Diffeomorphic Registration With Intensity Transformation and Missing Data: Application to 3D Digital Pathology of Alzheimer's Disease

Abstract

This paper examines the problem of diffeomorphic image registration in the presence of differing image intensity profiles and sparsely sampled, missing, or damaged tissue. Our motivation comes from the problem of aligning 3D brain MRI with 100-micron isotropic resolution to histology sections at 1 × 1 × 1,000-micron resolution with multiple varying stains. We pose registration as a penalized Bayesian estimation, exploiting statistical models of image formation where the target images are modeled as sparse and noisy observations of the atlas. In this injective setting, there is no assumption of symmetry between atlas and target. Cross-modality image matching is achieved by jointly estimating polynomial transformations of the atlas intensity. Missing data is accommodated via a multiple atlas selection procedure where several atlas images may be of homogeneous intensity and correspond to "background" or "artifact." The two concepts are combined within an Expectation-Maximization algorithm, where atlas selection posteriors and deformation parameters are updated iteratively and polynomial coefficients are computed in closed form. We validate our method with simulated images, examples from neuropathology, and a standard benchmarking dataset. Finally, we apply it to reconstructing digital pathology and MRI in standard atlas coordinates. By using a standard convolutional neural network to detect tau tangles in histology slices, this registration method enabled us to quantify the 3D density distribution of tauopathy throughout the medial temporal lobe of an Alzheimer's disease postmortem specimen.

Virtual Mouse Brain Histology from Multi-contrast MRI via Deep Learning

“…The present study focused on inferring maps of key cellular structures in the mouse brain from MRI signals. Previous works on this problem include: new MRI contrasts that capture specific aspects of cellular structures of interest [21][22][23][24] ; carefully constructed tissue models for MR signals [25][26][27][28] ; statistical methods to extract relevant information from multi-contrast MRI 8 ; and techniques to register histology and MRI data [29][30][31] to produce ground truth for validation [32][33][34] . Here, we built on these efforts by demonstrating that deep learning networks trained by co-registered histological and MRI data can improve our ability to detect target cellular structures.…”

CloudReg: Automatic Terabyte-Scale Cross-Modal Brain Volume Registration

“…(EM-LDDMM) registration algorithm that we previously developed. 15 Our extension of EM-LDDMM built into CloudReg enables cross-modal registration of a diversity of brain volume samples with artifacts, tears, and deformations (Supplemental Figure 4).…”

EM-LDDMM for 3D to 2D registration

“…Missing tissue or artifacts are incorporated via Gaussian mixture modeling at each pixel, as described in [12]. This model corresponds to a penalized likelihood optimization algorithm that minimizes weighted sum of square error with weight W i (y 1 , y 2 ).…”

“…Unknown parameters v, w, S, R, θ are estimated using the EM algorithm as described in [12]. In the E step, W is calculated as the posterior probability that each pixel corresponds to a deformation of the atlas (as opposed to an artifact or missing tissue).…”

“…This paper focuses on the 3D reconstruction of a sparse set of tissue slices, guided by using a well characterized atlas. Slices may be different modalities or have missing tissue or artifacts, using the approaches described in [12]. For accommodating sparse sectioning, no assumption of similarity between neighboring slices is necessary.…”