Solving the generalized Sylvester matrix equation AV +BW = VF via Kronecker map

This note considers the solution to the generalized Sylvester matrix equation AV ＋ BW = VF with F being an arbitrary matrix, where V and W are the matrices to be determined. With the help of the Kronecker map, an explicit parametric solution to this matrix equation is established. The proposed solution possesses a very simple and neat form, and allows the matrix F to be undetermined.     

Real-time building of a thinning-based topological map

An accurate and compact map is essential to an autonomous mobile robot system. A topological map, one of the most popular map types, can be used to represent the environment in terms of discrete nodes with edges connecting them. It is usually constructed by Voronoi-like graphs, but in this paper the topological map is incrementally built based on the local grid map by using a thinning algorithm. This algorithm, when combined with the application of the C-obstacle, can easily extract only the meaningful topological information in real-time and is robust to environment change, because this map is extracted from a local grid map generated based on the Bayesian update formula. In this paper, position probability is defined to evaluate the quantitative reliability of the end node extracted by the thinning process. Since the thinning process builds only local topological maps, a global topological map should be constructed by merging local topological maps according to nodes with high position probability. For real and complex environments, experiments showed that the proposed map building method based on the thinning process can accurately build a local topological map in real-time, with which an accurate global topological map can be incrementally constructed.     

A wavelet-VQ system for real-time video compression

This paper presents a scheme and its Field Programmable Gate Array (FPGA) implementation for a system based on combining the bi-dimensional discrete wavelet transformation (2D-DWT) and vector quantization (VQ) for image compression. The 2D-DWT works in a non-separable fashion using a parallel filter structure with distributed control to compute two resolution levels. The wavelet coefficients of the higher frequency sub-bands are vector quantized using multi-resolution codebook and those of the lower frequency sub-band at level two are scalar quantized and entropy encoded. VQ is carried out by self organizing feature map (SOFM) neural nets working at the recall phase. Codebooks are quickly generated off-line using the same nets functioning at the training phase. The complete system, including the 2D-DWT, the multi-resolution codebook VQ, and the statistical encoder, was implemented on a Xilinx Virtex 4 FPGA and is capable of performing real-time compression for digital video when dealing with grayscale 512 × 512 pixels images. It offers high compression quality (PSNR values around 35 dB) and acceptable compression rate values (0.62 bpp).

Predicting dam failure risk for sustainable flood retention basins: A generic case study for the wider Greater Manchester area

This study aims to provide a rapid screening tool for assessment of sustainable flood retention basins (SFRBs) to predict corresponding dam failure risks. A rapid expert-based assessment method for dam failure of SFRB supported by an artificial neural network (ANN) model has been presented. Flood storage was assessed for 110 SFRB and the corresponding Dam Failure Risk was evaluated for all dams across the wider Greater Manchester study area. The results show that Dam Failure Risk can be estimated by using the variables Dam Height, Dam Length, Maximum Flood Water Volume, Flood Water Surface Area, Mean Annual Rainfall (based on Met Office data), Altitude, Catchment Size, Urban Catchment Proportion, Forest Catchment Proportion and Managed Maximum Flood Water Volume. A cross-validation R² value of 0.70 for the ANN model signifies that the tool is likely to predict variables well for new data sets. Traditionally, dams are considered safe because they have been built according to high technical standards. However, many dams that were constructed decades ago do not meet the current state-of-the-art dam design guidelines. Spatial distribution maps show that dam failure risks of SFRB located near cities are higher than those situated in rural locations. The proposed tool could be used as an early warning system in times of heavy rainfall.     

A note on a problem on ω-limit sets of N–dimensional skew-product maps

In 2003, Balibrea et al. stated the problem of finding a skew-product map G on 𝕀³ holding ω _G ={0}×𝕀²=ω _G (x, y, z) for any (x, y, z)∈𝕀³, x≠0. We present a method for constructing skew-product maps F on 𝕀 ⁿ⁺¹ holding ω _F ={0}×𝕀 ⁿ =ω _F (x ₁, x ₂, …, x _n+1), (x ₁, x ₂, …, x _n+1)∈𝕀 ⁿ⁺¹, x ₁≠0.     

三角代数上的Jordan三重初等映射的可加性

主要研究了三角代数上的Jordan三重初等映射的可加性,给出了一个保证Jor-dan三重初等映射满足可加性的充分条件。     

一种改善Tent混沌序列随机性的方法

Tent混沌映射具有良好的遍历性和均匀性,但其随机性不理想。为此,提出一种改善Tent混沌序列随机性的方法。通过将Tent混沌映射变换为分段混沌映射,增大Lyapunov指数,改善相关系数和功率谱特性。对序列进行NIST随机性测试,结果表明,该分段Tent映射的序列具有较好的随机性,适用于通信与信息安全领域。     

一种基于相对海明距离的地图复杂性度量

提出一种适用于分层路径搜索算法的地图复杂性度量方法。针对不同规模的地图,将其实际复杂度与可达到的最大复杂度之比作为相对复杂度,提出基于相对海明距离的度量方法,并引入地图区域间方差,从而更好地计算障碍物分布不均匀地图的复杂度。实验结果证明,该方法能准确地反映不同规模与障碍物分布不均的地图复杂程度,并与HPA*算法的搜索效率有较强关联性。     

基于显著图的SIFT特征检测与匹配

基于尺度不变特征变换(SIFT)特征的图像匹配存在特征点数量大、运算时间长等问题。为此,引入视觉注意机制,提出一种基于显著图的SIFT特征检测与匹配方法。比较常用的显著图计算模型,选择谱残差方法提取图片的显著图。对显著图进行二值化和形态学等处理,得到规则合理的显著区域。在显著区域内提取SIFT特征,生成特征向量,进行图像匹配。实验结果表明,该方法能提高运算效率,并且得到的SIFT特征更加稳定。