Certain Curvature Conditions on P-Sasakian Manifolds Admitting a Quater-Symmetric Metric Connection

The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition Z(ξ,Y)·S=0,where Z,S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.

Automatic sub-pixel coastline extraction based on spectral mixture analysis using EO-1 Hyperion data

Many megacities (such as Shanghai) are located in coastal areas, therefore, coastline monitoring is critical for urban security and urban development sustainability. A shoreline is defined as the intersection between coastal land and a water surface and features seawater edge movements as tides rise and fall. Remote sensing techniques have increasingly been used for coastline extraction;however, traditional hard classification methods are performed only at the pixel-level and extracting subpixel accuracy using soft classification methods is both challenging and time consuming due to the complex features in coastal regions. This paper presents an automatic sub-pixel coastline extraction method (ASPCE) from high-spectral satellite imaging that performs coastline extraction based on spectral mixture analysis and, thus, achieves higher accuracy. The ASPCE method consists of three main components: 1) A Water-Vegetation-Impervious-Soil (W-V-I-S) model is first presented to detect mixed W-V-I-S pixels and determine the endmember spectra in coastal regions;2) The linear spectral mixture unmixing technique based on Fully Constrained Least Squares (FCLS) is applied to the mixed W-V-I-S pixels to estimate seawater abundance;and 3) The spatial attraction model is used to extract the coastline. We tested this new method using EO-1 images from three coastal regions in China: the South China Sea, the East China Sea, and the Bohai Sea. The results showed that the method is accurate and robust. Root mean square error (RMSE) was utilized to evaluate the accuracy by calculating the distance differences between the extracted coastline and the digitized coastline. The classifier’s performance was compared with that of the Multiple Endmember Spectral Mixture Analysis (MESMA), Mixture Tuned Matched Filtering (MTMF), Sequential Maximum Angle Convex Cone (SMACC), Constrained Energy Minimization (CEM), and one classical Normalized Difference Water Index (NDWI). The results from the three test sites indicated that the proposed ASPCE method extracted coastlines more efficiently than did the compared methods, and its coastline extraction accuracy corresponded closely to the digitized coastline, with 0.39 pixels, 0.40 pixels, and 0.35 pixels in the three test regions, showing that the ASPCE method achieves an accuracy below 12.0 m (0.40 pixels). Moreover, in the quantitative accuracy assessment for the three test sites, the ASPCE method shows the best performance in coastline extraction, achieving a 0.35 pixel-level at the Bohai Sea, China test site. Therefore, the proposed ASPCE method can extract coastline more accurately than can the hard classification methods or other spectral unmixing methods.