Toward Improving the Generation Quality of Autoregressive Slot VAEs.

Unconditional scene inference and generation are challenging to learn jointly with a single compositional model. Despite encouraging progress on models that extract object-centric representations ("slots") from images, unconditional generation of scenes from slots has received less attention. This is primarily because learning the multiobject relations necessary to imagine coherent scenes is difficult.

Learning Canonical Embeddings for Unsupervised Shape Correspondence With Locally Linear Transformations.

We present a new approach to unsupervised shape correspondence learning between pairs of point clouds. We make the first attempt to adapt the classical locally linear embedding algorithm (LLE)-originally designed for nonlinear dimensionality reduction-for shape correspondence. The key idea is to find dense correspondences between shapes by first obtaining high-dimensional neighborhood-preserving embeddings of low-dimensional point clouds and subsequently aligning the source and target embeddings using locally linear transformations.

Machine-Learning-Based Real-Time Multi-Camera Vehicle Tracking and Travel-Time Estimation.

Travel-time estimation of traffic flow is an important problem with critical implications for traffic congestion analysis. We developed techniques for using intersection videos to identify vehicle trajectories across multiple cameras and analyze corridor travel time. Our approach consists of (1) multi-object single-camera tracking, (2) vehicle re-identification among different cameras, (3) multi-object multi-camera tracking, and (4) travel-time estimation.

A model of crop diversification under labor shocks.

As demands on agriculture increase, food producers will need to employ management strategies that not only increase yields but reduce environmental impacts. Modeling is a powerful tool for informing decision-making about current and future practices. We present a model to evaluate the effects of crop diversification on the robustness of simulated farms under labor shocks.

A Grassmannian Graph Approach to Affine Invariant Feature Matching.

In this work, we present a novel, theoretical approach to address one of the longstanding problems in computer vision: 2D and 3D affine invariant feature matching. Our proposed Grassmannian Graph (GrassGraph) framework employs a two stage procedure that is capable of robustly recovering correspondences between two unorganized, affinely related feature (point) sets. In the ideal case, the first stage maps the feature sets to an affine invariant Grassmannian representation, where the features are mapped into the same subspace.

Visual Explanations From Deep 3D Convolutional Neural Networks for Alzheimer's Disease Classification.

We develop three efficient approaches for generating visual explanations from 3D convolutional neural networks (3D-CNNs) for Alzheimer's disease classification. One approach conducts sensitivity analysis on hierarchical 3D image segmentation, and the other two visualize network activations on a spatial map. Visual checks and a quantitative localization benchmark indicate that all approaches identify important brain parts for Alzheimer's disease diagnosis.

Spherical Minimum Description Length.

We consider the problem of model selection using the Minimum Description Length (MDL) criterion for distributions with parameters on the hypersphere. Model selection algorithms aim to find a compromise between goodness of fit and model complexity. Variables often considered for complexity penalties involve number of parameters, sample size and shape of the parameter space, with the penalty term often referred to as stochastic complexity.

Image Stacks as Parametric Surfaces: Application to Image Registration.

We introduce a framework in which a stack of images is considered to be a 2-D parametric surface embedded in a higher dimensional space. This is a simple yet powerful idea, known in the literature but not exploited to its fullest. We discuss the properties of image stacks as parametric surfaces, apply this framework to image registration by presenting the image stack surface relative area (ISSRA) registration measure.

A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing.

Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model, where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in real applications, the distribution of a material is often not Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent endmember variability.

A spatial compositional model for linear unmixing and endmember uncertainty estimation.

The normal compositional model (NCM) has been extensively used in hyperspectral unmixing. However, previous research has mostly focused on estimation of endmembers and/or their variability, based on the assumption that the pixels are independent random variables. In this paper, we show that this assumption does not hold if all the pixels are generated by a fixed endmember set.

A Riemannian framework for matching point clouds represented by the Schrödinger distance transform.

In this paper, we cast the problem of point cloud matching 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 equation in this setting. The SDT representation is an analytic expression and following the theoretical physics literature, can be normalized to have unit L norm-making it a square-root density, which is identified with a point on a unit Hilbert sphere, whose intrinsic geometry is fully known.

Image denoising using the higher order singular value decomposition.

In this paper, we propose a very simple and elegant patch-based, machine learning technique for image denoising using the higher order singular value decomposition (HOSVD). The technique simply groups together similar patches from a noisy image (with similarity defined by a statistically motivated criterion) into a 3D stack, computes the HOSVD coefficients of this stack, manipulates these coefficients by hard thresholding, and inverts the HOSVD transform to produce the final filtered image. Our technique chooses all required parameters in a principled way, relating them to the noise model.

