This paper introduces a deep learning based methodology for analyzing the self-assembled, fractal-like structures formed in evaporated droplets. To this end, an extensive image database of such structures of the plant extract Viscum album Quercus$$10^{-3}$$ 10 - 3 was used, prepared by three different mixing procedures (turbulent, laminar, and diffusion based). The proposed pattern analysis approach is based on two stages: (1) automatic selection of patches that exhibit rich texture along the database; and (2) clustering of patches in accordance with prevalent texture by means of a Dense Convolutional Neural Network. The fractality of the patterns in each cluster is verified through Local Connected Fractal Dimension histograms. Experiments with Gray-Level Co-Occurrence matrices are performed to determine the benefit of the proposed approach in comparison with well established image analysis techniques. For the investigated plant extract, significant differences were found between the production modalities; whereas the patterns obtained by laminar flow showed the highest fractal structure, the patterns obtained by the application of turbulent mixture exhibited the lowest fractality. Our approach is the first to analyze, at the pure image level, the clustering properties of regions of interest within a database of evaporated droplets. This allows a greater description and differentiation of the patterns formed through different mixing procedures.
The droplet evaporation method (DEM) is based on the evaporation-induced pattern formation in droplets and is applied mainly for diagnosis [1]. Here, we present a series of experiments performed by our team showing DEMs potential also for homeopathy basic research, in particular, for the investigation of (i) low potencies, (ii) low potency complexes (physical model), and (iii) the action of high potencies (plant-based model). DEM differentiated significantly between Luffa, Baptisia, Echinacea, and Spongia until 4x [2]. Furthermore, the patterns varied in function of the number of succussion strokes (0, 10, or 100) applied during potentization [3]. The performance of chaotic succussions vs. laminar flow vs. slight mixing during the potentization of Viscum album quercus 3x influenced the DEM patterns; the chaotic succussions reduced, whereas laminar flow enhanced the patterns complexity vs. the unsuccussed control. The addition of Mercurius bijodatus 9x to Luffa 4x changed significantly the DEM patterns, even if the material quantity present in the 9x potency lied far beyond that of ultrapure water. Leakages obtained by placing healthy or damaged wheat-seeds into Arsenicum album 45x or Zincum metallicum 30c vs. water created significantly different DEM structures [4, 5]. The damaged seeds put into the potency created structures characterized by a higher complexity than those obtained from damaged seeds put into control water. Furthermore, the potency action seemed to correlate positively with the number of succussion strokes applied during potentization, as could be shown by means of DEM patterns and germination rate using the same wheat-seed model [6]. In all our studies, the pattern evaluation was computerized or based on deep-learning algorithms and the robustness of the experimental system was checked by means of systematic control experiments. DEM together with other similar methods has also been reviewed by our team for what concerns the application in homeopathy basic research [7].
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