uniGradICON: A Foundation Model for Medical Image Registration

Conventional medical image registration approaches directly optimize over the parameters of a transformation model. These approaches have been highly successful and are used generically for registrations of different anatomical regions. Recent deep registration networks are incredibly fast and accurate but are only trained for specific tasks. Hence, they are no longer generic registration approaches. We therefore propose uniGradICON, a first step toward a foundation model for registration providing 1) great performance \emph{across} multiple datasets which is not feasible for current learning-based registration methods, 2) zero-shot capabilities for new registration tasks suitable for different acquisitions, anatomical regions, and modalities compared to the training dataset, and 3) a strong initialization for finetuning on out-of-distribution registration tasks. UniGradICON unifies the speed and accuracy benefits of learning-based registration algorithms with the generic applicability of conventional non-deep-learning approaches. We extensively trained and evaluated uniGradICON on twelve different public datasets. Our code and the uniGradICON model are available at https://github.com/uncbiag/uniGradICON.

Position Paper: Challenges and Opportunities in Topological Deep Learning

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

Latent SDEs on Homogeneous Spaces

We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the solution of a latent stochastic differential equation (SDE). Motivated by the challenges that arise when trying to learn an (almost arbitrary) latent neural SDE from large-scale data, such as efficient gradient computation, we take a step back and study a specific subclass instead. In our case, the SDE evolves on a homogeneous latent space and is induced by stochastic dynamics of the corresponding (matrix) Lie group. In learning problems, SDEs on the unit $n$-sphere are arguably the most relevant incarnation of this setup. Notably, for variational inference, the sphere not only facilitates using a truly uninformative prior SDE, but we also obtain a particularly simple and intuitive expression for the Kullback-Leibler divergence between the approximate posterior and prior process in the evidence lower bound. Experiments demonstrate that a latent SDE of the proposed type can be learned efficiently by means of an existing one-step geometric Euler-Maruyama scheme. Despite restricting ourselves to a less diverse class of SDEs, we achieve competitive or even state-of-the-art performance on various time series interpolation and classification benchmarks.

Inverse Consistency by Construction for Multistep Deep Registration

Inverse consistency is a desirable property for image registration. We propose a simple technique to make a neural registration network inverse consistent by construction, as a consequence of its structure, as long as it parameterizes its output transform by a Lie group. We extend this technique to multi-step neural registration by composing many such networks in a way that preserves inverse consistency. This multi-step approach also allows for inverse-consistent coarse to fine registration. We evaluate our technique on synthetic 2-D data and four 3-D medical image registration tasks and obtain excellent registration accuracy while assuring inverse consistency.

GradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency

Many registration approaches exist with early work focusing on optimization-based approaches for image pairs. Recent work focuses on deep registration networks to predict spatial transformations. In both cases, commonly used non-parametric registration models, which estimate transformation functions instead of low-dimensional transformation parameters, require choosing a suitable regularizer (to encourage smooth transformations) and its parameters. This makes models difficult to tune and restricts deformations to the deformation space permissible by the chosen regularizer. While deep-learning models for optical flow exist that do not regularize transformations and instead entirely rely on the data these might not yield diffeomorphic transformations which are desirable for medical image registration. In this work, we therefore develop GradICON building upon the unsupervised ICON deep-learning registration approach, which only uses inverse-consistency for regularization. However, in contrast to ICON, we prove and empirically verify that using a gradient inverse-consistency loss not only significantly improves convergence, but also results in a similar implicit regularization of the resulting transformation map. Synthetic experiments and experiments on magnetic resonance (MR) knee images and computed tomography (CT) lung images show the excellent performance of GradICON. We achieve state-of-the-art (SOTA) accuracy while retaining a simple registration formulation, which is practically important.

On Measuring Excess Capacity in Neural Networks

We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class -- in our case, Rademacher complexity -- how much can we (a-priori) constrain this class while maintaining an empirical error comparable to the unconstrained setting. To assess excess capacity in modern architectures, we first extend an existing generalization bound to accommodate function composition and addition, as well as the specific structure of convolutions. This then facilitates studying residual networks through the lens of the accompanying capacity measure. The key quantities driving this measure are the Lipschitz constants of the layers and the (2,1) group norm distance to the initializations of the convolution weights. We show that these quantities (1) can be kept surprisingly small and, (2) since excess capacity unexpectedly increases with task difficulty, this points towards an unnecessarily large capacity of unconstrained models.

Comparing object recognition in humans and deep convolutional neural networks -- An eye tracking study

Deep convolutional neural networks (DCNNs) and the ventral visual pathway share vast architectural and functional similarities in visual challenges such as object recognition. Recent insights have demonstrated that both hierarchical cascades can be compared in terms of both exerted behavior and underlying activation. However, these approaches ignore key differences in spatial priorities of information processing. In this proof-of-concept study, we demonstrate a comparison of human observers (N = 45) and three feedforward DCNNs through eye tracking and saliency maps. The results reveal fundamentally different resolutions in both visualization methods that need to be considered for an insightful comparison. Moreover, we provide evidence that a DCNN with biologically plausible receptive field sizes called vNet reveals higher agreement with human viewing behavior as contrasted with a standard ResNet architecture. We find that image-specific factors such as category, animacy, arousal, and valence have a direct link to the agreement of spatial object recognition priorities in humans and DCNNs, while other measures such as difficulty and general image properties do not. With this approach, we try to open up new perspectives at the intersection of biological and computer vision research.

Topological Attention for Time Series Forecasting

The problem of (point) forecasting $ \textit{univariate} $ time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time series observations. As an extension, we study whether $\textit{local topological properties}$, as captured via persistent homology, can serve as a reliable signal that provides complementary information for learning to forecast. To this end, we propose $\textit{topological attention}$, which allows attending to local topological features within a time horizon of historical data. Our approach easily integrates into existing end-to-end trainable forecasting models, such as $\texttt{N-BEATS}$, and in combination with the latter exhibits state-of-the-art performance on the large-scale M4 benchmark dataset of 100,000 diverse time series from different domains. Ablation experiments, as well as a comparison to a broad range of forecasting methods in a setting where only a single time series is available for training, corroborate the beneficial nature of including local topological information through an attention mechanism.

ICON: Learning Regular Maps Through Inverse Consistency

Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformations. Such maps relate feature vectors, or map between feature spaces. Well-behaved maps should be regular, which can be imposed explicitly or may emanate from the data itself. We explore what induces regularity for spatial transformations, e.g., when computing image registrations. Classical optimization-based models compute maps between pairs of samples and rely on an appropriate regularizer for well-posedness. Recent deep learning approaches have attempted to avoid using such regularizers altogether by relying on the sample population instead. We explore if it is possible to obtain spatial regularity using an inverse consistency loss only and elucidate what explains map regularity in such a context. We find that deep networks combined with an inverse consistency loss and randomized off-grid interpolation yield well behaved, approximately diffeomorphic, spatial transformations. Despite the simplicity of this approach, our experiments present compelling evidence, on both synthetic and real data, that regular maps can be obtained without carefully tuned explicit regularizers, while achieving competitive registration performance.