Kuankuan Cheng | Searcharxiv

arXiv2026

SemEllipsoid: Semantic-aware Shape Abstraction with Ellipsoid

Representing 3D shapes using a set of primitives - known as shape abstraction - is an actively studied problem in computer graphics with wide applications in shape understanding, analysis, and simulation due to the compactness and computational efficiency of the primitive-based representation. Prior work has primarily focused on geometry-aware shape abstraction, where the objective is to approximate the input shape with a minimal set of primitives while preserving geometric fidelity. However, these methods often overlook semantic consistency, inevitably leading to primitives that span across multiple semantic parts. Such inconsistency can cause undesirable artifacts in downstream tasks such as part-level shape editing or manipulation. In this paper, we introduce a new task - semantic-aware shape abstraction, where the goal is to produce abstractions that are both geometrically faithful and semantically consistent, ensuring that each primitive adheres strictly to a single semantic part without crossing semantic boundaries. We propose SemEllipsoid, a novel method to address this problem using ellipsoidal primitives. The core idea is to inject semantic constraints into the primitive optimization process leveraging the availability of semantic cues from large-scale foundation models. We design a fully differentiable projection-blending-evaluation scheme to measure semantic divergence against input semantic masks, and formulate an alternating optimization strategy to iteratively solve for optimal semantic assignment and primitive configurations. Our method is non-learning-based, requiring no data collection or network training, and generalizes well to shapes from arbitrary categories. It also supports different levels of abstraction according to user demand. Extensive experiments and evaluations validate the effectiveness of our approach across several 3D shape collections.

cs.GR↗

arXiv2023

Fast Gumbel-Max Sketch and its Applications

The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a non-negative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element $i$ in proportion to its positive weight $v_i$, the Gumbel-Max Trick first computes a Gumbel random variable $g_i$ for each positive weight element $i$, and then samples the element $i$ with the largest value of $g_i+\ln v_i$. Recently, applications including similarity estimation and weighted cardinality estimation require to generate $k$ independent Gumbel-Max variables from high dimensional vectors. However, it is computationally expensive for a large $k$ (e.g., hundreds or even thousands) when using the traditional Gumbel-Max Trick. To solve this problem, we propose a novel algorithm, FastGM, which reduces the time complexity from $O(kn^+)$ to $O(k \ln k + n^+)$, where $n^+$ is the number of positive elements in the vector of interest. FastGM stops the procedure of Gumbel random variables computing for many elements, especially for those with small weights. We perform experiments on a variety of real-world datasets and the experimental results demonstrate that FastGM is orders of magnitude faster than state-of-the-art methods without sacrificing accuracy or incurring additional expenses.

cs.LG↗