Algorithm to construct integro splines

We study some properties of integro splines. Using these properties, we design an algorithm to construct splines \(S_{m+1}(x)\) of neighbouring degrees to the given spline \(S_{m}(x)\) with degree \(m\). A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs. doi:10.1017/S1446181121000316

Algorithm for constructing a route to pass a narrow fairway

Modern navigation systems often employ the algorithms for plotting lines for the preliminary route construction. The current conditions of technological development imply the simplicity of constructing routes. However, the most important part was and remains the speed of the system that generates the route. The authors of the paper proposed a universal algorithm for constructing a navigation route in narrow channels of the sea. The presented algorithm identifies the middle of the fairway as the safest point at each narrow segment and connects them with track lines. The problem that can arise is smoothing, as the middle of the fairway can shift significantly. To solve this problem, new relative and absolute parameters that characterize plotting of turning points were introduced. In addition, a unified universal formula was proposed for finding the coordinates of these points on a line perpendicular to the current route of the vessel. It was experimentally proved that correctly selected empirical parameters enable the algorithm to quickly construct a route in any navigation area with a relatively low computational complexity. This approach is appropriate for clearly delineated zones of the fairway, and it is compatible with zone methods.

ALGORITHM TO CONSTRUCT INTEGRO SPLINES

We study some properties of integro splines. Using these properties, we design an algorithm to construct splines $S_{m+1}(x)$ of neighbouring degrees to the given spline $S_m(x)$ with degree m. A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs.

Large-scale phase retrieval

High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information. In computational phase imaging, phase retrieval (PR) is required to reconstruct both amplitude and phase in complex space from intensity-only measurements. The existing PR algorithms suffer from the tradeoff among low computational complexity, robustness to measurement noise and strong generalization on different modalities. In this work, we report an efficient large-scale phase retrieval technique termed as LPR. It extends the plug-and-play generalized-alternating-projection framework from real space to nonlinear complex space. The alternating projection solver and enhancing neural network are respectively derived to tackle the measurement formation and statistical prior regularization. This framework compensates the shortcomings of each operator, so as to realize high-fidelity phase retrieval with low computational complexity and strong generalization. We applied the technique for a series of computational phase imaging modalities including coherent diffraction imaging, coded diffraction pattern imaging, and Fourier ptychographic microscopy. Extensive simulations and experiments validate that the technique outperforms the existing PR algorithms with as much as 17dB enhancement on signal-to-noise ratio, and more than one order-of-magnitude increased running efficiency. Besides, we for the first time demonstrate ultra-large-scale phase retrieval at the 8K level ($$7680\times 4320$$ 7680 × 4320 pixels) in minute-level time.

UAV Object Tracking Application Based on Patch Color Group Feature on Embedded System

The discriminative object tracking system for unmanned aerial vehicles (UAVs) is widely used in numerous applications. While an ample amount of research has been carried out in this domain, implementing a low computational cost algorithm on a UAV onboard embedded system is still challenging. To address this issue, we propose a low computational complexity discriminative object tracking system for UAVs approach using the patch color group feature (PCGF) framework in this work. The tracking object is separated into several non-overlapping local image patches then the features are extracted into the PCGFs, which consist of the Gaussian mixture model (GMM). The object location is calculated by the similar PCGFs comparison from the previous frame and current frame. The background PCGFs of the object are removed by four directions feature scanning and dynamic threshold comparison, which improve the performance accuracy. In the terms of speed execution, the proposed algorithm accomplished 32.5 frames per second (FPS) on the x64 CPU platform without a GPU accelerator and 17 FPS in Raspberry Pi 4. Therefore, this work could be considered as a good solution for achieving a low computational complexity PCGF algorithm on a UAV onboard embedded system to improve flight times.