Morse decompositions have been proposed to compute and represent the topological structure of steady vector fields. Compared to the conventional differential topology, Morse decomposition and the resulting Morse Connection Graph (MCG) is numerically stable. However, the granularity of the original Morse decomposition is constrained by the resolution of the underlying spatial discretization, which typically results in non-smooth representation. In this work, an Image-Space Morse decomposition (ISMD) framework is proposed to address this issue. Compared to the original method, ISMD first projects the original vector field onto an image plane, then computes the Morse decomposition based on the projected field with pixels as the smallest elements. Thus, pixel-level accuracy can be achieved. This ISMD framework has been applied to a number of synthetic and real-world steady vector fields to demonstrate its utility. The performance of the ISMD is carefully studied and reported. Finally, with ISMD an ensemble Morse decomposition can be studied and visualized, which is shown useful for visualizing the stability of the Morse sets with respect to the error introduced in the numerical computation and the perturbation to the input vector fields.
Nuclear energy is a clean and popular form of energy, but leakage and loss of nuclear material pose a threat to public safety. Radiation detection in public spaces is a key part of nuclear security. Common security cameras equipped with complementary metal oxide semiconductor (CMOS) sensors can help with radiation detection. Previous work with these cameras, however, required slow, complex frame-by-frame processing. Building on the previous work, we propose a nuclear radiation detection method using convolution neural networks (CNNs). This method detects nuclear radiation in changing images with much less computational complexity. Using actual video images captured in the presence of a common Tc-99m radioactive source, we construct training and testing sets. After training the CNN and processing our test set, the experimental results show the high performance and effectiveness of our method.
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