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Keywords = Smale space

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22 pages, 4894 KB  
Article
SMALE: Hyperspectral Image Classification via Superpixels and Manifold Learning
by Nannan Liao, Jianglei Gong, Wenxing Li, Cheng Li, Chaoyan Zhang and Baolong Guo
Remote Sens. 2024, 16(18), 3442; https://doi.org/10.3390/rs16183442 - 17 Sep 2024
Cited by 2 | Viewed by 1408
Abstract
As an extremely efficient preprocessing tool, superpixels have become more and more popular in various computer vision tasks. Nevertheless, there are still several drawbacks in the application of hyperspectral image (HSl) processing. Firstly, it is difficult to directly apply superpixels because of the [...] Read more.
As an extremely efficient preprocessing tool, superpixels have become more and more popular in various computer vision tasks. Nevertheless, there are still several drawbacks in the application of hyperspectral image (HSl) processing. Firstly, it is difficult to directly apply superpixels because of the high dimension of HSl information. Secondly, existing superpixel algorithms cannot accurately classify the HSl objects due to multi-scale feature categorization. For the processing of high-dimensional problems, we use the principle of PCA to extract three principal components from numerous bands to form three-channel images. In this paper, a novel superpixel algorithm called Seed Extend by Entropy Density (SEED) is proposed to alleviate the seed point redundancy caused by the diversified content of HSl. It also focuses on breaking the dilemma of manually setting the number of superpixels to overcome the difficulty of classification imprecision caused by multi-scale targets. Next, a space–spectrum constraint model, termed Hyperspectral Image Classification via superpixels and manifold learning (SMALE), is designed, which integrates the proposed SEED to generate a dimensionality reduction framework. By making full use of spatial context information in the process of unsupervised dimension reduction, it could effectively improve the performance of HSl classification. Experimental results show that the proposed SEED could effectively promote the classification accuracy of HSI. Meanwhile, the integrated SMALE model outperforms existing algorithms on public datasets in terms of several quantitative metrics. Full article
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16 pages, 278 KB  
Article
Self-Similar Inverse Semigroups from Wieler Solenoids
by Inhyeop Yi
Mathematics 2020, 8(2), 266; https://doi.org/10.3390/math8020266 - 17 Feb 2020
Viewed by 1935
Abstract
Wieler showed that every irreducible Smale space with totally disconnected local stable sets is an inverse limit system, called a Wieler solenoid. We study self-similar inverse semigroups defined by s-resolving factor maps of Wieler solenoids. We show that the groupoids of germs [...] Read more.
Wieler showed that every irreducible Smale space with totally disconnected local stable sets is an inverse limit system, called a Wieler solenoid. We study self-similar inverse semigroups defined by s-resolving factor maps of Wieler solenoids. We show that the groupoids of germs and the tight groupoids of these inverse semigroups are equivalent to the unstable groupoids of Wieler solenoids. We also show that the C -algebras of the groupoids of germs have a unique tracial state. Full article
(This article belongs to the Special Issue Operator Algebras)
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