Enhancing a diffusion algorithm for 4D image segmentation using local information

Inspired by the diffusion of a particle, we present a novel approach for performing a semiautomatic segmentation of tomographic images in 3D, 4D or higher dimensions to meet the requirements of high-throughput measurements in a synchrotron X-ray microtomograph. Given a small number of 2D-slices with at least two manually labeled segments, one can either analytically determine the probability that an intelligently weighted random walk starting at one labeled pixel will be at a certain time at a specific position in the dataset or determine the probability approximately by performing several random walks. While the weights of a random walk take into account local information at the starting point, the random walk itself can be in any dimension. Starting a great number of random walks in each labeled pixel, a voxel in the dataset will be hit by several random walks over time. Hence, the image can be segmented by assigning each voxel to the label where the random walks most likely started from. Due to the high scalability of random walks, this approach is suitable for high throughput measurements. Additionally, we describe an interactively adjusted active contours slice by slice method considering local information, where we start with one manually labeled slice and move forward in any direction. This approach is superior with respect to accuracy towards the diffusion algorithm but inferior in the amount of tedious manual processing steps. The methods were applied on 3D and 4D datasets and evaluated by means of manually labeled images obtained in a realistic scenario with biologists.