Dataset of synthetic images
Description
This dataset contains 150 synthetic binary images created to test how the choice of box sizes relative to region-of-interest (ROI) size affects box-counting fractal dimension (FD) estimates. It accompanies a computational study of the ImageJ Fractal Box Counter and its default box-size sequence (2, 3, 4, 6, 8, 12, 16, 32, 64 pixels), which is widely applied in dental radiographic FD analysis irrespective of ROI dimension. Real trabecular bone images have no known fractal dimension, so the accuracy of an FD estimate cannot be assessed on them. The images here are self-similar branching-tree structures generated by a line-segment iterated function system satisfying the open set condition, for which the Moran–Hutchinson theorem prescribes the dimension exactly as D = log(N)/log(1/r). Two conditions were generated: D = 1.584963 (N = 3, r = 0.50) and D = 1.888849 (N = 4, r = 0.48), spanning the range of FD values reported in the dental radiographic literature. This prescribed value is the dimension of the ideal generating system; the finite, rasterised and skeletonised images are realisations of it, and the divergence between the two is itself part of what the dataset was built to measure. Each of the 25 replicates per condition is provided at three nested ROI sizes (64 × 64, 128 × 128 and 144 × 144 pixels), cropped concentrically from a common centre so that image content is held constant while the relationship between ROI size and box size changes. Images are 8-bit binary TIFF with the fractal structure white (255) on a black (0) background — the state a radiograph is in immediately after thresholding and before inversion — so they can be passed directly into an invert → skeletonise → box-count pipeline without further preprocessing. The archive also includes a manifest giving the generation seed and crop coordinates for every image (allowing exact regeneration), a table classifying every ROI-size × box-size combination as valid, near-degenerate or invalid, and the Python generation code. All fractal dimension measurements reported in the accompanying article were obtained in ImageJ 1.54t, not from the generation code. Supplementary File 1 reports the sequential decomposition under both orderings, Supplementary File 2 contains the image-generation code, and Supplementary File 3 contains the image manifest and box-classification reference table. Fractal dimension measurements were obtained in ImageJ 1.54t as described in the Methods.