Use of Lineal-Path Distribution Function as Statistical Descriptor of the Crumb Structure of Bread

The importance of the relation between food microstructure and their quality is recognized as crucial. In terms of bread quality, the precise characterization of the crumb structure is considered essential to evaluate its sensorial properties. A variety of different statistical correlation functions have been theoretically formulated in recent years to quantify the microstructure of general random heterogeneous materials but they have rarely been applied in food science. In this paper, we have developed a method to calculate the lineal-path distribution function L(x) for the void and solid matrix phases from two-dimensional (2D) images of bread. The method has been successfully employed here to characterize the microstructure for two type of commercial breads. Our results reveal that crumb structure may be modeled as a system of polydispersed overlapping disks. Moreover, we have quantified the dimensions of the voids and crumb phase statistically and differences in the homogeneity of crumb structure.     

Statistical Description of Food Microstructure. Extraction of Some Correlation Functions From 2D Images

Two algorithms able to compute lineal-path distribution function L(z) and two-point correlation function, S ₂ (r ₁ ,r ₂ ) from 2D digital images of foods were developed and validated. Particularly, “Altamura” and “White” breads as well as “Napoli” sausages were studied. Lineal-path function was modeled by considering the foods as two-phase random systems composed from polydisperse overlapping disks. Instead, two-point correlation function was modeled by using a Debye’s equation. In all cases a good agreement between experimental and theoretical trend was obtained stating the high accuracy of the algorithms in the extraction of correlation functions as well as the possibility to model breads and sausages as two-phase random systems. Also, important morphological properties such as pores distribution, pore size homogeneity and their spatial distribution, were obtained. For instance, although the estimated radius of the pores was lower for “Altamura” bread rather that for “White”, its slowest decay of L(z) highlighted that the pores showed a high dimensional inhomogeneity.