Figure 11.

Similarity Computed Across Images After Normalization with covariance matrix V ar(β̂) of the noise calculated using Eqn. (9), i.e. under heteroskedasticity of the noise in the tensor elements. To compute similarity between tensors across the two images normalized into the common space, we consider the tensors in the normalized image as perturbations of the tensors in the other image. The noise in the tensor elements is multivariate Gaussian that is assumed to be independently distributed across images from two individuals. Assuming heteroskedasticity, we computed noise variance in tensor elements using two methods: (a) because the noise in the two images is independently Gaussian distributed, we computed the covariance matrix of the noise as the sum of the two covariance matrices V ar(β̂) of the noise in the two images, and (b) using the larger matrix of the two covariance matrices in the two images. We then used the estimated covariance matrix to compute similarity between tensors at corresponding locations across the two images. The number of tensors with similarity greater than 0.5 in the normalized images increased by (a) 930 %, and (b) 422 % as compared to those in images before normalization (Fig. 9, top row).