Variational-based segmentation of bio-pores in tomographic images

X-ray computed tomography (CT) combined with a quantitative analysis of the resulting volume images is a fruitful technique in soil science. However, the variations in X-ray attenuation due to different soil components keep the segmentation of single components within these highly heterogeneous samples a challenging problem. Particularly demanding are bio-pores due to their elongated shape and the low gray value difference to the surrounding soil structure. Recently, variational models in connection with algorithms from convex optimization were successfully applied for image segmentation. In this paper we apply these methods for the first time for the segmentation of bio-pores in CT images of soil samples. We introduce a novel convex model which enforces smooth boundaries of bio-pores and takes the varying attenuation values in the depth into account. Segmentation results are reported for different real-world 3D data sets as well as for simulated data. These results are compared with two gray value thresholding methods, namely indicator kriging and a global thresholding procedure, and with a morphological approach. Pros and cons of the methods are assessed by considering geometric features of the segmented bio-pore systems. The variational approach features well-connected smooth pores while not detecting smaller or shallower pores. This is an advantage in cases where the main bio-pores network is of interest and where infillings, e.g., excrements of earthworms, would result in losing pore connections as observed for the other thresholding methods.