It is often a difficult task to accurately segment brain magnetic resonance (MR) images with intensity in-homogeneity and noise. This paper introduces a novel level set method for simultaneous brain MR image segmentation and intensity inhomogeneity correction. To reduce the effect of noise, novel anisotropic spatial information, which can preserve more details of edges and corners, is proposed by incorporating the inner relationships among the neighbor pixels. Then the proposed energy function uses the multivariate Student's t-distribution to fit the distribution of the intensities of each tissue. Furthermore, the proposed model utilizes Hidden Markov random fields to model the spatial correlation between neigh-boring pixels/voxels. The means of the multivariate Student's t-distribution can be adaptively estimated by multiplying a bias field to reduce the effect of intensity inhomogeneity. In the end, we reconstructed the energy function to be convex and calculated it by using the Split Bregman method, which allows our framework for random initialization, thereby allowing fully automated applications. Our method can obtain the final result in less than 1 second for 2D image with size 256 × 256 and less than 300 seconds for 3D image with size 256 × 256 × 171. The proposed method was compared to other state-of-the-art segmentation methods using both synthetic and clinical brain MR images and increased the accuracies of the results more than 3%.

Terrain plays an important role in the formation, development and distribution of local precipitation and is a major factor leading to locally abnormal weather in weather systems. Although small-scale topography has little influence on the spatial distribution of precipitation, it interferes with precipitation fitting. Due to the arbitrary combination of small, medium and large-scale terrain, complex terrain distribution is formed, and small-scale terrain cannot be clearly defined and removed. Based on the idea of bidimensional empirical mode decomposition (BEMD), this paper extracts small-scale terrain data layer by layer to smooth the terrain and constructs a macroterrain model for different scales in Central China. Based on the precipitation distribution model using multiple regression, precipitation models (B0, B1, B2 and B3) of different scales are constructed. The 18-year monthly average precipitation data of each station are compared with the precipitation simulation results under different scales of terrain and TRMM precipitation data, and the influence of different levels of small-scale terrain on the precipitation distribution is analysed. The results show that (1) in Central China, the accuracy of model B2 is much higher than that of TRMM model A and monthly precipitation model B0. The comprehensive evaluation indexes are increased by 3.31% and 1.92%, respectively. (2) The influence of different levels of small-scale terrain on the precipitation distribution is different. The first- and second-order small-scale terrain has interference effects on precipitation fitting, and the third-order small-scale terrain has an enhancement effect on precipitation. However, the effect of small-scale topography on the precipitation distribution is generally reflected as interference.

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