@article{brandoliPDE2013,
    author = {Bruno Brandoli Machado and Dalcimar Casanova and Wesley Nunes Gon{\c{c}}alves and Odemir Martinez Bruno},
    title = {Partial differential equations and fractal analysis to plant leaf identification},
    journal = {Journal of Physics: Conference Series},
	year = {2013},
	month = {Feb},
	volume = {410},
	pages = {012066},
    doi = {10.1088/1742-6596/410/1/012066},
    url = {https://doi.org/10.1088%2F1742-6596%2F410%2F1%2F012066},
    publisher = {IOP Publishing},
	abstract = {Texture is an important visual attribute used to plant leaf identification. Although there are many methods of texture analysis, some of them specifically for interpreting leaf images is still a challenging task because of the huge pattern variation found in nature. In this paper, we investigate the leaf texture modeling based on the partial differential equations and fractal dimension theory. Here, we are first interested in decomposing the original texture image into two components f = u + v, such that u represents a cartoon component, while v represents the oscillatory component. We demonstrate how this procedure enhance the texture component on images. Our modeling uses the non-linear partial differential equation (PDE) of Perona-Malik. Based on the enhanced texture component, we estimated the fractal dimension by the Bouligand-Minkowski method due to its precision in quantifying structural properties of images. The feature vectors are then used as inputs to our classification system, based on linear discriminant analysis. We validate our approach on a benchmark with 8000 leaf samples. Experimental results indicate that the proposed approach improves average classification rates in comparison with traditional methods. The results suggest that the proposed approach can be a feasible step for plant leaf identification, as well as different real-world applications.}
}