Linear multifractional stable motion for modeling of fluid-filled regions in retinal optical coherence tomography images

Fluid appears in several retinal disorders can be visualized by optical coherence tomography (OCT) images. Since manual survey of OCT images is challenging, automatic fluid detection is desirable. This paper develops a generalized multifractal framework to model the local scale-invariant property of retinal OCT signals and accordingly proposes a simple methodology for automatic localization of fluid-filled regions. The proposed framework comprises both local self-similarity and heavy tailed distribution of OCT signals by generalization of fractional Levy stable motion (fLsm) to the Riemann-Liouville multifractional Levy stable motion (RL-mLsm). In order to measure the multifractality appears in RL-mLsm, the scaling properties of Levy flights and stochastic differential equations (SDEs) are used to develop a fractional momentbased algorithm namely, multi-fractional Levy fluctuation analysis (MLFA) algorithm. Here, we apply MLFA to model OCT images. Modeling results indicate the significant difference between the multifractal bandwidth in non-fluid and fluid regions. In addition, by utilizing various surrogate series of the signals, we discover the source of multifractality of OCT signals. As an application of the proposed multifractal modeling, we propose a new method, based on simple clustering of estimated local scaling exponent of modeled OCT signals, to localize fluid regions in OCT images. The localization method is validated, and the experimental results reveal the superiority of proposed method. Overall, the proposed multifractal framework has full advantages on excellent improvement of fluid localization, which promises the proposed model is suitable for effective description of self-similar nature of normal and abnormal OCT images independent of capturing device.