Jiajun Tang

Jiashun Jin, Zheng Tracy Ke, Gabriel Moryoussef et al.

Given a $K$-vertex simplex in a $d$-dimensional space, suppose we measure $n$ points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the $K$ vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

Fan Fei, Jiajun Tang, Fei-Peng Tian et al.

We present PacTure, a novel framework for generating physically-based rendering (PBR) material textures from an untextured 3D mesh, a text description, and an optional image prompt. Early 2D generation-based texturing approaches generate textures sequentially from different views, resulting in long inference times and globally inconsistent textures. More recent approaches adopt multi-view generation with cross-view attention to enhance global consistency, which, however, limits the resolution for each view. In response to these weaknesses, we first introduce view packing, a novel technique that significantly increases the effective resolution for each view during multi-view generation without imposing additional inference cost, by formulating the arrangement of multi-view maps as a 2D rectangle bin packing problem. In contrast to UV mapping, it preserves the spatial proximity essential for image generation and maintains full compatibility with current 2D generative models. To further reduce the inference cost, we enable fine-grained control and multi-domain generation within the next-scale prediction autoregressive framework to create an efficient multi-view multi-domain generative backbone. Extensive experiments show that PacTure outperforms state-of-the-art methods in both quality of generated PBR textures and efficiency in training and inference.