Search

We introduce Coverage Axis++, a novel and efficient approach to 3D shape skeletonization. The current state-of-the-art approaches for this task often rely on the watertightness of the input or suffer from substantial computational costs, thereby limiting their practicality. To address this challenge, Coverage Axis++ proposes a heuristic algorithm to select skeletal points, offering a high-accuracy approximation of the Medial Axis Transform (MAT) while significantly mitigating computational intensity for various shape representations. We introduce a simple yet effective strategy that considers shape coverage, uniformity, and centrality to derive skeletal points. The selection procedure enforces consistency with the shape structure while favoring the dominant medial balls, which thus introduces a compact underlying shape representation in terms of MAT. As a result, Coverage Axis++ allows for skeletonization for various shape representations (e.g., water-tight meshes, triangle soups, point clouds), specification of the number of skeletal points, few hyperparameters, and highly efficient computation with improved reconstruction accuracy. Extensive experiments across a wide range of 3D shapes validate the efficiency and effectiveness of Coverage Axis++. Our codes are available at https://github.com/Frank-ZY-Dou/Coverage_Axis., Comment: SGP2024. Project Page: https://frank-zy-dou.github.io/projects/CoverageAxis++/index.html

With the increasing deployment of agricultural robots, the traditional manual spray of liquid fertilizer and pesticide is gradually being replaced by agricultural robots. For robotic precision spray application in vegetable farms, accurate plant phenotyping through instance segmentation and robust plant tracking are of great importance and a prerequisite for the following spray action. Regarding the robust tracking of vegetable plants, to solve the challenging problem of associating vegetables with similar color and texture in consecutive images, in this paper, a novel method of Multiple Object Tracking and Segmentation (MOTS) is proposed for instance segmentation and tracking of multiple vegetable plants. In our approach, contour and blob features are extracted to describe unique feature of each individual vegetable, and associate the same vegetables in different images. By assigning a unique ID for each vegetable, it ensures the robot to spray each vegetable exactly once, while traversing along the farm rows. Comprehensive experiments including ablation studies are conducted, which prove its superior performance over two State-Of-The-Art (SOTA) MOTS methods. Compared to the conventional MOTS methods, the proposed method is able to re-identify objects which have gone out of the camera field of view and re-appear again using the proposed data association strategy, which is important to ensure each vegetable be sprayed only once when the robot travels back and forth. Although the method is tested on lettuce farm, it can be applied to other similar vegetables such as broccoli and canola. Both code and the dataset of this paper is publicly released for the benefit of the community: https://github.com/NanH5837/LettuceMOTS.

We consider the Cauchy problem for the complex valued semi-linear heat equation $$ \partial_t u - \Delta u - u^m =0, \ \ u (0,x) = u_0(x), $$ where $m\geq 2$ is an integer and the initial data belong to super-critical spaces $E^s_\sigma$ for which the norms are defined by $$ \|f\|_{E^s_\sigma} = \|\langle \xi\rangle^\sigma 2^{s|\xi|}\hat{f}(\xi)\|_{L^2}, \ \ \sigma \in \mathbb{R}, \ s<0. $$ If $s<0$, then any Sobolev space $H^{r}$ is a subspace of $E^s_\sigma$, i.e., $\cup_{r \in \mathbb{R}} H^r \subset E^s_\sigma$. We obtain the global existence and uniqueness of the solutions if the initial data belong to $E^s_\sigma$ ($s<0, \ \sigma \geq d/2-2/(m-1)$) and their Fourier transforms are supported in the first octant, the smallness conditions on the initial data in $E^s_\sigma$ are not required for the global solutions. Moreover, we show that the error between the solution $u$ and the iteration solution $u^{(j)}$ is $C^j/(j\,!)^2$. Similar results also hold if the nonlinearity $u^m$ is replaced by an exponential function $e^u-1$., Comment: 37 Pages

Universal sensing the motion of mechanical resonators with high precision and low back-action is of paramount importance in ultra-weak signal detection which plays a fundamental role in modern physics. Here we present a universal scheme that transfer mechanically the motion of the resonator not directly measurable to the one can be precisely measured using mechanical frequency conversion. Demonstration of the scheme at room temperature shows that both the motion imprecision and the back-action force are below the intrinsic level of the objective resonator, which agree well with our theoretical prediction. The scheme developed here provides an effective interface between an arbitrary mechanical resonator and a high quantum efficient displacement sensor, and is expected to find extensive applications in high-demanding mechanical-based force measurements., Comment: 4 pages, 4 figures