Abstract
Adequate models of the bread crumb structure can be critical for understanding flow and transport processes in bread manufacturing, creating synthetic bread crumb images for photo-realistic rendering, evaluating similarities, and establishing quality features of different bread crumb types. In this article, multifractal analysis, employing the multifractal spectrum (MFS), has been applied to study the structure of the bread crumb in four varieties of bread (baguette, sliced, bran, and sandwich). The computed spectrum can be used to discriminate among bread crumbs from different types. Also, high correlations were found between some of these parameters and the porosity, coarseness, and heterogeneity of the samples. These results demonstrate that the MFS is an appropriate tool for characterising the internal structure of the bread crumb, and thus, it may be used to establish important quality properties it should have. The MFS has shown to provide local and global image features that are both robust and low-dimensional, leading to feature vectors that capture essential information for classification tasks. Results show that the MFS-based classification is able to distinguish different bread crumbs with very high accuracy. Multifractal modelling of the underlying structure can be an appropriate method for parameterising and simulating the appearance of different bread crumbs.
Highlights
The goals of this research are (1) to evaluate if the multifractal spectrum (MFS) [1] can be applied to characterise and discriminate the bread crumb structure for different bread types from digital images and (2) to investigate the effectiveness of the method in the classification of these structures.One of the most important factors to evaluate the quality of a bread loaf is related to its crumb structure
3.1 Data analysis Self-organising maps (SOM) [20] of the feature vectors associated with each bread image were useful to represent them in a lower dimensional view, in order to better understand the meaning of their respective MFS
Unsupervised SOM of the multifractal representation of bread and non-bread images are shown in Figure 4 in a grid of 10 × 10 cells
Summary
The goals of this research are (1) to evaluate if the MFS [1] can be applied to characterise and discriminate the bread crumb structure for different bread types from digital images and (2) to investigate the effectiveness of the method in the classification of these structures.One of the most important factors to evaluate the quality of a bread loaf is related to its crumb structure. Fractal and multifractal analysis has been applied in the study of apple tissues [5], pork sirloins [6], and in chocolate, potato, Data analysis of the results of the feature extraction process is useful for obtaining key properties of materials. This information could be used in quality measurements of real samples and in the validation of synthetic representations of them. In [9], several fractal features were obtained for one type of bread, demonstrating that a vector of FDs would be capable of obtaining key features of the crumb texture more accurately than using a single FD
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