We present a novel learning-based spherical registration method, called SPHARM-Reg, tailored for establishing cortical shape correspondence. SPHARM-Reg aims to reduce warp distortion that can introduce biases in downstream shape analyses. To achieve this, we tackle two critical challenges: (1) joint rigid and non-rigid alignments and (2) rotation-preserving smoothing. Conventional approaches perform rigid alignment only once before a non-rigid alignment. The resulting rotation is potentially sub-optimal, and the subsequent non-rigid alignment may introduce unnecessary distortion. In addition, common velocity encoding schemes on the unit sphere often fail to preserve the rotation component after spatial smoothing of velocity. To address these issues, we propose a diffeomorphic framework that integrates spherical harmonic decomposition of the velocity field with a novel velocity encoding scheme. SPHARM-Reg optimizes harmonic components of the velocity field, enabling joint adjustments for both rigid and non-rigid alignments. Furthermore, the proposed encoding scheme using spherical functions encourages consistent smoothing that preserves the rotation component. In the experiments, we validate SPHARM-Reg on healthy adult datasets. SPHARM-Reg achieves a substantial reduction in warp distortion while maintaining a high level of registration accuracy compared to existing methods. In the clinical analysis, we show that the extent of warp distortion significantly impacts statistical significance.

The identification of cortical sulci is key for understanding functional and structural development of the cortex. While large, consistent sulci (or primary/secondary sulci) receive significant attention in most studies, the exploration of smaller and more variable sulci (or putative tertiary sulci) remains relatively under-investigated. Despite its importance, automatic labeling of cortical sulci is challenging due to (1) the presence of substantial anatomical variability, (2) the relatively small size of the regions of interest (ROIs) compared to unlabeled regions, and (3) the scarcity of annotated labels. In this paper, we propose a novel end-to-end learning framework using a spherical convolutional neural network (CNN). Specifically, the proposed method learns to effectively warp geometric features in a direction that facilitates the labeling of sulci while mitigating the impact of anatomical variability. Moreover, we introduce a guided-attention mechanism that takes into account the extent of deformation induced by the learned warping. This extracts discriminative features that emphasize sulcal ROIs, while suppressing irrelevant information of unlabeled regions. In the experiments, we evaluate the proposed method on 8 sulci of the posterior medial cortex. Our method outperforms existing methods particularly in the putative tertiary sulci. The code is publicly available at https://github.com/Shape-Lab/DSPHARM-Net.

We present a spherical harmonics-based convolutional neural network (CNN) for cortical parcellation, which we call SPHARM-Net. Recent advances in CNNs offer cortical parcellation on a fine-grained triangle mesh of the cortex. Yet, most CNNs designed for cortical parcellation employ spatial convolution that depends on extensive data augmentation and allows only predefined neighborhoods of specific spherical tessellation. On the other hand, a rotation-equivariant convolutional filter avoids data augmentation, and rotational equivariance can be achieved in spectral convolution independent of a neighborhood definition. Nevertheless, the limited resources of a modern machine enable only a finite set of spectral components that might lose geometric details. In this paper, we propose (1) a constrained spherical convolutional filter that supports an infinite set of spectral components and (2) an end-to-end framework without data augmentation. The proposed filter encodes all the spectral components without the full expansion of spherical harmonics. We show that rotational equivariance drastically reduces the training time while achieving accurate cortical parcellation. Furthermore, the proposed convolution is fully composed of matrix transformations, which offers efficient and fast spectral processing. In the experiments, we validate SPHARM-Net on two public datasets with manual labels: Mindboggle-101 (N=101) and NAMIC (N=39). The experimental results show that the proposed method outperforms the state-of-the-art methods on both datasets even with fewer learnable parameters without rigid alignment and data augmentation. Our code is publicly available at https://github.com/Shape-Lab/SPHARM-Net.

Body part regression is a promising new technique that enables content navigation through self-supervised learning. Using this technique, the global quantitative spatial location for each axial view slice is obtained from computed tomography (CT). However, it is challenging to define a unified global coordinate system for body CT scans due to the large variabilities in image resolution, contrasts, sequences, and patient anatomy. Therefore, the widely used supervised learning approach cannot be easily deployed. To address these concerns, we propose an annotation-free method named blind-unsupervised-supervision network (BUSN). The contributions of the work are in four folds: (1) 1030 multi-center CT scans are used in developing BUSN without any manual annotation. (2) the proposed BUSN corrects the predictions from unsupervised learning and uses the corrected results as the new supervision; (3) to improve the consistency of predictions, we propose a novel neighbor message passing (NMP) scheme that is integrated with BUSN as a statistical learning based correction; and (4) we introduce a new pre-processing pipeline with inclusion of the BUSN, which is validated on 3D multi-organ segmentation. The proposed method is trained on 1,030 whole body CT scans (230,650 slices) from five datasets, as well as an independent external validation cohort with 100 scans. From the body part regression results, the proposed BUSN achieved significantly higher median R-squared score (=0.9089) than the state-of-the-art unsupervised method (=0.7153). When introducing BUSN as a preprocessing stage in volumetric segmentation, the proposed pre-processing pipeline using BUSN approach increases the total mean Dice score of the 3D abdominal multi-organ segmentation from 0.7991 to 0.8145.

Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate numerical scheme to solve heat diffusion on surface meshes. This is achieved by approximating the heat kernel convolution using high degree orthogonal polynomials in the spectral domain. We also derive the closed-form expression of the spectral decomposition of the Laplace-Beltrami operator and use it to solve heat diffusion on a manifold for the first time. The proposed fast polynomial approximation scheme avoids solving for the eigenfunctions of the Laplace-Beltrami operator, which is computationally costly for large mesh size, and the numerical instability associated with the finite element method based diffusion solvers. The proposed method is applied in localizing the male and female differences in cortical sulcal and gyral graph patterns obtained from MRI in an innovative way. The MATLAB code is available at http://www.stat.wisc.edu/~mchung/chebyshev.

Big data medical image processing applications involving multi-stage analysis often exhibit significant variability in processing times ranging from a few seconds to several days. Moreover, due to the sequential nature of executing the analysis stages enforced by traditional software technologies and platforms, any errors in the pipeline are only detected at the later stages despite the sources of errors predominantly being the highly compute-intensive first stage. This wastes precious computing resources and incurs prohibitively higher costs for re-executing the application. The medical image processing community to date remains largely unaware of these issues and continues to use traditional high-performance computing clusters, which incur a high operating cost due to the use of dedicated resources and expensive centralized file systems. To overcome these challenges, this paper proposes an alternative approach for multi-stage analysis in medical image processing by using the Apache Hadoop ecosystem and offering it as a service in the cloud. We make the following contributions. First, we propose a concurrent pipeline execution framework and an associated semi-automatic, real-time monitoring and checkpointing framework that can detect outliers and achieve quality assurance without having to completely execute the expensive first stage of processing thereby expediting the entire multi-stage analysis. Second, we present a simulator to rapidly estimate the execution time for a given multi-stage analysis, which can aid the users in deciding the appropriate approach for their use cases. We conduct empirical evaluation of our framework and show that it requires 76.75% lesser wall time and 29.22% lesser resource time compared to the traditional approach that lacks such a quality assurance mechanism.

We present novel spherical deformation for a landmark-free shape correspondence in a group-wise manner. In this work, we aim at both addressing template selection bias and minimizing registration distortion in a single framework. The proposed spherical deformation yields a non-rigid deformation field without referring to any particular spherical coordinate system. Specifically, we extend a rigid rotation represented by well-known Euler angles to general non-rigid local deformation via spatial-varying Euler angles. The proposed method employs spherical harmonics interpolation of the local displacements to simultaneously solve rigid and non-rigid local deformation during the optimization. This consequently leads to a continuous, smooth, and hierarchical representation of the deformation field that minimizes registration distortion. In addition, the proposed method is group-wise registration that requires no specific template to establish a shape correspondence. In the experiments, we show an improved shape correspondence with high accuracy in cortical surface parcellation as well as significantly low registration distortion in surface area and edge length compared to the existing registration methods while achieving fast registration in 3 mins per subject.

A proper geometric representation of the cortical regions is a fundamental task for cortical shape analysis and landmark extraction. However, a significant challenge has arisen due to the highly variable, convoluted cortical folding patterns. In this paper, we propose a novel topological graph representation for automatic sulcal curve extraction (TRACE). In practice, the reconstructed surface suffers from noise influences introduced during image acquisition/surface reconstruction. In the presence of noise on the surface, TRACE determines stable sulcal fundic regions by employing the line simplification method that prevents the sulcal folding pattern from being significantly smoothed out. The sulcal curves are then traced over the connected graph in the determined regions by the Dijkstra's shortest path algorithm. For validation, we used the state-of-the-art surface reconstruction pipelines on a reproducibility data set. The experimental results showed higher reproducibility and robustness to noise in TRACE than the existing method (Li et al. 2010) with over 20% relative improvement in error for both surface reconstruction pipelines. In addition, the extracted sulcal curves by TRACE were well-aligned with manually delineated primary sulcal curves. We also provided a choice of parameters to control quality of the extracted sulcal curves and showed the influences of the parameter selection on the resulting curves.