Baba Vemuri

• PhD
• Professor at University of Florida

Nonrigid registration is vital to medical image analysis but remains challenging for diffusion MRI (dMRI) due to its high-dimensional, orientation-dependent nature. While classical methods are accurate, they are computationally demanding, and deep neural networks, though efficient, have been underexplored for nonrigid dMRI registration compared to...

Distributional comparison is a fundamental problem in statistical data analysis with numerous applications in a variety of fields including but not limited to Sciences and Engineering. Numerous methods exist for distributional comparison but Kernel Stein Discrepancy (KSD) has gained significant popularity in recent times. In this paper, we present...

Distributional approximation is a fundamental problem in machine learning with numerous applications across all fields of science and engineering and beyond. The key challenge in most approximation methods is the need to tackle the intractable normalization constant present in the candidate distributions used to model the data. This intractability...

Deep learning based models for registration predict a transformation directly from moving and fixed image appearances. These models have revolutionized the field of medical image registration, achieving accuracy on-par with classical registration methods at a fraction of the computation time. Unfortunately, most deep learning based registration met...

With the advent of group equivariant convolutions in deep networks literature, spherical CNNs with $\mathsf{SO}(3)$-equivariant layers have been developed to cope with data that are samples of signals on the sphere $S^2$. One can implicitly obtain $\mathsf{SO}(3)$-equivariant convolutions on $S^2$ with significant efficiency gains by explicitly req...

Distributional approximation is a fundamental problem in machine learning with numerous applications across all fields of science and engineering and beyond. The key challenge in most approximation methods is the need to tackle the intractable normalization constant pertaining to the parametrized distributions used to model the data. In this paper,...

Hyperbolic spaces have been quite popular in the recent past for representing hierarchically organized data. Further, several classification algorithms for data in these spaces have been proposed in the literature. These algorithms mainly use either hyperplanes or geodesics for decision boundaries in a large margin classifiers setting leading to a...

Stein's method has been widely used to achieve distributional approximations for probability distributions defined in Euclidean spaces. Recently, techniques to extend Stein's method to manifold-valued random variables with distributions defined on the respective manifolds have been reported. However, several of these methods impose strong regularit...

The James–Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of problems. Nonetheless, research on shrinkage estimation for manifold-valued data is scarce. In this art...

Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space namely, the Hyperbolic space. Hyperbolic space is a homogeneous Riemannian manifold of the Lorentz group whic...

In the recent past, nested structure of Riemannian manifolds has been studied in the context of dimensionality reduction as an alternative to the popular principal geodesic analysis (PGA) technique, for example, the principal nested spheres. In this paper, we propose a novel framework for constructing a nested sequence of homogeneous Riemannian man...

Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space namely, the Hyperbolic space. Hyperbolic space is a homogeneous Riemannian manifold of the Lorentz group. Mos...

Grassmann manifolds have been widely used to represent the geometry of feature spaces in a variety of problems in medical imaging and computer vision including but not limited to shape analysis, action recognition, subspace clustering and motion segmentation. For these problems, the features usually lie in a very high-dimensional Grassmann manifold...

In this paper, we present a novel generalization of the Volterra Series, which can be viewed as a higher-order convolution, to manifold-valued functions. A special case of the manifold-valued Volterra Series (MVVS) gives us a natural extension of the ordinary convolution to manifold-valued functions that we call, the manifold-valued convolution (MV...

Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to non-Euclidean spaces and shown group equivariance of the generalized convolution operation. In this paper, we pre...

Convolutional neural networks have been extremely successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to non-Euclidean spaces and shown group equivariance of the generalized convolution operation. In this paper, we...

Grassmann manifolds have been widely used to represent the geometry of feature spaces in a variety of problems in computer vision including but not limited to face recognition, action recognition, subspace clustering and motion segmentation. For these problems, the features usually lie in a very high-dimensional Grassmann manifold and hence an appr...

Data in non-Euclidean spaces are commonly encountered in many fields of Science and Engineering. For instance, in Robotics, attitude sensors capture orientation which is an element of a Lie group. In the recent past, several researchers have reported methods that take into account the geometry of Lie Groups in designing parameter estimation algorit...

The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of problems. Nonetheless, research on shrinkage estimation for manifold-valued data is scarce. In this pap...

Geometric deep learning is a relatively nascent field that has attracted significant attention in the past few years. This is partly due to the availability of data acquired from non-euclidean domains or features extracted from euclidean-space data that reside on smooth manifolds. For instance, pose data commonly encountered in computer vision resi...

Principal component analysis (PCA) and Kernel principal component analysis (KPCA) are fundamental methods in machine learning for dimensionality reduction. The former is a technique for finding this approximation in finite dimensions and the latter is often in an infinite dimensional reproducing Kernel Hilbert-space (RKHS). In this paper, we presen...

