Spatial scaling transformation modeling based on fractal theory for the leaf area index retrieved from remote sensing imagery

Wu, Ling; Liu, Xiangnan; Zheng, Xiaopo; Qin, Qiming; Ren, Huazhong; Sun, Yuanheng

doi:10.1117/1.jrs.9.096015

Cited by 13 publications

(7 citation statements)

References 20 publications

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“…Fractals and multifractals provide a suitable way of describing the scale-independence of Earth science variables (e.g., topography (Pradhan et al, 2010) and climate variables (Deidda, 2000)). In particular, many fractal and multifractal methods have been used to scale leaf area index (Jiang et al, 2015;Wu et al, 2015), and downscale satellite-based remote sensing rainfall data (Espinosa et al, 2017;Tao and Barros, 2010). Unlike the above fractal methods, several scale-independent properties have been used in scaling.…”

Section: Scaling Based On Scale-independent Variationmentioning

confidence: 99%

Principles and methods of scaling geospatial Earth science data

Jin

Stein

et al. 2019

Earth-Science Reviews

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The properties of geographical phenomena vary with changes in the scale of measurement. The information observed at one scale often cannot be directly used as information at another scale. Scaling addresses these changes in properties in relation to the scale of measurement, and plays an important role in Earth sciences by providing information at the scale of interest, which may be required for a range of applications, and may be useful for inferring geographical patterns and processes. This paper presents a review of geospatial scaling methods for Earth science data. Based on spatial properties, we propose a methodological framework for scaling addressing upscaling, downscaling and side-scaling. This framework combines scale-independent and scale-dependent properties of geographical variables. It allows treatment of the varying spatial heterogeneity of geographical phenomena, combines spatial autocorrelation and heterogeneity, addresses scale-independent and scale-dependent factors, explores changes in information, incorporates geospatial Earth surface processes and uncertainties, and identifies the optimal scale(s) of models. This study shows that the classification of scaling methods according to various heterogeneities has great potential utility as an underpinning conceptual basis for advances in many Earth science research domains.

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Section: Scaling Based On Scale-independent Variationmentioning

confidence: 99%

Principles and methods of scaling geospatial Earth science data

Jin

Stein

et al. 2019

Earth-Science Reviews

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“…2018, 10, x FOR PEER REVIEW 3 of 20 not be applied to scaling effect correction. Subsequently, an image-based LAI scaling transfer model was established [40], which could only correct the scaling bias of the entire image. With extension from the image-based method, Wu et al [41] developed a pixel-based model based on the Fractal Theory (FT) to correct the LAI scaling effect.…”

Section: Principle Of Scaling Effectmentioning

confidence: 99%

“…Zhang et al [12] defined the information fractal of quantitative remote sensing products to describe the scaling transformation law of LAIs on different scales, but it could not be applied to scaling effect correction. Subsequently, an image-based LAI scaling transfer model was established [40], which could only correct the scaling bias of the entire image. With extension from the image-based method, Wu et al [41] developed a pixel-based model based on the Fractal Theory (FT) to correct the LAI scaling effect.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Three Techniques for Correcting the Spatial Scaling Bias of Leaf Area Index

Jiang

Yao

et al. 2018

Remote Sensing

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Abstract:The correction of spatial scaling bias on the estimate of leaf area index (LAI) retrieved from remotely sensed data is an essential issue in quantitative remote sensing for vegetation monitoring. We analyzed three techniques, including Taylor's theorem (TT), Wavelet-Fractal technique (WF), and Fractal theory (FT), for correcting the scaling bias of LAI with empirical models in different functions (i.e., power, exponential, logarithmic and polynomial) on both simulated data and a real dataset over a cropland site. The results demonstrated that the scaling bias became greater when the model non-linearity increased. The spatial heterogeneity, which was characterized by the class-specific proportion, the between-class spectral difference and the number of classes within each coarse pixel, was found to be the primary factor in the scaling effect. These factors influenced the scaling effect collectively and existed dependently. With the RMSE less than 0.3 × 10 −6 m 2 /m 2 , TT was suggested for the correction with a polynomial LAI-NDVI functions. WF was preferred for neighboring scales rather than continuous scales. FT was not recommended for correcting the scaling bias caused by the significant non-linearity in LAI estimation models. This study illustrates the main causes of the scaling effect and provides a reference of technique selection for scaling bias correction to improve the application of remotely sensed estimates.

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“…Although the information fractal is an efficient tool for the description of scaling effect, the proposed method based on information fractal in reference [7] was neither suitable for LAI calculation at different resolutions nor for scaling effect correction. Through extending the method of Zhang et al [7], the authors established an image-based LAI scaling transfer model by using the information fractal dimension (D) [37]. The LAI scaling transfer model was developed by establishing the double logarithmic linear relationship between the scale (spatial resolution) and average LAIs of the image at different scales.…”

Section: Introductionmentioning

confidence: 99%

“…This proposed method in this paper could efficiently realize the scaling effect correction of the estimated LAI at different spatial resolutions with high accuracy. Inspired by the image-based model in reference [37], a pixel-based LAI spatial scaling transfer model using the information fractal dimension D was developed in the current study. In this method, each up-scaling pixel was considered an "image" for using the image-based model to correct the LAI scaling effect of the up-scaling pixel.…”

Section: Introductionmentioning

confidence: 99%

Spatial Up-Scaling Correction for Leaf Area Index Based on the Fractal Theory

Qin

Liu

et al. 2016

Remote Sensing

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Abstract:The scaling effect correction of retrieved parameters is an essential and difficult issue in analysis and application of remote sensing information. Based on fractal theory, this paper developed a scaling transfer model to correct the scaling effect of the leaf area index (LAI) estimated from coarse spatial resolution image. As the key parameter of the proposed model, the information fractal dimension (D) of the up-scaling pixel was calculated by establishing the double logarithmic linear relationship between D-2 and the normalized difference vegetation index (NDVI) standard deviation (σ NDV I ) of the up-scaling pixel. Based on the calculated D and the fractal relationship between the exact LAI and the approximated LAI estimated from the coarse resolution pixel, a LAI scaling transfer model was established. Finally, the model accuracy in correcting the scaling effect was discussed. Results indicated that the D increases with increasing σ NDV I , and the D-2 was highly linearly correlated with σ NDV I on the double logarithmic coordinate axis. The scaling transfer model corrected the scaling effect of LAI with a maximum value of root-mean-square error (RMSE) of 0.011. The maximum absolute correction error (ACE) and relative correction error (RCE) were only 0.108% and 8.56%, respectively. The spatial heterogeneity was the primary cause resulting in the scaling effect and the key influencing factor of correction effect. The results indicated that the developed method based on fractal theory could effectively correct the scaling effect of LAI estimated from the heterogeneous pixels.

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Spatial scaling transformation modeling based on fractal theory for the leaf area index retrieved from remote sensing imagery

Cited by 13 publications

References 20 publications

Principles and methods of scaling geospatial Earth science data

Principles and methods of scaling geospatial Earth science data

Evaluation of Three Techniques for Correcting the Spatial Scaling Bias of Leaf Area Index

Spatial Up-Scaling Correction for Leaf Area Index Based on the Fractal Theory

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