The Boltzmann distribution was derived in this chapter. The Boltzmann equation was explained next to the main difficulty of this equation, the integral of the collision operator, which was solved by the BGK-approximation where a long-term substitute is essential. The discretization of the Boltzmann comparison with the BGK-approximation was introduced along with the lattice and the different lattice configurations to define the lattice framework where the method is applied. Also, in this framework, the algorithm of the process was described. The boundary conditions were summarised, where one can see that they represent macroscopic conditions acting locally in every node.
TopInteractive Image Segmentation
Interactive segmentation techniques are essential for fast and reliable extraction of the ROI. The level of user interaction in different methods varies in terms of the amount and type of information provided by the users because it requires iterative manual inputs, an acceptable interactive segmentation method has to minimise the human effort and produce a result quickly. That is to say, the seeds needed to obtain the desired outcome must be neither too accurately localised nor too numerous, and the time to compute a segmentation must aim to a few seconds (Y. Chen, A. Cremers and Z. Cao, 2014). The user chooses some pixels named seeds and indicators for each of them the element to which it belongs. Features like location, colour, texture, etc. of desired regions deduced by analysing and adding or removing some seeds can improve the produced result, allowing the user to get any desired segmentation results. It generally accepted that segmentation methods could be classified into an edge-based, region-based and energy-based methods. When an interactive segmentation method searches for the boundaries, then the user gives some points of these boundaries. One of the most representative edge-based interactive segmentation methods is Intelligent Scissors (N. Suetake, E. Uchino and K. Hirata, 2007). However, for highly textured images, a lot of boundary pixels are used for detection of the correct object that makes segmentation task complex.
Regarding most of the region based methods; the user must draw some strokes on the different areas. With this modality of interaction, if picture elements are small when compared to the brush size, sometimes the user selects the wrong initialisation of the seed that gives false processing results. Some methods attempt to deal with this noise needs image preprocessing for getting better results Weiner filter is better for correction of distortion in the images that results can be significantly better.