Fig. 5

Applying fractal analysis to a 2D cine CMR slice (a) at the mid-left ventricular level [9]. Trabecular detail is extracted by a region-based level-set segmentation [40], followed by binarisation (b) and edge-detection (c). Binarisation eliminates pixel detail originating from the blood pool. The edge image is covered by a series of grids (d). The total number of sized d boxes making up this exemplar grid is 16, and the number of boxes N(d) required to completely cover the contour, 14 (2 boxes overlie blank space). For this set, box-counting will involve the application of 86 grid sizes. The minimum size is set to 2 pixels. The maximum size of the grid series is dictated by the dimensions of the bounding box (discontinuous red line) where ‘bounding box’ refers to the smallest rectangle that encloses the foreground pixels. The box diameter for each successive grid is set to drop by d-1 pixels each time. Through the implementation of this 2D box-counting approach, a fractal output of between 1 and 2 is expected. The log-lot plot (e) produces a good fit using linear regression and yields a gradient equivalent to - FD (1.363). d = box dimension; Ln = natural logarithm; N(d) = number of boxes. Other abbreviations as in Figs. 1 and 2