Maize root complexity analysis using a Support Vector Machine method

Abstract

Root complexity is an important factor in the growth and survivability of maize plants under biotic and abiotic stress conditions. To genetically improve root structure in the future, there is a need to identify the genes that govern root complexity. Root complexity itself is ill defined, but indicators derived from images of the root system such as Fractal Dimension can be used as proxies. A disadvantage of using Fractal Dimension as a complexity indicator is that the complexity of the root as seen in the images is captured into a single parameter.

This paper describes an alternative method, which translates a root image into a set of parameters. The method consists of computing the intercepts of circles drawn around the centre of the root image with the root branches. This led to characteristic curves from which parameters can be extracted using curve fitting. In addition to the parameters obtained by curve fitting, the density of the root images was included. All parameters were evaluated on their ability to classify the roots among their original genotypes using a method from the realm of Artificial Intelligence, the Support Vector Machine (SVM).

The results showed that whilst using merely three parameters originating from the characteristic curves, the SVM algorithm was capable of correctly classifying 99.95% of roots among 235 original genotypes.

Introduction

The ability of plants to grow and produce seeds is directly related to a healthy, functional and efficient root system. Generally, root complexity and root development depend on genetic and environmental factors and their interactions (O’Toole and Bland, 1987). To assess the genetic basis of root complexity, earlier research determined the Fractal Dimension (FD) of thousands of maize roots recovered from specifically designed field trials using images of the roots (Bohn et al., 2006). A combined analysis of molecular linkage information and FD results led to the identification of Quantitative Trait Loci (QTL) for FD on most of the ten maize chromosomes. QTL are regions in the genome that carry genes involved in the inheritance of a quantitative trait, in this case root complexity. The FD has been shown suitable to describe the complexity of natural objects (Mandelbrot, 1983). A considerable amount of work has been done to capture biological complexity using FD, including studies on root systems (Tatsumi et al., 1989, Lynch et al., 1993, Shibusawa, 1994, Nielsen et al., 1997, Masi and Maranville, 1998, Oppelt et al., 2000, Eghball et al., 2003, Walk et al., 2004, Lontoc-Roy et al., 2006, Soethe et al., 2007), soil clod formation (Shibusawa, 1992), shoot systems and canopies of young trees (Morse et al., 1985, Foroutan-pour et al., 1999), seaweeds (Kubler and Dugeon, 1996), plant foliage (Da Silva et al., 2006), sponges (Abraham, 2001), neurons (Fernandez et al., 1994), and fungal mycelia (Mihail et al., 1995).

A disadvantage of the use of FD is that the complexity of the whole root as contained in gray scale images is captured in a single indicator. Therefore as an alternative, a method was devised which transforms the two-dimensional gray scale image into a set of parameters. This was accomplished by drawing circles around the known centre location of a root image, and to accumulate the intercepting pixels of these circles with the root branches. This method yielded a characteristic function where the accumulated number of intercepting pixels was plotted against the radius of the circles. This characteristic function was approximated by fit curves and the parameters of these curves were used to classify the roots among their original genotypes using the Support Vector Machine (SVM) algorithm (Vapnik, 1995). The SVM method is essentially a binary classifier based on finding the maximal margin hyper-plane between two or more classes (Burges, 1998, Suykens and Vandewalle, 1999). The SVM method has been applied in a variety of applications such as in weed and nitrogen stress detection (Karimi et al., 2005), tissue classification (Furey et al., 2000, Pavlidis et al., 2004), face detection (Osuna et al., 1997), gene selection for cancer (Guyon et al., 2002), as well as shape extraction and classification (Cai et al., 2001).

The objective of this study was to develop an alternative method of root image analysis, based on the Support Vector Machine method, enabling classification of maize roots among their original genotypes.