Currently

images

such as 3D medical and high-resolution satellite images

provide considerable information

and image processing results are required in real time in many cases

such as clinical and meteorological. Parallel image processing devices

such as graphics processing unit (GPU) and field-programmable gate arrays

have been created for engineers at a convenient price. Partial differential equation (PDE) method is extensively used in image processing. However

its solution methods are time-consuming and difficult to be directly mapped to GPU. Traditional PDE solution methods are contradictory to the assumption that space and time are continuous. Thus

a method that is naturally parallel and simple and with clear physical meaning is required to simulate the macro model described by the PDE. Recently

lattice Boltzmann (LB) method has been applied to image denoising

inpainting

registration

and segmentation as an efficient and flexible method for modeling and solving PDE. However

a systematic review of the applications of LB for image processing has not been found in previous studies. Therefore

this paper proposes the abovementioned literature review to support scholars in gaining further insights into the frontier development of the topic. In this work

numerous public reports on the applications of LB for image denoising

inpainting

segmentation

and other 3D image processing were initially surveyed using the keywords

"lattice Boltzmann" and "image processing." These reports were classified according to their differences when scholars proposed LB mathematical models

namely

"top-down" or "bottom-up" approaches in terms of macro or micro

respectively. Then

programming algorithms

computing complexities

and application scenarios of LB for image processing were analyzed and summarized. Finally

essential differences between LB and other PDE-solving methods were concluded

and further research directions on this topic were proposed. First

LB model has a clear physical meaning. The general LB method consists of two steps as follows:a streaming step in which particles (or particle densities) move from node to node on a lattice and a collision step in which particles (or particle densities) are redistributed at each node. The two steps are governed by the LB evolution equation

where parameters relaxation time and source term decide the movement of the particles. The state of each node at the next moment is only related to the state of its neighboring nodes because the particles move along the links. In image processing

each pixel value is considered particle densities

and changes in pixel value can be considered redistribution of particles that are decided by relaxation time and source term in which image information

such as gradient and curvature

are embedded. Second

macro models can be classified into anisotropic

nonlinear

and linear diffusion models according to diffusion tensor. The microdifferences among the abovementioned macro models are decided by relaxation time. In the anisotropic diffusion model

has a different value on the links

and the value changes along each link according to image information. In the nonlinear diffusion model

has the same value on the links

and the value changes similarly to the anisotropic model. In the linear model

has the same and constant value on the links. changes in the anisotropic and nonlinear models because the pixel value changes after each iteration; changes in the model with external force terms. Two parameters must be computed in each iteration. Consequently

the computing complexities of the anisotropic

nonlinear

and linear diffusion models are decreased. The computing complexity of the LB models that include external force terms is also decided by source terms. Third

"top-down" approach uses the LB evolution equation to construct a macro model

which appears similar to existing image processing PDE. Then

and are determined by PDE diffusion tensor and external force term separately. "Bottom-up" approach constructs and directly according to the physical meaning of the LB method. The first approach uses the LB method as an alternative solving approach to PDE and requires high mathematical skill. The second approach used in constructing the mathematical model is easy and flexible. Fourth

the LB method is inherently parallel and naturally suited for GPU

which is ideally fit for explicit

local

and lattice-based computations. The advantage of LB in computing speed is obvious when image amount is large. The GPU/CPU speedup factors are larger in large 3D volumes than in small volumes. The programming of LB is simple. The core LB algorithm can be implemented with a few lines of codes and a brief coding time. Fifth

the anisotropic and nonlinear diffusion models can be used in image denoising and inpainting. The design of the external force terms significantly influences the quality of image segmentation. The LB method has a high research value as a natural parallel algorithm in fast image processing

such as 3D image denoising

inpainting

and segmentation. However

several problems must still be further studied

such as image boundary processing

parallel platform selection

and optimization.