Metal artifacts arise in CT images when X-rays traverse the high attenuating objects such as metal bodies. Portions of projection data become unavailable. In this paper, we present an Euler's elastica and curvature based sinogram inpainting (EECSI) algorithm for metal artifacts reduction, where "inpainting" is a synonym for "image interpolation". In EECSI, the unavailable data are regarded as occlusion and can be inpainted inside the inpainting domain based on elastica interpolants. Numerical simulations demonstrate that, compared to conventional interpolation methods, the algorithm proposed connects the unavailable projection region more smoothly and accurately, thus better reduces metal artifacts and more accurately reveals cross section structures, especially in the immediate neighborhood of the metallic objects.
Image segmentation is a classical and challenging problem in image processing and computer vision. Most of the segmentation algorithms, however, do not consider overlapped objects. Due to the special characteristics of X-ray imaging, the overlapping of objects is very commonly seen in X-ray images and needs to be carefully dealt with. In this paper, we propose a novel energy functional to solve this problem. The Euler-Lagrange equation is derived and the segmentation is converted to a front propagating problem that can be efficiently solved by level set methods. We noticed that the proposed energy functional has no unique extremum and the solution relies on the initialization. Thus, an initialization method is proposed to get satisfying results. The experiment on real data validated our proposed method.