COLLATOR: Consistent spatial-temporal longitudinal atlas construction via implicit neural representation

Longitudinal brain atlases that present brain development trend along time, are essential tools for brain development studies. However, conventional methods construct these atlases by independently averaging brain images from different individuals at discrete time points. This approach could introduce temporal inconsistencies due to variations in ontogenetic trends among samples, potentially affecting accuracy of brain developmental characteristic analysis. In this paper, we propose an implicit neural representation (INR)-based framework to improve the temporal consistency in longitudinal atlases. We treat temporal inconsistency as a 4-dimensional (4D) image denoising task, where the data consists of 3D spatial information and 1D temporal progression. We formulate the longitudinal atlas as an implicit function of the spatial-temporal coordinates, allowing structural inconsistency over the time to be considered as 3D image noise along age. Inspired by recent self-supervised denoising methods (e.g. Noise2Noise), our approach learns the noise-free and temporally continuous implicit function from inconsistent longitudinal atlas data. Finally, the time-consistent longitudinal brain atlas can be reconstructed by evaluating the denoised 4D INR function at critical brain developing time points. We evaluate our approach on three longitudinal brain atlases of different MRI modalities, demonstrating that our method significantly improves temporal consistency while accurately preserving brain structures. Additionally, the continuous functions generated by our method enable the creation of 4D atlases with higher spatial and temporal resolution. Code: https://github.com/maopaom/COLLATOR.