Abstract
An improved technique for fractal characterization called the modified blanket method is introduced that can quantify surrounding fractal structures on a pixel by pixel basis without artifacts associated with scale-dependent image features such as object size. The method interprets images as topographical maps, obtaining information regarding the local surface area as a function of image resolution. Local fractal dimension (FD) can be quantified from the power law exponent derived from the surface area and image resolution relationship. We apply this technique on simulated cell images of known FD and compared the obtained values to power spectral density (PSD) analysis. Our method is sensitive to a wider FD range (2.0-4.5), having a mean error of 1.4% compared to 6% for PSD analysis. This increased sensitivity and an ability to compute regional FD properties enabled the discrimination of the differences in radiation resistant cancer cell responses that could not be detected using PSD analysis.
Highlights
Fractal patterns are very common in nature and can be observed in different types of biological structures and functions [1,2]
Utilizing simulated microscopy images of cells with intracellular fractal clouds of known fractal dimension (FD), we demonstrated that the Modified Blanket Method (MBM) can compute FD values that successfully estimate true FDs ranging from 2.00 to 4.50 (Fig. 2(a), (b))
Our study demonstrates that the MBM is capable of rapidly and accurately quantifying FD within individual cells
Summary
Fractal patterns are very common in nature and can be observed in different types of biological structures and functions [1,2]. Image analysis of these self-repeating patterns over length- or time-scales is an attractive approach to quantify changes in biological structures [3]. The power law relationship between the number of boxes intersected by the pattern of interest and the size of the boxes is used to estimate fractal organization [1,17]. To quantify the fractal dimension of grayscale images, Fourier-based approaches have been used, in mitochondrial clustering analysis. Through radial sampling of two-dimensional power spectral density (PSD) maps, fractal dimension (FD) can be determined from images by measuring the exponent, β, from the power law relationship between PSD and spatial frequency as shown in Eq (1) [8]
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