The use of transport and diffusion equations in the three-dimensional reconstruction of computerized tomographic images

The visualization of a computerized tomographic (TC) exam in 3D increases the quality of the medical diagnosis and, consequently, the success probability in the treatment. To obtain a high quality image it is necessary to obtain slices which are close to one another. Motivated towards the goal of reaching an improved balance between quantity of slices and visualization quality, this research work presents a digital inpainting technique of 3D interpolation for CT slices used in the visualization of human body structures. The inpainting is carried out via non-linear partial differential equations (PDE). The PDE’s have been used, in the image-processing context to fill in the damaged regions in a digital 2D image. Inspired by this idea, this article proposes an interpolation method for the filling in of the empty regions between the CT slices. To do it, considering the high similarity between two consecutive real slice, the first step of the proposed method is to create the virtual slices. The virtual slices contain all similarity between the intercaleted slices and, when there aren’t similarities between real slices, the virtual slices will contain indefinite portions. In the second step of the proposed method, the created virtual slices will be used together with the real slices images, in the reconstruction of the structure in three dimensions, mapped onto the exam. The proposed method is capable of reconstructing the curvatures of the patient’s internal structures without using slices that are close to one another. The experiments carried out show the proposed method’s efficiency.