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Figure 1 | Journal of Cardiovascular Magnetic Resonance

Figure 1

From: CMR trabecular fractal analysis - technical development of a measurement system

Figure 1

Using the Pascal analogy triangle, we constructed mathematical fractal phantoms: Sierpinski gaskets of px heights:16-32-64-128-256 and known FD. 16, 32 and 64 px gaskets are reproduced here(left). Predicted/measured FD demonstrate high concordance. To the right is a cardiac contour after extraction from DICOM data in MATLAB, undergoing fractal analysis. Each slice is scaled using a magnification algorithm with bicubic interpolation(Stanescu E et al.), masked and then segmented using a region-based level set method(Li C. et al). The contour, composed of N pairs of positive long X/Y coordinates, is overlaid by a series of meshgrids, replicated over 4 random start points. Starting box-size = 45% that of the minimum circumscribed box with parallel constraint; terminal box-size = 4 px to maintain stable regression. Box size decreases by one px per iteration. At every level, scale and box count are recorded and formulated into a natural logarithmic plot. The slope determines the FD. Px = pixel.

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