• Utilizing Granger causality to precisely reconstruct biological neuronal networks. • Uncovering the theoretical mechanism ensuring the effective reconstruction. • Demonstraing the adaptability of the method to multiple neural data types. • Showing the effectiveness of reconstruction approach on real experimental data. Accessing to the anatomical connectivity of the cortical network is crucial for understanding the dynamics and functions of the brain. While direct experimental measurements of anatomical connectivity are costly, effective connectivity methods offer a potential alternative approach to reconstructing anatomical connections with the help of statistical tools. Granger causality (GC) is one of the most widely used tools for network effective connection estimations in brain networks. However, whether the effective connectivity estimated by GC can help to reliably capture the information of the underlying anatomical connectivity of neuronal networks remains largely unknown. In this work, we demonstrate that GC can effectively reconstruct the anatomical connectivity of Hodgkin-Huxley (HH) neuronal networks using neuronal voltage time series data across various dynamical regimes. Moreover, we uncover the quantitative mechanisms underlying the accurate reconstruction capabilities of GC. Furthermore, we extend our analysis from HH type point neuronal networks to multi-compartment neuronal networks, and from voltage data to spike-train data. The GC-based reconstruction remains consistently effective across these different scenarios. Finally, we investigate GC-based reconstruction using real experimental data from Allen Institute, demonstrating that GC-reconstructed connectivities exhibit high consistency across different stimulus conditions. Overall, our findings provide a strong theoretical foundation for the use of GC in realistic neuronal network reconstructions.

We present an efficient approach to generating uniformly distributed resampling points of raw 3D point clouds. A key contribution for making such a resampling method both practical and efficient is the construction of the centroidal Voronoi tessellation on the given point cloud efficiently achieved by applying the proposed Anderson-accelerated Lloyd's method. The calculations involved in the method are mainly carried out over a group of locally approximated quadratic surfaces, instead of directly on the given point cloud, providing us a great advantage in filtering out the affection of distribution of original points on output results. Once the resampling points are initialized, the resampling quality can be improved progressively by optimizing resampling points and updating the local approximated surfaces. In addition, by restricting the movement of resampling points, we can deal with unclosed point clouds without any boundary detection. Our approach outperforms existing resampling methods in generating uniform results, and extensive experiments are conducted to demonstrate its efficacy.

Abstract We propose a novel image triangulation method to reduce the complexity of image triangulation under the color error‐bounded constraint and the triangle quality constraint. Meanwhile, we realize a variety of visual effects by supporting different types of triangles (e.g., linear or curved) and color approximation functions (e.g., constant, linear, or quadratic). To adapt to these discontinuous and combinatorial objectives and constraints, we formulate it as a constrained optimization problem that is solved by a series of tailored local remeshing operations. The feasibility and practicability of our method are demonstrated over various types of images, such as organisms, landscapes, portraits and cartoons. Compared to state‐of‐the‐art methods, our method generates far fewer triangles for the same color error or much smaller color errors using the same number of triangles.

Abstract Image triangulation aims to generate an optimal partition with triangular elements to represent the given image. One bottleneck in ensuring approximation quality between the original image and a piecewise approximation over the triangulation is the inaccurate alignment of straight edges to the curved features. In this paper, we propose a novel variational method called curved optimal triangulation, where not all edges are straight segments, but may also be quadratic Bézier curves. The energy function is defined as the total approximation error determined by vertex locations, connectivity and bending of edges. The gradient formulas of this function are derived explicitly in closed form to optimize the energy function efficiently. We test our method on several models to demonstrate its efficacy and ability in preserving features. We also explore its applications in the automatic generation of stylization and Lowpoly images. With the same number of vertices, our curved optimal triangulation method generates more accurate and visually pleasing results compared with previous methods that only use straight segments.

Vector image representation methods that can faithfully reconstruct objects and color variations in a raster image are desired in many practical applications. This article presents triangular configuration B-spline (referred to as TCB-spline)-based vector graphics for raster image vectorization. Based on this new representation, an automatic raster image vectorization paradigm is proposed. The proposed framework first detects sharp curvilinear features in the image and constructs knot meshes based on the detected feature lines. It iteratively optimizes color and position of control points and updates the knot meshes. By using collinear knots at feature lines, both smooth and discontinuous color variations can be efficiently modeled by the same set of quadratic TCB-splines. A variational knot mesh generation method is designed to adaptively introduce knots and update their connectivity to satisfy the local reconstruction quality. Experiments and comparisons show that our framework outperforms the existing state-of-the-art methods in providing more faithful reconstruction results. In particular, our method is able to model undetected features and subtle or complicated color variations in-between features, which the previous methods cannot handle efficiently. Our vectorization representation also facilitates a variety of editing operations performed directly over vector images.