Hough Based Evolutions for Enhancing Structures in 3D Electron Microscopy

Connecting interrupted line-like structures is a frequent problem in image processing. Here we focus on the specific needs that occur in 3D biophysical data analysis in electron microscopy (EM). We introduce a powerful framework for connecting line-like structures in 3D data sets by combining a specific semilocal Hough transform with a directional evolution equation. The Hough transform allows to find the principal orientations of the local structures in a robust way, and the evolution equation is designed as a partial differential equation that smoothes along these principal orientations. We evaluate the performance of our method for enhancing structures in both synthetic and real-world EM data. In contrast to traditional structure tensor based methods such as coherence-enhancing diffusion, our method can handle the missing wedge problem in EM, also known as limited angle tomography problem. A modified version of our approach is also able to tackle the discontinuities created due to the contrast transfer function correction of EM images.