P. Thomas Fletcher

Aman Shrivastava, P. Thomas Fletcher

In recent years, computational pathology has seen tremendous progress driven by deep learning methods in segmentation and classification tasks aiding prognostic and diagnostic settings. Nuclei segmentation, for instance, is an important task for diagnosing different cancers. However, training deep learning models for nuclei segmentation requires large amounts of annotated data, which is expensive to collect and label. This necessitates explorations into generative modeling of histopathological images. In this work, we use recent advances in conditional diffusion modeling to formulate a first-of-its-kind nuclei-aware semantic tissue generation framework (NASDM) which can synthesize realistic tissue samples given a semantic instance mask of up to six different nuclei types, enabling pixel-perfect nuclei localization in generated samples. These synthetic images are useful in applications in pathology pedagogy, validation of models, and supplementation of existing nuclei segmentation datasets. We demonstrate that NASDM is able to synthesize high-quality histopathology images of the colon with superior quality and semantic controllability over existing generative methods.

Haocheng Dai, Martin Bauer, P. Thomas Fletcher et al.

The goal of diffusion-weighted magnetic resonance imaging (DWI) is to infer the structural connectivity of an individual subject's brain in vivo. To statistically study the variability and differences between normal and abnormal brain connectomes, a mathematical model of the neural connections is required. In this paper, we represent the brain connectome as a Riemannian manifold, which allows us to model neural connections as geodesics. This leads to the challenging problem of estimating a Riemannian metric that is compatible with the DWI data, i.e., a metric such that the geodesic curves represent individual fiber tracts of the connectomics. We reduce this problem to that of solving a highly nonlinear set of partial differential equations (PDEs) and study the applicability of convolutional encoder-decoder neural networks (CEDNNs) for solving this geometrically motivated PDE. Our method achieves excellent performance in the alignment of geodesics with white matter pathways and tackles a long-standing issue in previous geodesic tractography methods: the inability to recover crossing fibers with high fidelity.

Yinzhu Jin, Jonathan C. Garneau, P. Thomas Fletcher

This paper introduces feature gradient flow, a new technique for interpreting deep learning models in terms of features that are understandable to humans. The gradient flow of a model locally defines nonlinear coordinates in the input data space representing the information the model is using to make its decisions. Our idea is to measure the agreement of interpretable features with the gradient flow of a model. To then evaluate the importance of a particular feature to the model, we compare that feature's gradient flow measure versus that of a baseline noise feature. We then develop a technique for training neural networks to be more interpretable by adding a regularization term to the loss function that encourages the model gradients to align with those of chosen interpretable features. We test our method in a convolutional neural network prediction of distant metastasis of head and neck cancer from a computed tomography dataset from the Cancer Imaging Archive.

Yinzhu Jin, Matthew B. Dwyer, P. Thomas Fletcher

This paper introduces a new technique to measure the feature dependency of neural network models. The motivation is to better understand a model by querying whether it is using information from human-understandable features, e.g., anatomical shape, volume, or image texture. Our method is based on the principle that if a model is dependent on a feature, then removal of that feature should significantly harm its performance. A targeted feature is "removed" by collapsing the dimension in the data distribution that corresponds to that feature. We perform this by moving data points along the feature dimension to a baseline feature value while staying on the data manifold, as estimated by a deep generative model. Then we observe how the model's performance changes on the modified test data set, with the target feature dimension removed. We test our method on deep neural network models trained on synthetic image data with known ground truth, an Alzheimer's disease prediction task using MRI and hippocampus segmentations from the OASIS-3 dataset, and a cell nuclei classification task using the Lizard dataset.

Shen Zhu, Yinzhu Jin, Ifrah Zawar et al.

We propose a diffusion model designed to generate point-based shape representations with correspondences. Traditional statistical shape models have considered point correspondences extensively, but current deep learning methods do not take them into account, focusing on unordered point clouds instead. Current deep generative models for point clouds do not address generating shapes with point correspondences between generated shapes. This work aims to formulate a diffusion model that is capable of generating realistic point-based shape representations, which preserve point correspondences that are present in the training data. Using shape representation data with correspondences derived from Open Access Series of Imaging Studies 3 (OASIS-3), we demonstrate that our correspondence-preserving model effectively generates point-based hippocampal shape representations that are highly realistic compared to existing methods. We further demonstrate the applications of our generative model by downstream tasks, such as conditional generation of healthy and AD subjects and predicting morphological changes of disease progression by counterfactual generation.

