Three-dimensional meshes are central to computer graphics, animation and simulation, where they are almost always stored as a set of vertices connected by faces. While this is the standard representation for meshes, it is difficult to work with in machine learning applications, since raw vertex coordinates only describe the absolute position of the geometry and are easily disrupted by any rigid body transformation. Nonlinear Rotation-Invariant Coordinates, or NRIC, offer a different starting point, describing a mesh through the lengths of its edges and the dihedral angles between two faces intersecting at each edge. The advantage of NRIC is twofold. It is invariant to all rigid body motions, which isolates the geometric structure of the mesh from its position and orientation, and it tends to make deformations between mesh states more linear and structured.

This thesis sets out to compare NRIC and raw vertex coordinates as inputs for machine learning, in order to determine whether NRIC can be a more beneficial starting point. The comparison is carried out across two tasks, mesh sequence compression through overfitting and latent space extraction with a variational autoencoder, each evaluated on both representations. The architectures are kept as identical as possible between the two inputs, so that any difference can be attributed to the representation itself rather than the application.

The experimental results show that NRIC is not always an improvement over raw vertices. For compression, models trained on NRIC lose quality in their predictions, from errors which are amplified by the reconstruction steps that return the NRIC features to a 3D mesh for evaluation. With latent space learning, however, NRIC shows clear promise, encoding collections of meshes in a more organized manner that usually improves over the standard 3D representation. In both applications, NRIC carries trade-offs, both in the overhead it adds during training and evaluation and in its tendency to benefit only certain types of meshes and settings. NRIC is therefore not the right choice for most applications, but that is not to say it cannot excel in others, where its benefits outweigh the costs. ... Read more

Trees are essential components of both real and digital environments. Therefore, it is important to have 3D models of trees that are of high quality and computationally efficient. One way to achieve this is by compressing a high-quality model using billboard rendering, which involves partitioning the tree into multiple planes to produce a similar result to the original. Our study explores the compression of 3D models using an optimization loop and adapting billboard rendering techniques. We use computer vision primitives to render basic models, which we then optimize by adjusting the texture to resemble the original tree. The models consist of multiple upright planes that are rotated around the central vertical axis of the original tree. We use different optimization functions, such as L1 and L2 losses, to determine the best approach. We can improve the initial models by bounding the billboards and limiting their heights and widths to that of the trees. Additionally, we can use double-sided textures for the billboards to allow more flexibility for optimizing different species of trees. However, optimizing multiple tree types performs differently for each species, leading to improvements that only benefit certain trees in specific scenarios. Using quantitative metrics, we determined which models perform best and how similar they are to the original after training. We found that our compressed models generally resemble the original while having only a fraction of the original size. ... Read more