Multifractals in image processing and process imaging

Cola, Lee De

doi:10.3133/ofr91301

Cited by 5 publications

(5 citation statements)

References 12 publications

(13 reference statements)

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“…As noted above, the fractal dimension serves poorly in distinguishing between scarps formed by different processes. The recognition of scale limitations of self-similar formative processes has led to the recognition of multi-fractals and techniques for identifying the multiple fractal dimensions and the scales of transition (e.g., Evertsz and Mandelbrot, 1992;De Cola, 1993;Lavalee et al, 1993). Nonetheless, if geomorphologists wish to contrast landscapes or compare models with reality, the restriction of comparative statistics to estimates of fractal dimension(s) will afford limited discriminatory power and poor confirmation.…”

Section: Discussionmentioning

confidence: 99%

Simulation modeling and statistical classification of escarpment planforms

Howard

1995

Geomorphology

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Nearly horizontal sedimentary sequences are typically eroded into escarpments capped by resistant rock layers. These escarpments record in planform the spatial variation in erosional processes. Simulation models have been constructed of scarp development by three processes, scarp backwasting, fluvial erosion, and groundwater sapping, acting singly or in combination. Scarp backwasting produces planforms characterized by broad, shallow reentrants and sharply pointed headlands. Fluvial erosion creates dendritic, sharply terminated canyons which gradually widen downstream because of superimposed backwasting. Groundwater sapping produces weakly branched canyons of nearly constant width with generally rounded headwalls. A number of morphometric variables are measured on natural and simulated scarps as well as lava flows, glacially eroded mountain fronts, and eroded tabular igneous intrusions. A discriminant analysis is able to classify 478 of these planforms into 9 categories with 87% accuracy.

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Section: Discussionmentioning

confidence: 99%

Simulation modeling and statistical classification of escarpment planforms

Howard

1995

Geomorphology

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“…There are problems in classifying such images into land-use categories, but there is much research on this frontier at present within remote sensing, which bodes well for better classifications. There are even possibilities for improving image analysis by means of fractal statistics, which are naturally occurring measures for such images (de Cola, 1993).…”

Section: Conclusion: Future Researchmentioning

confidence: 99%

Morphology from Imagery: Detecting and Measuring the Density of Urban Land Use

et al. 1995

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Abstract. Defining urban morphology in terms of the shape and density of urban land use has hitherto depended upon the informed yet subjective recognition of patterns consistent with spatial theory. In this paper we exploit the potential of urban image analysis from remotely sensed data to detect, then measure, various elements of urban form and its land use, thus providing a basis for consistent definition and thence comparison. First, we introduce methods for classifying urban areas and individual land uses from remotely sensed images by using conventional maximum likelihood discriminators which utilize the spectral densities associated with different elements of the image. As a benchmark to our classifications, we use smoothed UK Population Census data. From the analysis we then extract various definitions of the urban area and its distinct land uses which we represent in terms of binary surfaces arrayed on fine grids with resolutions of approximately 20 m and 30 m. These images form surfaces which reveal both the shape of land use and its density in terms of the amount of urban space filled, and these provide the data for subsequent density analysis. This analysis is based upon fractal theory in which densities of occupancy at different distances from fixed points are modeled by means of power functions. We illustrate this for land use in Bristol, England, extracted from Landsat TM-5 and SPOT HRV images and dimensioned from population census data for 1981 and 1991. We provide for the first time, not only fractal measurements of the density of different land uses but measures of the temporal change in these densities.

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“…It also illustrates the more general fact pointed out by Gagalowicz [22], that the information provided by the second-order variogram may not be sufficient to discriminate the image spatial structures. Similarly to (24), the experimental first-order variogram is computed according to…”

Section: Experimental Results On Simulated Imagesmentioning

confidence: 99%

“…Two point statistics which describe the spatial relationships between data are thus more appropriate [21]- [23]. Garrigues et al [14] provide a comparison of some two point statistics metrics used to explore the spatial variations within an image which includes Haralick indexes [23], fractal and multifractal analysis [24]- [28], Fourier transform [29], [30], wavelet transform [6], [25], [30], and second-order variogram [15], [31]- [37]. Among these metrics, it is shown in Garrigues et al [14] that modeling the second-order variogram of high spatial resolution NDVI image is an efficient method to characterize the spatial structures of the landscape.…”

Section: Introductionmentioning

confidence: 99%

Using First- and Second-Order Variograms for Characterizing Landscape Spatial Structures From Remote Sensing Imagery

Garrigues

Allard

Baret

2007

IEEE Trans. Geosci. Remote Sensing

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The spatial structures displayed by remote sensing imagery are essential information characterizing the nature and the scale of spatial variation of Earth surface processes. This paper provides a new approach to characterize the spatial structures within remote sensing imagery using stochastic models and geostatistic metrics. Up to now, the second-order variogram has been widely used to describe the spatial variations within an image. In this paper, we demonstrate its limitation to discriminate distinct image spatial structures. We introduce a different geostatistic metric, the first-order variogram, which used in combination with the second-order variogram, will prove its efficiency to describe the image spatial structures. We then develop a method based on the simultaneous use of both first-and second-order variogram metrics to model the image spatial structures as the weighted linear combination of two stochastic models: a Poisson line mosaic model and a multi-Gaussian model. The image spatial structures are characterized by the variance weight and the variogram range related to each model. This method is applied to several SPOT-HRV Normalized Difference Vegetation Index (NDVI) images from the VALERI database in order to characterize the nature of the processes structuring different types of landscape. The mosaic model is an indicator of strong NDVI discontinuities within the image mainly generated by anthropogenic processes such as the mosaic pattern of crop sites. The multi-Gaussian model shows evidence of diffuse and continuous variation of NDVI generally engendered by ecological and environmental processes such as the fuzzy pattern observed over forest and natural vegetation sites.Index Terms-First-order variogram, landscape, multiGaussian model, normalized difference vegetation index (NDVI), Poisson line mosaic model, second-order variogram, spatial structure, stochastic simulation.

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Multifractals in image processing and process imaging

Cited by 5 publications

References 12 publications

Simulation modeling and statistical classification of escarpment planforms

Simulation modeling and statistical classification of escarpment planforms

Morphology from Imagery: Detecting and Measuring the Density of Urban Land Use

Using First- and Second-Order Variograms for Characterizing Landscape Spatial Structures From Remote Sensing Imagery

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