Partitioning of complex scenes of geometric objects

Author(s):  
H. Noltemeier ◽  
T. Roos ◽  
C. Zirkelbach

2010 ◽  
Author(s):  
Maura C. Lohrenz ◽  
Melissa R. Beck
Keyword(s):  


Author(s):  
O. M. Korchazhkina

The article presents a methodological approach to studying iterative processes in the school course of geometry, by the example of constructing a Koch snowflake fractal curve and calculating a few characteristics of it. The interactive creative environment 1C:MathKit is chosen to visualize the method discussed. By performing repetitive constructions and algebraic calculations using ICT tools, students acquire a steady skill of work with geometric objects of various levels of complexity, comprehend the possibilities of mathematical interpretation of iterative processes in practice, and learn how to understand the dialectical unity between finite and infinite parameters of flat geometric figures. When students are getting familiar with such contradictory concepts and categories, that replenishes their experience of worldview comprehension of the subject areas they study through the concept of “big ideas”. The latter allows them to take a fresh look at the processes in the world around. The article is a matter of interest to schoolteachers of computer science and mathematics, as well as university scholars who teach the course “Concepts of modern natural sciences”.



2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.



Author(s):  
Tingchao Shi ◽  
Mingyong Liu ◽  
Yang Yang ◽  
Sainan Li ◽  
Peixin Wang ◽  
...  


Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1643
Author(s):  
Ming Liu ◽  
Shichao Chen ◽  
Fugang Lu ◽  
Mengdao Xing ◽  
Jingbiao Wei

For target detection in complex scenes of synthetic aperture radar (SAR) images, the false alarms in the land areas are hard to eliminate, especially for the ones near the coastline. Focusing on the problem, an algorithm based on the fusion of multiscale superpixel segmentations is proposed in this paper. Firstly, the SAR images are partitioned by using different scales of superpixel segmentation. For the superpixels in each scale, the land-sea segmentation is achieved by judging their statistical properties. Then, the land-sea segmentation results obtained in each scale are combined with the result of the constant false alarm rate (CFAR) detector to eliminate the false alarms located on the land areas of the SAR image. In the end, to enhance the robustness of the proposed algorithm, the detection results obtained in different scales are fused together to realize the final target detection. Experimental results on real SAR images have verified the effectiveness of the proposed algorithm.



Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1240
Author(s):  
Yang Liu ◽  
Hailong Su ◽  
Cao Zeng ◽  
Xiaoli Li

In complex scenes, it is a huge challenge to accurately detect motion-blurred, tiny, and dense objects in the thermal infrared images. To solve this problem, robust thermal infrared vehicle and pedestrian detection method is proposed in this paper. An important weight parameter β is first proposed to reconstruct the loss function of the feature selective anchor-free (FSAF) module in its online feature selection process, and the FSAF module is optimized to enhance the detection performance of motion-blurred objects. The proposal of parameter β provides an effective solution to the challenge of motion-blurred object detection. Then, the optimized anchor-free branches of the FSAF module are plugged into the YOLOv3 single-shot detector and work jointly with the anchor-based branches of the YOLOv3 detector in both training and inference, which efficiently improves the detection precision of the detector for tiny and dense objects. Experimental results show that the method proposed is superior to other typical thermal infrared vehicle and pedestrian detection algorithms due to 72.2% mean average precision (mAP).



Author(s):  
Felicitas Pielsticker ◽  
Ingo Witzke ◽  
Amelie Vogler

AbstractDigital media have become increasingly important in recent years and can offer new possibilities for mathematics education in elementary schools. From our point of view, geometry and geometric objects seem to be suitable for the use of computer-aided design software in mathematics classes. Based on the example of Tinkercad, the use of CAD software — a new and challenging context in elementary schools — is discussed within the approach of domains of subjective experience and the Toulmin model. An empirical study examined the influence of Tinkercad on fourth-graders’ development of a model of a geometric solid and related reasoning processes in mathematics classes.



IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Chen Baoyuan ◽  
Liu Yitong ◽  
Sun Kun




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