Branches of tubular structures (vasculature, trachea, neuron, etc.) in medical images are critical for the topology of these structures. In many applications, It is very helpful to be able to decompose tubular structures and identify every individual branch. For example, quantification of geometric vascular features, registration of trachea movement due to respiration, tracing of neuron path. However, manual decomposition can be tedious, time-consuming, and subject to operator bias. In this paper, we propose a novel method to decompose tubular structures automatically and describe how to implement it in ITK framework. The input is a 2D/3D binary image that can be obtained from any segmentation techniques, as well as the junctions, which can be generated automatically from our previously contributed ITK class: itk::JunctionDetectionFilter. The output will be branches with their labels and their connection. There are only two parameters which need to be set by the user. We provide here the implementation as a ITK class: itk::BranchDecompositionFilter.