Visualization of boundaries in CT volumetric data sets using dynamic M−|∇f|M−|∇f| histogram

•We build a generalized boundary model contaminated by noise.•We prove boundary middle value has a good statistical property in our boundary model.•A dynamic M−|∇f|M−|∇f| histogram is established with a novel strategy of boundary extraction to avoid misclassification.•A complete application is designed to implement our boundary visualization method.

Direct volume rendering is widely used for three-dimensional medical data visualization such as computed tomography and magnetic resonance imaging. Distinct visualization of boundaries is able to provide valuable and insightful information in many medical applications. However, it is conventionally challenging to detect boundaries reliably due to limitations of the transfer function design. Meanwhile, the interactive strategy is complicated for new users or even experts. In this paper, we build a generalized boundary model contaminated by noise and prove boundary middle value (M) has a good statistical property. Based on the model we propose a user-friendly strategy for the boundary extraction and transfer function design, using M  , boundary height (Δh)(Δh), and gradient magnitude (|∇f|)(|∇f|). In fact, it is a dynamic iterative process. First, potential boundaries are sorted orderly from high to low according to the value of their height. Then, users iteratively extract the boundary with the highest value of ΔhΔh in a newly defined domain, where different boundaries are transformed to disjoint vertical bars using M−|∇f|M−|∇f| histogram. In this case, the chance of misclassification among different boundaries decreases.