FRACTAL ANALYSIS AS A TOOL FOR POMOLOGY STUDIES: CASE STUDY IN APPLE

Abstract

This study evaluated the possibility of characterization and discrimination of apple cultivars by fractal analysis of the shape of leaves. The geometry of the leaf lamina from five apple cultivars (Delicios de Voineşti, Florina, Generos, Jonathan and Pionier) was studied by fractal analysis, box-counting method, for obtaining fractal dimensions (D). Leaf lamina descriptor parameters (length - L, width – W, perimeter – P, and leaf area - LA) were determined for the comparative analysis with fractal dimensions in order to characterize the cultivars studied. Based on fractal dimensions (D) obtained from the analysis of the geometry of the leaf, the five apple cultivars studied were characterized and discriminated safely statistics (Cophenetic coefficient = 0.967). Regression analysis revealed the relationship of interdependence between leaf area and fractal dimensions (D) for each apple cultivar. From comparing the coefficient of variation of foliar parameters studied (L, W, P, LA), that the fractal dimensions (D) had the smallest variation within each apple cultivar, which shows that the fractal dimension (D) is a more stable parameter for characterization of the apple cultivars studied compared with other elements of the leaf lamina. According to the values of the correlation coefficient R2 and safety parameters (p and RMSE), the fractal dimensions (D) facilitated the prediction of leaf area certainly higher than in the classics descriptors parameters of the leaves L, W and P ( RD2 = 0.991 for Florina; RD2 = 0.985 for Generos and Pionier; RD2 = 0.982 for Delicios de Voinești and RD2 = 0.979 for Jonathan). Fractal analysis has proven to be a tool with great power for the analysis, characterization and discrimination of the five apple cultivars studied, and predicting of the leaf area based on fractal dimension (D), which recommends it as a tool in pomology studies.