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Fractal dimension Based Shot Transition Detection in Sport Videos

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Journal of Software Engineering and Applications 2011年第4期4卷 235-243页

作者： Efnan Sora Gunal Selcuk Canbek Nihat Adar 不详

Increase in application fields of video has boosted the demand to analyze and organize video libraries for efficient scene analysis and information retrieval. This paper addresses the detection of shot transitions, which plays a crucial role in scene analysis, using a novel method based on fractal dimension (FD) that carries information on roughness of image intensity surface and textural structure. The proposed method is tested on sport videos including soccer and tennis matches that contain considerable amount of abrupt and gradual shot transitions. Experimental results indicate that the FD based shot transition detection method offers promising performance with respect to pixel and histogram based methods available in the literature.

关键词： Scene Analysis Shot Transition Fractal dimension Differential Box Counting

Texture Filters and Fractal dimension on Image Segmentation

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Journal of Signal and Information Processing 2018年第3期9卷 229-238页

作者： Beatriz Marrón Universidad Nacional del Sur Bahía Blanca Argentina

Texture analysis is important in several image segmentation and classification problems. Different image textures manifest themselves by dissimilarity in both the property values and the spatial interrelationships of their component texture primitives. We use this fact in a texture discrimination system. This paper focuses on how to apply texture operators based on co-occurrence matrix, texture filters and fractal dimension to the problem of object recognition and image segmentation.

关键词： Textural Features Co-Occurrence Matrix Texture Spectrum Texture Classification Fractal dimension

Computation of Local Fractal dimension Values of the Human Cerebral Cortex

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Applied Mathematics 2014年第12期5卷 1733-1740页

作者： Richard D. King Center for Alzheimer’s Care Imaging and Research Department of Neurology University of Utah Salt Lake City USA

Objectives: The purpose of this paper is to describe a technique for computing the local fractal dimension of the human cerebral cortex as extracted from high-resolution magnetic resonance imaging scans. Methods: 3D models of the human cerebral cortex were extracted from high resolution magnetic resonance images of 10 healthy adult volunteers using FreeSurfer. The local fractal dimension of the cortex was computed using a custom-written cube-counting algorithm. The effect of constraining the maximum region size on the measured value of local fractal dimension was examined. A proof of principle was demonstrated by comparing an individual with Alzheimer’s disease to a healthy individual. Results: Local values of cortical fractal dimension can be obtained by constraining the size of the region over which the cube counting is performed. Cubic regions of intermediate size (30 × 30 × 30 mm) yielded a profile that demonstrated greater regional variability compared to smaller (15 × 15 × 15 mm) or larger (60 × 60 × 60 mm) region sizes. Conclusions: Local fractal dimension of the cerebral cortex is a novel measure that may yield additional, quantitative insight into the clinical meaning of cortical shape changes.

关键词： Fractal dimension Cortex Imaging Biomarkers Local

The Construction dimension and value Orientation of Contemporary Chinese Discourse on Human Rights

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The Journal of Human Rights 2020年第4期19卷 423-438页

作者：鲁广锦 CHEN Feng China Society for Human Rights Studies 不详

In his 2016 New Year Address,Chinese President Xi Jinping said that"the world is so big and there are so many problems.The international community expects to hear China’s voice and see China’s solutions.China cannot be absent."As China increasingly moves toward the center of the world stage,accelerating the construction of the human rights discourse in contemporary China,speaking out on China’s human rights,and putting forward Chinese solutions for human rights protection have become important and urgent tasks.More so in the face of the major changes occurring worldwide,and the fierce and complex international debate around human rights.

关键词： dimension Human urgent

Studying Relationships between the Fractal dimension of the Drainage Basins and Some of Their Geomorphological Characteristics

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International Journal of Geosciences 2013年第3期4卷 636-642页

作者： Zahra Khanbabaei Amir Karam Ghobad Rostamizad Kharazmi University of Tehran Tehran Iran Watershed Management Sciences and Engineering Natural Resources Faculty Tehran University Tehran Iran

Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.

关键词： Fractal Geometry Fractal dimension Drainage Networks Horton-Strahler

ON THE dimension AND MINIMUM DISTANCE OF BCH CODES OVER GF(q)

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Journal of Electronics(China) 1996年第3期13卷 216-221页

作者： Yue Dianwu Hu Zhengming(Dept. of Information Engineering, Beijing University of Posts & Telecommunications, Beijing 300088)

In this paper, only narrow-sense primitive BCH codes over GF(q) are considered. A formula, that can be used in many cases, is first presented for computing the dimension of BCH codes. It improves the result given by MacWilliams and Sloane in 1977. A new method for finding the dimension of all types of BCH codes is proposed. In second part, it is proved that the BCH bound is the leader of some cyclotomic coset, and we guess that the minimum distance for any BCH code is also the leader of some cyclotomic coset.

关键词： BCH code Cyclotomic coset dimension Minimum distance

Hausdorff dimension and Fractal dimension of the Global Attractor for the Higher-Order Coupled Kirchhoff-Type Equations

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Journal of Applied Mathematics and Physics 2017年第12期5卷 2411-2424页

作者： Guoguang Lin Sanmei Yang Department of Mathematics Yunnan University Kunming China

This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausd... 详细信息

关键词： Higher-Order Coupled Kirchhoff-Type Equations Source Term Hausdorff dimension Fractal dimension Nonlinear Dissipation

The Fracture Density and Fractal dimension Prediction Based on Support Vector Machine

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International Journal of Geosciences 2013年第4期4卷 672-679页

作者： Lei Zhao Liehui Zhang Yilin Wang CNOOC Shanghai Branch Shanghai China State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation of Southwest Petroleum University Chengdu China

The key of effective development for the fractured reservoir is to describe the distribution of the fracture and build the fracture geological model. To acquire more optimal exploration and development of the oilfield, objective geologic model of reservoir fractures is needed for further knowledge of the spatial distribution condition of fractures. Adopting well-logging and seismic techniques can be expensive and usually yield multiple solutions, yet resolution will disturb the seismic method, making it difficult to acquire accurate and sound fracture parameters from seismic data. In this paper, the theoretical foundation for support vector machine, fractal geometry, combined the various information in geology, logging, well core, seism and field outcrop about the fracture and calculate the parameters of the fracture (fracture density and fractal dimension), and the good foundation is established for fractured reservoir description of discrete fracture network model. Based on analysis of conventional prediction methods of development indices and factor influencing the parameters of the fracture, a support vector machine method is established to predict the parameters of the fracture. The new support vector machine method is based on time series analysis to select the kernel function. Trains and tests the support vector machine network with historical data to construct the support vector regression prediction model. A case was fit into the model to test and analyse its reliability, the results suggested that the model had a high prediction performance, and could be well applied to the prediction of fracture parameters.

关键词： Fractured Reservoir Support Vector Machine Fracture Density Fractal dimension MATLAB

Hausdorff dimension of Multi-Layer Neural Networks

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Advances in Pure Mathematics 2013年第9期3卷 9-14页

作者： Jung-Chao Ban Chih-Hung Chang Department of Applied Mathematics Feng Chia University Taichung Taiwan Department of Applied Mathematics National Dong Hwa University Hualien Taiwan

This elucidation investigates the Hausdorff dimension of the output space of multi-layer neural networks. When the factor map from the covering space of the output space to the output space has a synchronizing word, the Hausdorff dimension of the output space relates to its topological entropy. This clarifies the geometrical structure of the output space in more details.

关键词： Multi-Layer Neural Networks Hausdorff dimension Sofic Shift Output Space