Efficient Pairwise Neuroimage Analysis using the Soft Jaccard Index and 3D Keypoint Sets

We propose a novel pairwise distance measure between variable-sized sets of image keypoints for the purpose of large-scale medical image indexing. Our measure generalizes the Jaccard index to account for soft set equivalence (SSE) between set elements, via an adaptive kernel framework accounting for uncertainty in keypoint appearance and geometry. Novel kernels are proposed to quantify the variability of keypoint geometry in location and scale. Our distance measure may be estimated between $N^2$ image pairs in $O(N~\log~N)$ operations via keypoint indexing. Experiments validate our method in predicting 509,545 pairwise relationships from T1-weighted MRI brain volumes of monozygotic and dizygotic twins, siblings and half-siblings sharing 100%-25% of their polymorphic genes. Soft set equivalence and keypoint geometry kernels outperform standard hard set equivalence (HSE) in predicting family relationships. High accuracy is achieved, with monozygotic twin identification near 100% and several cases of unknown family labels, due to errors in the genotyping process, are correctly paired with family members. Software is provided for efficient fine-grained curation of large, generic image datasets.