Geometric deep learning has attracted significant attention in recent years, in part due to the availability of exotic data types for which traditional neural network architectures are not well suited. Our goal in this paper is to generalize convolutional neural networks (CNN) to the manifold-valued image case which arises commonly in medical imagi...

Diffusion-weighted magnetic resonance imaging (dMRI) is a non-invasive technique to probe the complex micro-architecture of the tissue being imaged. The diffusional properties of the tissue at the imaged resolution are well captured by the ensemble average propagator (EAP), which is a probability density function characterizing the probability of w...

Developing deep neural networks (DNNs) for manifold-valued data sets has gained significant interest of late in the deep learning research community. Examples of manifold-valued data in the medical imaging domain include (but are not limited to) diffusion magnetic resonance imaging, tensor-based morphometry, shape analysis and more. In this paper w...

The James-Stein shrinkage estimator was proposed in the field of Statistics as an estimator of the mean for samples drawn from a Gaussian distribution and shown to dominate the maximum likelihood estimator (MLE) in terms of the risk. This seminal work lead to a flurry of activity in the field of shrinkage estimation. However, there has been very li...

Accurate reconstruction of the ensemble average propagators (EAPs) from undersampled diffusion MRI (dMRI) measurements is a well-motivated, actively researched problem in the field of dMRI acquisition and analysis. A number of approaches based on compressed sensing (CS) principles have been developed for this problem, achieving a considerable accel...

Deep neural networks have become the main work horse for many tasks involving learning from data in a variety of applications in Science and Engineering. Traditionally, the input to these networks lie in a vector space and the operations employed within the network are well defined on vector-spaces. In the recent past, due to technological advances...

Deep networks have gained immense popularity in Computer Vision and other fields in the past few years due to their remarkable performance on recognition/classification tasks surpassing the state-of-the art. One of the keys to their success lies in the richness of the automatically learned features. In order to get very good accuracy, one popular o...

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several recent papers have shown how convolutional neural networks (CNNs) can be extended to learn with graph-based data...

Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used as is when data naturally reside on commonly encountered manifolds such as the sphere, the special orthogonal group, the Grassmanian, the manifold of symmetric positive definite matrices and others. Most rece...

In this paper, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new formulation does not explicitly incorporate any sparsity inducing norm in the cost function being optimized b...

A Stiefel manifold of the compact type is often encountered in many fields of Engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space but not a symmetric space. In previous work, researchers have defined probability distributions on symmetric spa...

Analyzing data representing multifarious trajectories is central to the many fields in Science and Engineering; for example, trajectories representing a tennis serve, a gymnast's parallel bar routine, progression/remission of disease and so on. We present a novel geometric algorithm for performing statistical analysis of trajectories with distinct...

A Stiefel manifold of the compact type is often encountered in many fields of Engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space but not a symmetric space. In previous work, researchers have defined probability distributions on symmetric spa...

Statistical machine learning models that operate on manifold-valued data are being extensively studied in vision, motivated by applications in activity recognition, feature tracking and medical imaging. While non-parametric methods have been relatively well studied in the literature, efficient formulations for parametric models (which may offer ben...

In this paper, we present novel algorithms to compute robust statistics from manifold-valued data. Specifically, we present algorithms for estimating the robust Fréchet Mean (FM) and performing a robust exact-principal geodesic analysis (ePGA) for data lying on known Riemannian manifolds. We formulate the minimization problems involved in both thes...

Principal Component Analysis (PCA) is a fundamental method for estimating a linear subspace approximation to high-dimensional data. Many algorithms exist in literature to achieve a statistically robust version of PCA called RPCA. In this paper, we present a geometric framework for computing the principal linear subspaces in both situations that amo...

The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing challenge is to develop Riemannian-geometric tools which are adapted to structured covariance matrices. The present...

The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing challenge is to develop Riemannian-geometric tools which are adapted to structured covariance matrices. The present...

Manifold-valued datasets are widely encountered in many computer vision tasks. A non-linear analog of the PCA, called the Principal Geodesic Analysis (PGA) suited for data lying on Riemannian manifolds was reported in literature a decade ago. Since the objective function in PGA is highly non-linear and hard to solve efficiently in general, research...

Regression is an essential tool in Statistical analysis of data with many applications in Computer Vision, Machine Learning, Medical Imaging and various disciplines of Science and Engineering. Linear and nonlinear regression in a vector space setting has been well studied in literature. However, generalizations to manifold-valued data are only rece...

Parkinson’s disease (PD) is a common and debilitating neurodegenerative disorder that affects patients in all countries and of all nationalities. Magnetic resonance imaging (MRI) is currently one of the most widely used diagnostic imaging techniques utilized for detection of neurologic diseases. Changes in structural biomarkers will likely play an...

In this work, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new formulation {\it does not explicitly incorporate any sparsity inducing norm in the cost function but yet yield...

