Precise 3D environmental mapping with semantics is essential in robotics. Existing methods often rely on pre-defined concepts during training or are time-intensive when generating semantic maps. This paper presents Open-Fusion, an approach for real-time open-vocabulary 3D mapping and queryable scene representation using RGB-D data. Open-Fusion harnesses the power of a pretrained vision-language foundation model (VLFM) for open-set semantic comprehension and employs the Truncated Signed Distance Function (TSDF) for swift 3D scene reconstruction. By leveraging the VLFM, we extract region-based embeddings and their associated confidence maps. These are then integrated with the 3D knowledge from TSDF using an enhanced Hungarian-based feature-matching mechanism. In particular, Open-Fusion delivers outstanding annotation-free 3D segmentation for open vocabulary query without the need for additional 3D training. Benchmark tests on the ScanNet dataset against leading zero-shot methods highlight Open-Fusion’s superiority. Furthermore, it seamlessly combines the strengths of region-based VLFM and TSDF, facilitating real-time 3D scene comprehension that includes object concepts and open-world semantics. We encourage the readers to view the demos on our project page: https://uark-aicv.github.io/OpenFusion

In this paper, we study the Erdös--Falconer distance problem in five dimensions for sets of Cartesian product structures. More precisely, we show that for $A\subset \mathbb{F}_p$ with $|A|\gg p^{\frac{13}{22}}$, then $\Delta(A^5)=\mathbb{F}_p$. When $|A-A|\sim |A|$, we are able to obtain stronger conclusions as follows: łinebreak 1. If $p^{13/22}\ll |A|\ll p^{\frac{2}{3}}$, then $(A-A)^2+A^2+A^2+A^2+A^2=\mathbb{F}_p$. 2. If $p^{4/7}\ll |A|\ll p^{\frac{2}{3}}$, then $(A-A)^2+(A-A)^2+A^2+A^2+A^2+A^2=\mathbb{F}_p$. We also prove that if $p^{4/7}\ll |A-A|=K|A|\le p^{5/8}$, then $|A^2+A^2|\gg \min \{ \frac{p}{K^4}, \frac{|A|^{8/3}}{K^{7/3}p^{2/3}}\}$. As a consequence, $|A^2+A^2|\gg p$ when $|A|\sim p^{5/8}$ and $K\sim 1$, where $A^2=\{x^2: x\in A\}$.

Joining the European Arrowhead Project, which looks forward to a modern collaborative automation, we will present in this positioning paper the irrigation network control problems and corresponding multi-layer approach. The first layer is the hydraulic network, itself represented by a complex model obtained in coupling Shallow Water Equations for free surface flows and Lattice Boltzmann Method to get a tractable model for optimization and supervision purposes. The second layer is the heterogeneous communication network using hybrid architectures and 6LoWPAN, a unified protocol for wired and wireless sensor networks. The third layer is the optimal reactive control system, itself developed using methods from decentralized artificial intelligent systems (namely multi-agent systems). Detailed discussions of each layer with some analytical results will be described in this paper. We will outline the potential interest of the multi-layer approach, more precisely its efficiency and reliability for supervision, energy optimization and hydraulic control of complex water transportation systems.