Binary morphology has innumerable applications in biomedical imaging, from segmentation to denoising. However, it suffers from inherently low precision. This is primarily because binary morphology is a binary technique, where each image voxel is all-or-nothing included or excluded. Many desirable structuring element shapes, especially circles or spheres, are poorly approximated on regular grids. Making things worse, common workflows involving multiple binary morphology iterations, such as opening or closing, compound this error. Also, small structuring elements often cannot be applied to 3D anisotropic image volumes. This work describes an extension to the theory of binary morphology, dubbed partial volume morphology or PVM, which allows the structuring element and/or image to hold fractional gray values to account for partial volumes. Partial volume morphology enables arbitrarily shaped structuring elements to be used, regardless of the underlying image resolution, with arbitrary precision. This technique also extends to 3D anisotropic volumes, allowing high precision morphological operations in anisotropic datasets heretofore impossible with binary morphology. This technique can be applied to a binary segmentation, where it provides subtle improvements and eliminates precision error in the intermediate steps of a multiple-operation workflow. Additionally, PVM is particularly suited for use on ‘soft’ segmentated data, where the partial volume contribution or probability at each point can be found. With segmentation and structuring elements both partial volume aware, partial volume morphology reaches its full potential as a high precision analytical tool. An open source reference implementation in Python, pvmpy, is provided.