Fully labeled manual segmentation—a cornerstone of neuro-anatomical structure segmen-tation, is known to be a tedious, time-consuming and error-prone task even for trained experts. In this paper, we propose a novel partially labeled multiple atlas-based segmentation algorithm which can simultaneously segment multiple structures from a given image....

Manifold-valued datasets are widely encountered in many computer vision tasks. A non-linear analog of the PCA, called the Principal Geodesic Analysis (PGA) suited for data lying on Riemannian manifolds was reported in literature a decade ago. Since the objective function in PGA is highly non-linear and hard to solve efficiently in general, research...

Computing the Riemannian center of mass or the finite sample Fréchet mean has attracted enormous attention lately due to the easy availability of data that are manifold valued. Manifold-valued data are encountered in numerous domains including but not limited to medical image computing, mechanics, statistics, machine learning. It is common practice...

Probability density functions (PDFs) are fundamental objects in mathematics with numerous applications in computer vision, machine learning and medical imaging. The feasibility of basic operations such as computing the distance between two PDFs and estimating a mean of a set of PDFs is a direct function of the representation we choose to work with....

Regression in its most common form where independent and dependent variables are in ℝn is a ubiquitous tool in Sciences and Engineering. Recent advances in Medical Imaging has lead to a wide spread availability of manifold-valued data leading to problems where the independent variables are manifold-valued and dependent are real-valued or vice-versa...

Diffusion tensor imaging (DTI) tractography reconstruction of white matter pathways can help guide brain tumor resection. However, DTI tracts are complex mathematical objects and the validity of tractography-derived information in clinical settings has yet to be fully established. To address this issue, we initiated the DTI Challenge, an internatio...

Compressed Sensing (CS) for the acceleration of MR scans has been widely investigated in the past decade. Lately, considerable progress has been made in achieving similar speed ups in acquiring multi-shell high angular resolution diffusion imaging (MS-HARDI) scans. Existing approaches in this context were primarily concerned with sparse reconstruct...

Statistical models for manifold-valued data permit capturing the intrinsic nature of the curved spaces in which the data lie and have been a topic of research for several decades. Typically, these formulations use geodesic curves and distances defined locally for most cases — this makes it hard to design parametric models globally on smooth manifol...

Canonical correlation analysis (CCA) is a widely used statistical technique to capture correlations between two sets of multi-variate random variables and has found a multitude of applications in computer vision, medical imaging and machine learning. The classical formulation assumes that the data live in a pair of vector spaces which makes its use...

The nonlinear version of the well known PCA called the Prinicipal Geodesic Analysis (PGA) was introduced in the past decade for statistical analysis of shapes as well as diffusion tensors. PGA of diffusion tensor fields or any other manifold-valued fields can be a computationally demanding task due to the dimensionality of the problem and thus esta...

Canonical correlation analysis (CCA) is a widely used statistical technique to capture correlations between two sets of multi-variate random variables and has found a multitude of applications in computer vision, medical imaging and machine learning. The classical formulation assumes that the data live in a pair of vector spaces which makes its use...

A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multi-tensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion t...

In this paper, we cast the problem of point cloud match-ing as a shape matching problem by transforming each of the given point clouds into a shape representation called the Schrödinger distance transform (SDT) representation. This is achieved by solving a static Schrödinger equation instead of the corresponding static Hamilton-Jacobi equa-tion in...

Tractography refers to the process of tracing out the nerve fiber bundles from diffusion Magnetic Resonance Images (dMRI) data acquired either in vivo or ex-vivo. Tractography is a mature research topic within the field of diffusion MRI analysis, nevertheless, several new methods are being proposed on a regular basis thereby justifying the need, as...

Symmetric positive-definite (SPD) matrices are ubiquitous in Computer Vision, Machine Learning and Medical Image Analysis. Finding the center/average of a population of such matrices is a common theme in many algorithms such as clustering, segmentation, principal geodesic analysis, etc. The center of a population of such matrices can be defined usi...

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ d , and the dictionary is learned from the training data using the vector space structure of ℝ d and its Euclidean L2-metric. However, in many applications, features and data often originated from a Riemannian manifold that...

This paper presents an application of a recently introduced novel framework for computing the diffeomorphic path between two given diffeomorphisms computed from two pairs of image frames in a motion sequence [1]. The specific application we address here is that of cardiac motion analysis. The framework involves a two-step algorithm wherein we first...

In this paper, we present a novel dictionary learning framework for data lying on the manifold of square root densities and apply it to the reconstruction of diffusion propagator (DP) fields given a multi-shell diffusion MRI data set. Unlike most of the existing dictionary learning algorithms which rely on the assumption that the data points are ve...

