Reading photographs as a spatial system
A single photograph records colour on a flat image plane but does not state where the depicted surfaces lie in three-dimensional space. Reconstruction becomes possible when the same features appear across overlapping photographs taken from different positions. Their relative displacement, known as parallax, allows camera poses and scene structure to be estimated. For the Karzer, repeated views of inscriptions, mouldings, wall junctions and other stable details connect the 177 images into one spatially consistent camera network.
This preparatory calculation was already included in the Greifswald publication. Its COLMAP model contains camera intrinsics, camera poses and 263,336 sparse 3D points matched across the image set. The sparse points are not the final visual reconstruction. They are reliable anchors used to initialise the Gaussian optimisation and to associate every training image with a known viewpoint.
What is a 3D Gaussian?
In this context, a Gaussian can be imagined as a small translucent ellipsoid suspended in space. It has a centre position, three-dimensional scale, orientation, opacity and colour. “Anisotropic” means that the primitive may stretch differently along each axis: it can become thin and broad for a wall fragment or compact for a small detail. Its mathematically smooth footprint avoids the hard edges associated with an ordinary point cloud.
During training, the model is rendered from a camera position already known from COLMAP. The rendered pixels are compared with the corresponding source photograph, and differentiable rasterisation calculates how each Gaussian should change to reduce the image error. Position, covariance, opacity and appearance are updated through gradient descent. Regions requiring more detail are densified by adding or splitting primitives, while weak or redundant contributions can be removed. After 30,000 iterations, the initially sparse scene has become a dense appearance representation containing 2,152,624 optimised Gaussians.
Why can it render interactively?
At viewing time, the ellipsoids are projected onto the screen as two-dimensional splats. The renderer sorts them by depth and combines their colour and transparency from back to front. This operation maps efficiently to parallel graphics hardware and avoids reconstructing a new neural image one pixel at a time. The result is a continuous view that can respond to camera motion in real time, provided that the browser can allocate and sort the full primitive set.
