We present a method for tracking Maximally Stable Homogeneous Regions (MSHR) in images with an arbitrary number of channels. MSHR are conceptionally very similar to Maximally Stable Extremal Regions (MSER) and Maximally Stable Color Regions (MSCR), but can also be applied to hyperspectral and color images while remaining extremely efficient. The presented approach makes use of the edge-based component-tree which can be calculated in linear time. In the tracking step, the MSHR are localized by matching them to the nodes in the component-tree. We use rotationally invariant region and gray-value features that can be calculated through first and second order moments at low computational complexity. Furthermore, we use a weighted feature vector to improve the data association in the tracking step. The algorithm is evaluated on a collection of different tracking scenes from the literature. Furthermore, we present two different applications: 2D object tracking and the 3D segmentation of organs.