Einfluss der Bildfilterung auf die Landnutzungsklassifizierung durch fraktale und multifraktale Merkmale

Applicability of multifractal features as global characteristics of WorldView-2 panchromatic satellite images

“…However, we emphasize that D q can also be applied to any measures [Ott, 1993, chapter 9], what was confirmed by numerous studies [Meneveau and Sreenivasan, 1991;Wawrzaszek and Macek, 2010;Chakraborty et al, 2014;Wawrzaszek et al, 2014]. In the frame o this work for the direct estimation of the function D q from the experimental data we use the Box-Counting Based Moment method [Halsey et al, 1986], presented together with schematic diagram in Wawrzaszek et al [2014]. In the first step of this method the image of the size m×m is divided into N m δ δ δ δ ( ( ) ) = = ( ( ) ) 2 of square boxes of the size δ×δ (starting with a single pixel size δ = 1 and ending with a box of image the size δ = m, (see Wawrzaszek et al [2014], Fig.1).…”

“…In multifractal analysis, during the process of measure construction and its scaling all values of pixels in a given box are taken into account. It means that not only a span of pixels dynamic is considered but also their spatial relations [Wawrzaszek et al, 2014]. Degree of multifractality values calculated using different measures differs from each other.…”

“…The definition of D q was formulated in the context of analysis of natural measure of chaotic attractors by Grassberger [1983] and Hentschel and Procaccia [1983]. However, we emphasize that D q can also be applied to any measures [Ott, 1993, chapter 9], what was confirmed by numerous studies [Meneveau and Sreenivasan, 1991;Wawrzaszek and Macek, 2010;Chakraborty et al, 2014;Wawrzaszek et al, 2014]. In the frame o this work for the direct estimation of the function D q from the experimental data we use the Box-Counting Based Moment method [Halsey et al, 1986], presented together with schematic diagram in Wawrzaszek et al [2014].…”

“…In the frame o this work for the direct estimation of the function D q from the experimental data we use the Box-Counting Based Moment method [Halsey et al, 1986], presented together with schematic diagram in Wawrzaszek et al [2014]. In the first step of this method the image of the size m×m is divided into N m δ δ δ δ ( ( ) ) = = ( ( ) ) 2 of square boxes of the size δ×δ (starting with a single pixel size δ = 1 and ending with a box of image the size δ = m, (see Wawrzaszek et al [2014], Fig.1). For a given box the normalized measure is calculated according to the formula:…”

What Can Multifractal Analysis Tell Us about Hyperspectral Imagery?

“…A number of experiments have shown, however, that a fractal formalism may not be sufficient for satellite imagery description, and that multifractals (an extension of fractal theory) should be used instead (e.g., [24][25][26]). The multifractal approach is based on the assumption that it is necessary to use a number of non-trivially connected fractals, each with a different dimension of self-similarity, to describe data complexity.…”