Leaf shape analysis using the multiscale Minkowski fractal dimension, a new morphometric method: a study with Passiflora (Passifloraceae)

Abstract

A new method is proposed for the extraction of morphometric characteristics of plant leaf structures. A sample of 10 species of the genus Passiflora (P. coriacea Juss., P. foetida L., P. miersii Mast., P. organensis Gardner, P. pohlii Mast., P. suberosa L., P. amethystina J.C. Mikan, P. caerulea L., P. gibertii N.E.Br., P. maliformis L.) was used in an experiment to test the method. This genus shows a wide range of leaf forms, but there are some species pairs or groups whose morphological similarity makes their correct identification difficult. The multiscale function of the Minkowski fractal dimension was applied to digital images of leaves to generate complexity measures of their internal (veins) and external (leaf outline) form. The results of the leaf characteristic extraction method, as well as its potential as the basis for an identification mechanism, are discussed for the 10 species. The method was very accurate in correctly differentiating among species, since no leaf was erroneously identified. A small number of leaves per species was sufficient for establishing a characteristic pattern for each of them, which constitutes an important advantage of the method in the recognition and classification procedure.Key words: image processing, fractal dimension, plant taxonomy, morphometry, Passiflora.

A Graph-Based Approach for Shape Skeleton Analysis

“…In this approach shape characterization is performed using the 50 most meaningful points of the curve [3,10].…”

“…The method was originally proposed to deal with shape contours [7] and in this work, we propose its use in the skeleton analysis. Experiments compare the method with contour based methods [8], signal processing [9] and fractal dimension [10]. Results demonstrate that the method is suitable to the skeleton analysis and overcome traditional contour approaches.…”

Characterizing 3D Shapes Using Fractal Dimension

“…Among the many approaches developed to estimate this parameter, Bouligand-Minkowski method [5,11,12] has emerged as the one that presents the most accurate results and has shown to be very sensitive to structural changes of the object. This method was originally developed for shape analysis.…”

“…Regardless of the large sensitiveness of the method to structural changes, there are cases where a single non-integer value is not sufficient to describe all levels of detail present in the influence volume V (r) for a specific object. A better description of the 3D model, in terms of its complexity, is achieved by using the concept of Multi-Scale Fractal Dimension [14,15,11]. Different from linear interpolation, which is commonly used to compute the angular coefficient of the log-log curve r × V (r), this approach exploits the infinitesimal limit of the linear interpolation by using the derivative of the log-log curve.…”

<i>Camellia</i> (Theaceae) classification with support vector machines based on fractal parameters and Red, Green, and Blue intensity of leaves

“…Leaf characters have been successfully exploited to solve plant taxonomy problems (Plotze et al, 2005, Lin et al, 2008Ye and Weng, 2011). Traditionally, leaf traits such as shape (Ming, 2000), morphology research (Barthlott et al, 2009), and leaf anatomy Jiang et al, 2010) have been used for classification.…”