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This thesis focuses on the study of Heterogeneous Networks (HetNets), analyzing the system performance and the allocation of available resources, such as serving BSs, spectrum, power supply and storage. Specifically, four main research focuses are included. The first focus is load balancing problem in HetNets. First, a factor graph model is developed to represent the user association problem and decompose the network-wide objective into local utility functions. Then, a distributed belief propagation (BP) algorithm is proposed to find out the optimal user association. Furthermore, several properties of the factor graph relevant to the performance of the BP algorithm are analyzed using stochastic geometry. The second focus is inter-cell interference in HetNets. To mitigate the inter-cell interference and maximizing the system sum rate, a BP algorithm to jointly optimize the user association, sub-channel assignment and power allocation is proposed. Importantly, a novel factor graph model is developed that not only decomposes the network-wide objective but also transforms the constraints into local functions. The third focus is probabilistic small-cell caching in HetNets, where each SBS caches a subset of the popular content with a specific caching probability. The theoretical results of the successful download probability (SDP) are derived using stochastic geometry theory, i.e., the probability that users can successfully download required content from SBSs. Importantly, I optimize the caching probabilities in two network architectures by maximizing the SDP. The fourth focus is cooperative inter-working of LTE and wireless fidelity (Wi-Fi). A new framework is proposed that considers both systems, downlink and uplink transmissions, and interference in both time and spatial domains. Based on this framework, I theoretically study the performance of a large-scale Wi-Fi network, and the network performance of several inter-working strategies.

Data missing was always when scanning plant organs by using 3D laser scanner, and this could lead to holes appearing in the mesh surface generated from the scanned point cloud. Basing on the analyzing to the geometrical features of different types of plant organs, a hole-filling algorithm was proposed which based on the normal vector of the mesh to make the repair area as close as possible to the original model of the organs mesh. The algorithm firstly extracts the hole boundary in the surface mesh, and compute the positions of new points based on the normal vector and normal curvature of the mesh boundary, then connects the new points and boundary points to generate a new triangular mesh. Experiments on different plant organs of geometric shapes were taken and new triangular mesh qualities were evaluated. Results show that the algorithm can fill holes in several kinds of scanned plant organs mesh quickly and efficiently.