Partial volume effects (PVE) present a source of confound for the analysis of functional imaging data. Correction for PVE requires estimates of the partial volumes (PVs) present in an image. These estimates are conventionally obtained via volumetric segmentation, but such an approach may not be accurate for complex structures such as the cortex. An alternative is to use surface-based segmentation, which is well-established within the literature. Toblerone is a new method for estimating PVs using such surfaces. It uses a purely geometric approach that considers the intersection between a surface and the voxels of an image. In contrast to existing surface-based techniques, Toblerone is not restricted to use with any particular structure or modality. Evaluation in a neuroimaging context has been performed on simulated surfaces, simulated T1-weighted MRI images and finally a Human Connectome Project test-retest dataset. A comparison has been made to two existing surface-based methods; in all analyses Toblerone's performance either matched or surpassed the comparator methods. Evaluation results also show that compared to an existing volumetric method (FSL FAST), a surface-based approach with Toblerone offers improved robustness to scanner noise and field non-uniformity, and better inter-session repeatability in brain volume. In contrast to volumetric methods, a surface-based approach negates the need to perform resampling which is advantageous at the resolutions typically used for neuroimaging.