Three-Dimensional Data Compression with Anisotropic Diffusion

In 2-D image compression, recent approaches based on image inpainting with edge-enhancing anisotropic diffusion (EED) rival the transform-based quasi-standards JPEG and JPEG 2000 and are even able to surpass it. In this paper, we extend successful concepts from these 2-D methods to the 3-D setting, thereby establishing the first PDE-based 3-D image compression algorithm. This codec uses a cuboidal subdivision strategy to select and efficiently store a small set of sparse image data and reconstructs missing image parts with EED-based inpainting. An evaluation on real-world medical data substantiates the superior performance of this new algorithm in comparison to 2-D inpainting methods and the compression standard DICOM for medical data.