/gaussian-splatting" rel="nofollow">here</a>.</p> <p data-svelte-h="svelte-kkz8p5"><img src="https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/blog/124_ml-for-games/gaussian/bicycle.png" alt="Final"></p> <h2 class="relative group"><a id="generative-3d" class="header-link block pr-1.5 text-lg no-hover:hidden with-hover:absolute with-hover:p-1.5 with-hover:opacity-0 with-hover:group-hover:opacity-100 with-hover:right-full" href="#generative-3d"><span><svg class="" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 256"><path d="M167.594 88.393a8.001 8.001 0 0 1 0 11.314l-67.882 67.882a8 8 0 1 1-11.314-11.315l67.882-67.881a8.003 8.003 0 0 1 11.314 0zm-28.287 84.86l-28.284 28.284a40 40 0 0 1-56.567-56.567l28.284-28.284a8 8 0 0 0-11.315-11.315l-28.284 28.284a56 56 0 0 0 79.196 79.197l28.285-28.285a8 8 0 1 0-11.315-11.314zM212.852 43.14a56.002 56.002 0 0 0-79.196 0l-28.284 28.284a8 8 0 1 0 11.314 11.314l28.284-28.284a40 40 0 0 1 56.568 56.567l-28.285 28.285a8 8 0 0 0 11.315 11.314l28.284-28.284a56.065 56.065 0 0 0 0-79.196z" fill="currentColor"></path></svg></span></a> <span>Generative 3D</span></h2> <p data-svelte-h="svelte-1ig1r3c">The original approach is suitable for learning individual scenes from photos. However, the concept of differentiable rasterization generalizes to more complex models like neural networks.</p> <p data-svelte-h="svelte-5hw3d">This is the case with generative 3D models like <a href="https://huggingface.co/spaces/dylanebert/LGM-mini" rel="nofollow">LGM</a>, which we’ll be using in the next section to build our own generative 3D demo.</p> <a class="!text-gray-400 !no-underline text-sm flex items-center not-prose mt-4" href="https://github.com/huggingface/ml-for-3d-course/blob/main/units/en/unit3/what-is-it.mdx" target="_blank"><svg class="mr-1" xmlns="http://www.w3.org/2000/svg" aria-hidden="true" fill="currentColor" focusable="false" role="img" width="1em" height="1em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 32 32"><path d="M31,16l-7,7l-1.41-1.41L28.17,16l-5.58-5.59L24,9l7,7z"></path><path d="M1,16l7-7l1.41,1.41L3.83,16l5.58,5.59L8,23l-7-7z"></path><path d="M12.419,25.484L17.639,6.552l1.932,0.518L14.351,26.002z"></path></svg> <span data-svelte-h="svelte-zjs2n5"><span class="underline">Update</span> on GitHub</span></a> <p></p>

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