经典教材：朴素李理论_Stillwell

Naive Lie Theory John Stillwell It seems to have been decided that undergraduate mathematics today rests on two foundations: calculus and linear algebra. These may not be the best foundations for, say, number theory or combinatorics, but they serve quite well for undergraduate analysis and several varieties of undergraduate algebra and geometry. The really perfect sequel to calculus and linear algebra, however, would be a blend of the two—a subject in which calculus throws light on linear algebra and vice versa. Look no further! This perfect blend of calculus and linear algebra is Lie theory (named to honor the Norwegian mathematician Sophus Lie—pronounced “Lee ”). So why is Lie theory not a standard undergraduate topic?

semantic human matting

阿里 acm2018论文 Semantic Human Matting Human maŠing, high quality extraction of humans from natural images, is crucial for a wide variety of applications. Since the maŠing problem is severely under-constrained, most previous methods require user interactions to take user designated trimaps or scribbles as constraints. Œis user-in-the-loop nature makes them dicult to be applied to large scale data or time-sensitive scenarios. In this paper, instead of using explicit user input constraints, we employ implicit semantic constraints learned from data and propose an automatic human maŠing algorithm Semantic Human Maˆing (SHM). SHM is the €rst algorithm that learns to jointly €t both semantic information and high quality details with deep networks. In practice, simultaneously learning both coarse semantics and €ne details is challenging. We propose a novel fusion strategy which naturally gives a probabilistic estimation of the alpha maŠe. We also construct a very large dataset with high quality annotations consisting of 35,513 unique foregrounds to facilitate the learning and evaluation of human maŠing. Extensive experiments on this dataset and plenty of real images show that SHM achieves comparable results with state-of-the-art interactive matting methods.