Tools for quantitative form description : an evaluation of different software packages for semi-landmark analysis

The challenging complexity of biological structures has led to the development of several methods for quantitative analyses of form. Bones are shaped by the interaction of historical (phylogenetic), structural, and functional constrains. Consequently, bone shape has been investigated intensively in an evolutionary context. Geometric morphometric approaches allow the description of the shape of an object in all of its biological complexity. However, when biological objects present only few anatomical landmarks, sliding semi-landmarks may provide good descriptors of shape. The sliding procedure, mandatory for sliding semi-landmarks, requires several steps that may be time-consuming. We here compare the time required by two different software packages ('Edgewarp' and 'Morpho') for the same sliding task, and investigate potential differences in the results and biological interpretation. 'Morpho' is much faster than 'Edgewarp,' notably as a result of the greater computational power of the 'Morpho' software routines and the complexity of the 'Edgewarp' workflow. Morphospaces obtained using both software packages are similar and provide a consistent description of the biological variability. The principal differences between the two software packages are observed in areas characterized by abrupt changes in the bone topography. In summary, both software packages perform equally well in terms of the description of biological structures, yet differ in the simplicity of the workflow and time needed to performthe analyses

A flexible geometric model for leaf shape descriptions with high accuracy

Accurate assessment of canopy structure is crucial in studying plant-environment interactions. The advancement of functional-structural plant models (FSPM), which incorporate the 3D structure of individual plants, increases the need for a method for accurate mathematical descriptions of leaf shape. A model was developed as an improvement of an existing leaf shape algorithm to describe a large variety of leaf shapes. Modelling accuracy was evaluated using a spatial segmentation method and shape differences were assessed using principal component analysis (PCA) on the optimised parameters. Furthermore, a method is presented to calculate the mean shape of a dataset, intended for obtaining a representative shape for modelling purposes. The presented model is able to accurately capture a large range of single, entire leaf shapes. PCA illustrated the interpretability of the parameter values and allowed evaluation of shape differences. The model parameters allow straightforward digital reconstruction of leaf shapes for modelling purposes such as FSPMs

Classification of lung disease in HRCT scans using integral geometry measures and functional data analysis

A framework for classification of chronic lung disease from high-resolution CT scans is presented. We use a set of features which measure the local morphology and topology of the 3D voxels within the lung parenchyma and apply functional data classification to the extracted features. We introduce the measures, Minkowski functionals, which derive from integral geometry and show results of classification on lungs containing various stages of chronic lung disease: emphysema, fibrosis and honey-combing. Once trained, the presented method is shown to be efficient and specific at characterising the distribution of disease in HRCT slices

Optimal designs for three-dimensional shape analysis with spherical harmonic descriptors

We determine optimal designs for some regression models which are frequently used for describing three-dimensional shapes. These models are based on a Fourier expansion of a function defined on the unit sphere in terms of spherical harmonic basis functions. In particular, it is demonstrated that the uniform distribution on the sphere is optimal with respect to all $\Phi_p$ criteria proposed by Kiefer in 1974 and also optimal with respect to a criterion which maximizes a $p$ mean of the $r$ smallest eigenvalues of the variance--covariance matrix. This criterion is related to principal component analysis, which is the common tool for analyzing this type of image data. Moreover, discrete designs on the sphere are derived, which yield the same information matrix in the spherical harmonic regression model as the uniform distribution and are therefore directly implementable in practice. It is demonstrated that the new designs are substantially more efficient than the commonly used designs in three-dimensional shape analysis.Comment: Published at http://dx.doi.org/10.1214/009053605000000552 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org