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Spherical trigonometry formulae are widely adopted to solve various navigation problems. However, these formulae only express the relationships between the sides and angles of a single spherical triangle. In fact, many problems may involve different types of spherical shapes. If we can develop the different formulae for specific spherical shapes, it will help us solve these problems directly. Thus, we propose two types of formulae for combined spherical triangles. The first set are the formulae of the divided spherical triangle, and the second set are the formulae of the spherical quadrilateral. By applying the formulae of the divided spherical triangle, waypoints on a great circle track can be obtained directly without finding the initial great circle course angle in advance. By applying the formulae of the spherical quadrilateral, the astronomical vessel position can be yielded directly from two celestial bodies, and the calculation process concept is easier to comprehend. The formulae we propose can not only be directly used to solve corresponding problems, but also expand the spherical trigonometry research field. [ABSTRACT FROM AUTHOR]

Conventional visual ship tracking methods employ single and shallow features for the ship tracking task, which may fail when a ship presents a different appearance and shape in maritime surveillance videos. To overcome this difficulty, we propose to employ a multi-view learning algorithm to extract a highly coupled and robust ship descriptor from multiple distinct ship feature sets. First, we explore multiple distinct ship feature sets consisting of a Laplacian-of-Gaussian (LoG) descriptor, a Local Binary Patterns (LBP) descriptor, a Gabor filter, a Histogram of Oriented Gradients (HOG) descriptor and a Canny descriptor, which present geometry structure, texture and contour information, and more. Then, we propose a framework for integrating a multi-view learning algorithm and a sparse representation method to track ships efficiently and effectively. Finally, our framework is evaluated in four typical maritime surveillance scenarios. The experimental results show that the proposed framework outperforms the conventional and typical ship tracking methods. [ABSTRACT FROM AUTHOR]