A Parallel Differential Box-Counting Algorithm Applied to Hyperspectral Image Classification

Tzeng, Y.C.; Fan, Kuo-Tai; Chen, Kun-Shan

doi:10.1109/lgrs.2011.2166243

Cited by 19 publications

(2 citation statements)

References 16 publications

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“…Recently, the fractal theory has been used in the application of remotely sensed data of high-spatial resolution to solve the problems including the analysis of the scaling difference quantitative remote sensing products [10], the segmentation and classification of remote sensing imagery [29], and target detection [30]. 'Fractal' is characterized by the fine structure, the anomalous shape and the self-similarity [21,26].…”

Section: The Calculation Of Multi-fractal Spectrum and Parametersmentioning

confidence: 99%

A novel logistic multi-class supervised classification model based on multi-fractal spectrum parameters for hyperspectral data

Zhao

Huang

et al. 2014

International Journal of Computer Mathematics

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A novel logistic multi-class supervised classification model based on multi-fractal spectrum parameters is proposed to avoid the error that is caused by the difference between the real data distribution and the hypothetic Gaussian distribution and avoid the computational burden working in the logistic regression classification directly for hyperspectral data. The multi-fractal spectra and parameters are calculated firstly with training samples along the spectral dimension of hyperspectral data. Secondly, the logistic regression model is employed in our work because the logistic regression classification model is a distribution-free nonlinear model which is based on the conditional probability without the Gaussian distribution assumption of the random variables, and the obtained multi-fractal parameters are applied to establish the multi-class logistic regression classification model. Finally, the Newton-Raphson method is applied to estimate the model parameters via the maximum likelihood algorithm. The classification results of the proposed model are compared with the logistic regression classification model based on an adaptive bands selection method by using theAirborne Visible/Infrared Imaging Spectrometer and airborne Push Hyperspectral Imager data. The results illuminate that the proposed approach achieves better accuracy with lower computational cost simultaneously.

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Section: The Calculation Of Multi-fractal Spectrum and Parametersmentioning

confidence: 99%

A novel logistic multi-class supervised classification model based on multi-fractal spectrum parameters for hyperspectral data

Zhao

Huang

et al. 2014

International Journal of Computer Mathematics

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“…GMST is a global method which does not require estimating the multivariate density of the dataset, but the drawback of GMST is the restriction to isometric embeddings. Fractal dimension [20,21] is a statistical index of complexity of a dataset, which is commonly calculated by box-counting method [22][23][24] and CD method [25,26].…”

Section: Introductionmentioning

confidence: 99%

Dimension Estimation Using Weighted Correlation Dimension Method

Liu

Zhang

et al. 2015

Discrete Dynamics in Nature and Society

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Dimension reduction is an important tool for feature extraction and has been widely used in many fields including image processing, discrete-time systems, and fault diagnosis. As a key parameter of the dimension reduction, intrinsic dimension represents the smallest number of variables which is used to describe a complete dataset. Among all the dimension estimation methods, correlation dimension (CD) method is one of the most popular ones, which always assumes that the effect of every point on the intrinsic dimension estimation is identical. However, it is different when the distribution of a dataset is nonuniform. Intrinsic dimension estimated by the high density area is more reliable than the ones estimated by the low density or boundary area. In this paper, a novel weighted correlation dimension (WCD) approach is proposed. The vertex degree of an undirected graph is invoked to measure the contribution of each point to the intrinsic dimension estimation. In order to improve the adaptability of WCD estimation,k-means clustering algorithm is adopted to adaptively select the linear portion of the log-log sequence(log⁡δk,log⁡C(n,δk)). Various factors that affect the performance of WCD are studied. Experiments on synthetic and real datasets show the validity and the advantages of the development of technique.

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