In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms. Direct computation of a geodesic path on the space of diffeomorphisms Diff(Ω) is difficult, and it can be attributed mainly to the infinite dimensionality of Diff(Ω). Our proposed framework, to some degree, bypasses this di...

In this paper, we present algorithms for the computation of the median of a set of symmetric positive-definite matrices using different distances/divergences. The novelty of this paper lies in the median computation using the Bhattacharya distance on diffusion tensors. The numerical computation of the median is achieved using the gradient descent a...

We address the problem of video tracking using covariance descriptors constructed from simple features extracted from a given image sequence. Theoretically, this can be posed as a tracking problem in the space of (n×n) symmetric positive definite (SPD) matrices denoted by P n . A novel probabilistic dynamic model in P n based on Riemannian geometry...

In this paper, we propose a novel framework for computing single or multiple atlases (templates) from a large population of images. Unlike many existing methods, our proposed approach is distinguished by its emphasis on the sharpness of the computed atlases and the requirement of rotational invariance. In particular, we argue that sharp atlas image...

Computing matrix means is becoming more and more important in modern signal processing involving processing of matrix-valued images. In this communication, we define the mean for a set of symmetric positive definite (SPD) matrices with respect to information-theoretic divergences as the unique minimizer of the average divergence, and compare it wit...

This work deals with Bhattacharyya mean, Bhattacharyya and Riemannian medians on the space of symmetric positive-definite matrices. A comparison between these averaging methods is given in two different areas which are mean (median) filtering to denoise a set of high angular resolution diffusion images (HARDI) and clustering data. For the second ap...

The unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multi-tensor estimation and tractography. This UKF however was not intrinsic to the space of diffusion tensors. Lack of this key property leads to inaccuracies in the multi-tensor estimation as well as in tractography. In this paper, we propose an novel intrins...

Estimating diffusion tensors is an essential step in many applications- such as diffusion tensor image (DTI) registration, segmentation and fiber tractography. Most of the methods proposed in the literature for this task are not simultaneously statistically robust and feature preserving techniques. In this paper, we propose a novel and robust varia...

A proper distance metric is fundamental in many computer vision and pattern recognition applications such as classification, image retrieval, face recognition and so on. However, it is usually not clear what metric is appropriate for specific applications, therefore it becomes more reliable to learn a task oriented metric. Over the years, many metr...

Computation of the mean of a collection of symmetric positive definite (SPD) matrices is a fundamental ingredient of many algorithms in diffusion tensor image (DTI) processing. For instance, in DTI segmentation, clustering, etc. In this paper, we present novel recursive algorithms for computing the mean of a set of diffusion tensors using several d...

In this paper, we propose a novel variational framework for multi-class DTI segmentation based on global convex optimization. The existing variational approaches to the DTI segmentation problem have mainly used gradient-descent type optimization techniques which are slow in convergence and sensitive to the initialization. This paper on the other ha...

In this paper we present a dictionary-based framework for the reconstruction of a field of ensemble average propagators (EAPs), given a high angular resolution diffusion MRI data set. Existing techniques often consider voxel-wise reconstruction of the EAP field thereby leading to a noisy reconstruction across the field. We present a dictionary lear...

Fiber tracking from diffusion tensor images is an essential step in numerous clinical applications. There is a growing demand for an accurate and efficient framework to perform quantitative analysis of white matter fiber bundles. In this paper, we propose a robust framework for fiber clustering. This framework is composed of two parts: accessible f...

Jensen Divergence Based SPD Matrix Means and Applications

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of ev...

We consider the family of total Bregman divergences (tBDs) as an efficient and robust "distance" measure to quantify the dissimilarity between shapes.The tBD based L1-norm center is used as the representative of a set of shapes, called the t-center. We then prove that for any tBD, there exists a distribution which belongs to the lifted exponential...

Brain atlas construction has attracted significant attention lately in the neuroimaging community due to its application to the characterization of neuroanatomical shape abnormalities associated with various neurodegenerative diseases or neuropsychiatric disorders. Existing shape atlas construction techniques usually focus on the analysis of a sing...

In this paper, we propose an interlaced multi-shell sampling scheme for the reconstruction of the diffusion propagator from diffusion weighted magnetic resonance imaging (DW-MRI). In standard multi-shell sampling schemes, sample points are uniformly distributed on several spherical shells in q-space. The distribution of sample points is the same fo...

Finding mean of matrices becomes increasingly important in modern signal processing problems that involve matrix-valued images. In this paper, we define the mean for a set of symmetric positive definite (SPD) matrices based on information-theoretic divergences as the unique minimizer of the averaged divergences, and compare it with the means comput...

We present a novel image classification system that is built around a core of trainable filter ensemble that we call Volterra kernel classifiers. Our system treats images as a collection of possibly overlapping patches and is composed of three components: (a) A scheme for single patch classification that seeks a smooth, possibly non-linear, functio...