Solving Zero-Shot 3D Visual Grounding as Constraint Satisfaction Problems

3D visual grounding (3DVG) aims to locate objects in a 3D scene with natural language descriptions. Supervised methods have achieved decent accuracy, but have a closed vocabulary and limited language understanding ability. Zero-shot methods mostly utilize large language models (LLMs) to handle natural language descriptions, yet suffer from slow inference speed. To address these problems, in this work, we propose a zero-shot method that reformulates the 3DVG task as a Constraint Satisfaction Problem (CSP), where the variables and constraints represent objects and their spatial relations, respectively. This allows a global reasoning of all relevant objects, producing grounding results of both the target and anchor objects. Moreover, we demonstrate the flexibility of our framework by handling negation- and counting-based queries with only minor extra coding efforts. Our system, Constraint Satisfaction Visual Grounding (CSVG), has been extensively evaluated on the public datasets ScanRefer and Nr3D datasets using only open-source LLMs. Results show the effectiveness of CSVG and superior grounding accuracy over current state-of-the-art zero-shot 3DVG methods with improvements of $+7.0\%$ (Acc@0.5 score) and $+11.2\%$ on the ScanRefer and Nr3D datasets, respectively. The code of our system is publicly available at https://github.com/sunsleaf/CSVG.