Tyler Spears, Shen Zhu, Yinzhu Jin et al.

In this work, we introduce MedIL, a first-of-its-kind autoencoder built for encoding medical images with heterogeneous sizes and resolutions for image generation. Medical images are often large and heterogeneous, where fine details are of vital clinical importance. Image properties change drastically when considering acquisition equipment, patient demographics, and pathology, making realistic medical image generation challenging. Recent work in latent diffusion models (LDMs) has shown success in generating images resampled to a fixed-size. However, this is a narrow subset of the resolutions native to image acquisition, and resampling discards fine anatomical details. MedIL utilizes implicit neural representations to treat images as continuous signals, where encoding and decoding can be performed at arbitrary resolutions without prior resampling. We quantitatively and qualitatively show how MedIL compresses and preserves clinically-relevant features over large multi-site, multi-resolution datasets of both T1w brain MRIs and lung CTs. We further demonstrate how MedIL can influence the quality of images generated with a diffusion model, and discuss how MedIL can enhance generative models to resemble raw clinical acquisitions.

Shen Zhu, Yinzhu Jin, Tyler Spears et al.

We propose image-to-image diffusion models that are designed to enhance the realism and details of generated brain images by introducing sharp edges, fine textures, subtle anatomical features, and imaging noise. Generative models have been widely adopted in the biomedical domain, especially in image generation applications. Latent diffusion models achieve state-of-the-art results in generating brain MRIs. However, due to latent compression, generated images from these models are overly smooth, lacking fine anatomical structures and scan acquisition noise that are typically seen in real images. This work formulates the realism enhancing and detail adding process as image-to-image diffusion models, which refines the quality of LDM-generated images. We employ commonly used metrics like FID and LPIPS for image realism assessment. Furthermore, we introduce new metrics to demonstrate the realism of images generated by RealDeal in terms of image noise distribution, sharpness, and texture.

Sofia Ivolgina, P. Thomas Fletcher, Baba C. Vemuri

Batch normalization (BN) is a ubiquitous operation in deep neural networks used primarily to achieve stability and regularization during network training. BN involves feature map centering and scaling using sample means and variances, respectively. Since these statistics are being estimated across the feature maps within a batch, this problem is ideally suited for the application of Stein's shrinkage estimation, which leads to a better, in the mean-squared-error sense, estimate of the mean and variance of the batch. In this paper, we prove that the Stein shrinkage estimator for the mean and variance dominates over the sample mean and variance estimators in the presence of adversarial attacks when modeling these attacks using sub-Gaussian distributions. This facilitates and justifies the application of Stein shrinkage to estimate the mean and variance parameters in BN and use it in image classification (segmentation) tasks with and without adversarial attacks. We present SOTA performance results using this Stein corrected batch norm in a standard ResNet architecture applied to the task of image classification using CIFAR-10 data, 3D CNN on PPMI (neuroimaging) data and image segmentation using HRNet on Cityscape data with and without adversarial attacks.

Tyler Spears, P. Thomas Fletcher

Our understanding of the human connectome is fundamentally limited by the resolution of diffusion MR images. Reconstructing a connectome's constituent neural pathways with tractography requires following a continuous field of fiber directions. Typically, this field is found with simple trilinear interpolation in low-resolution, noisy diffusion MRIs. However, trilinear interpolation struggles following fine-scale changes in low-quality data. Recent deep learning methods in super-resolving diffusion MRIs have focused on upsampling to a fixed spatial grid, but this does not satisfy tractography's need for a continuous field. In this work, we propose FENRI, a novel method that learns spatially-continuous fiber orientation density functions from low-resolution diffusion-weighted images. To quantify FENRI's capabilities in tractography, we also introduce an expanded simulated dataset built for evaluating deep-learning tractography models. We demonstrate that FENRI accurately predicts high-resolution fiber orientations from realistic low-quality data, and that FENRI-based tractography offers improved streamline reconstruction over the current use of trilinear interpolation.

Kristen M. Campbell, Haocheng Dai, Zhe Su et al.

The structural network of the brain, or structural connectome, can be represented by fiber bundles generated by a variety of tractography methods. While such methods give qualitative insights into brain structure, there is controversy over whether they can provide quantitative information, especially at the population level. In order to enable population-level statistical analysis of the structural connectome, we propose representing a connectome as a Riemannian metric, which is a point on an infinite-dimensional manifold. We equip this manifold with the Ebin metric, a natural metric structure for this space, to get a Riemannian manifold along with its associated geometric properties. We then use this Riemannian framework to apply object-oriented statistical analysis to define an atlas as the Fréchet mean of a population of Riemannian metrics. This formulation ties into the existing framework for diffeomorphic construction of image atlases, allowing us to construct a multimodal atlas by simultaneously integrating complementary white matter structure details from DWMRI and cortical details from T1-weighted MRI. We illustrate our framework with 2D data examples of connectome registration and atlas formation. Finally, we build an example 3D multimodal atlas using T1 images and connectomes derived from diffusion tensors estimated from a subset of subjects from the Human Connectome Project.

Kristen M. Campbell, Haocheng Dai, Zhe Su et al.

The structural connectome is often represented by fiber bundles generated from various types of tractography. We propose a method of analyzing connectomes by representing them as a Riemannian metric, thereby viewing them as points in an infinite-dimensional manifold. After equipping this space with a natural metric structure, the Ebin metric, we apply object-oriented statistical analysis to define an atlas as the Fréchet mean of a population of Riemannian metrics. We demonstrate connectome registration and atlas formation using connectomes derived from diffusion tensors estimated from a subset of subjects from the Human Connectome Project.

Chenxiao Zhao, P. Thomas Fletcher, Mixue Yu et al.

Many deep learning models are vulnerable to the adversarial attack, i.e., imperceptible but intentionally-designed perturbations to the input can cause incorrect output of the networks. In this paper, using information geometry, we provide a reasonable explanation for the vulnerability of deep learning models. By considering the data space as a non-linear space with the Fisher information metric induced from a neural network, we first propose an adversarial attack algorithm termed one-step spectral attack (OSSA). The method is described by a constrained quadratic form of the Fisher information matrix, where the optimal adversarial perturbation is given by the first eigenvector, and the model vulnerability is reflected by the eigenvalues. The larger an eigenvalue is, the more vulnerable the model is to be attacked by the corresponding eigenvector. Taking advantage of the property, we also propose an adversarial detection method with the eigenvalues serving as characteristics. Both our attack and detection algorithms are numerically optimized to work efficiently on large datasets. Our evaluations show superior performance compared with other methods, implying that the Fisher information is a promising approach to investigate the adversarial attacks and defenses.

Hang Shao, Abhishek Kumar, P. Thomas Fletcher

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. However, further investigation into this phenomenon is warranted, to identify if there are other architectures or datasets where curvature plays a more prominent role. We believe that exploring the Riemannian geometry of deep generative models, using the tools developed in this paper, will be an important step in understanding the high-dimensional, nonlinear spaces these models learn.

Abhishek Kumar, Prasanna Sattigeri, P. Thomas Fletcher

Semi-supervised learning methods using Generative Adversarial Networks (GANs) have shown promising empirical success recently. Most of these methods use a shared discriminator/classifier which discriminates real examples from fake while also predicting the class label. Motivated by the ability of the GANs generator to capture the data manifold well, we propose to estimate the tangent space to the data manifold using GANs and employ it to inject invariances into the classifier. In the process, we propose enhancements over existing methods for learning the inverse mapping (i.e., the encoder) which greatly improves in terms of semantic similarity of the reconstructed sample with the input sample. We observe considerable empirical gains in semi-supervised learning over baselines, particularly in the cases when the number of labeled examples is low. We also provide insights into how fake examples influence the semi-supervised learning procedure.

Anant Raj, Abhishek Kumar, Youssef Mroueh et al.

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distribution over the group which in turn induces distributions in the input feature space. We learn a decision function over these distributions by appealing to the powerful framework of kernel methods and generate local invariant random feature maps via kernel approximations. We show uniform convergence bounds for kernel approximation and provide excess risk bounds for learning with these features. We evaluate our method on three real datasets, including Rotated MNIST and CIFAR-10, and observe that it outperforms competing kernel based approaches. The proposed method also outperforms deep CNN on Rotated-MNIST and performs comparably to the recently proposed group-equivariant CNN.

Jacob Hinkle, Prasanna Muralidharan, P. Thomas Fletcher et al.

In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Bookstein as well as the analysis of the shape changes associated with aging of the corpus callosum from the OASIS Alzheimer's study.