Construction of a neuroanatomical shape complex atlas from 3D MRI brain structures.

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 single anatomical structure in which the important inter-structural information is lost. This paper proposes a novel technique for constructing a neuroanatomical shape complex atlas based on an information geometry framework.

Mixture of segmenters with discriminative spatial regularization and sparse weight selection.

This paper presents a novel segmentation algorithm which automatically learns the combination of weak segmenters and builds a strong one based on the assumption that the locally weighted combination varies w.r.t.

CAVIAR: CLASSIFICATION VIA AGGREGATED REGRESSION AND ITS APPLICATION IN CLASSIFYING OASIS BRAIN DATABASE.

This paper presents a novel classification via aggregated regression algorithm - dubbed CAVIAR - and its application to the OASIS MRI brain image database. The CAVIAR algorithm simultaneously combines a set of weak learners based on the assumption that the weight combination for the final strong hypothesis in CAVIAR depends on both the weak learners and the training data. A regularization scheme using the nearest neighbor method is imposed in the testing stage to avoid overfitting.

Construction of neuroanatomical shape complex atlas from 3D brain MRI.

This paper proposes a novel technique for constructing a neuroanatomical shape complex atlas using an information geometry framework. A shape complex is a collection of shapes in a local neighborhood. We represent the boundary of the entire shape complex using the zero level set of a distance function S(x).

PET image reconstruction using information theoretic anatomical priors.

We describe a nonparametric framework for incorporating information from co-registered anatomical images into positron emission tomographic (PET) image reconstruction through priors based on information theoretic similarity measures. We compare and evaluate the use of mutual information (MI) and joint entropy (JE) between feature vectors extracted from the anatomical and PET images as priors in PET reconstruction. Scale-space theory provides a framework for the analysis of images at different levels of detail, and we use this approach to define feature vectors that emphasize prominent boundaries in the anatomical and functional images, and attach less importance to detail and noise that is less likely to be correlated in the two images.

Group-wise Point-set registration using a novel CDF-based Havrda-Charvát Divergence.

This paper presents a novel and robust technique for group-wise registration of point sets with unknown correspondence. We begin by defining a Havrda-Charvát (HC) entropy valid for cumulative distribution functions (CDFs) which we dub the HC Cumulative Residual Entropy (HC-CRE). Based on this definition, we propose a new measure called the CDF-HC divergence which is used to quantify the dis-similarity between CDFs estimated from each point-set in the given population of point sets.

A method for compact image representation using sparse matrix and tensor projections onto exemplar orthonormal bases.

We present a new method for compact representation of large image datasets. Our method is based on treating small patches from a 2-D image as matrices as opposed to the conventional vectorial representation, and encoding these patches as sparse projections onto a set of exemplar orthonormal bases, which are learned a priori from a training set. The end result is a low-error, highly compact image/patch representation that has significant theoretical merits and compares favorably with existing techniques (including JPEG) on experiments involving the compression of ORL and Yale face databases, as well as a database of miscellaneous natural images.

Probability density estimation using isocontours and isosurfaces: applications to information-theoretic image registration.

We present a new, geometric approach for determining the probability density of the intensity values in an image. We drop the notion of an image as a set of discrete pixels, and assume a piecewise-continuous representation. The probability density can then be regarded as being proportional to the area between two nearby isocontours of the image surface.

Closed-form Jensen-Renyi divergence for mixture of Gaussians and applications to group-wise shape registration.

In this paper, we propose a generalized group-wise non-rigid registration strategy for multiple unlabeled point-sets of unequal cardinality, with no bias toward any of the given point-sets. To quantify the divergence between the probability distributions--specifically Mixture of Gaussians--estimated from the given point sets, we use a recently developed information-theoretic measure called Jensen-Renyi (JR) divergence. We evaluate a closed-form JR divergence between multiple probabilistic representations for the general case where the mixture models differ in variance and the number of components.

Information geometry for landmark shape analysis: unifying shape representation and deformation.

Shape matching plays a prominent role in the comparison of similar structures. We present a unifying framework for shape matching that uses mixture models to couple both the shape representation and deformation. The theoretical foundation is drawn from information geometry wherein information matrices are used to establish intrinsic distances between parametric densities.

Simultaneous nonrigid registration of multiple point sets and atlas construction.

Groupwise registration of a set of shapes represented by unlabeled point sets is a challenging problem since, usually, this involves solving for point correspondence in a nonrigid motion setting. In this paper, we propose a novel and robust algorithm that is capable of simultaneously computing the mean shape, represented by a probability density function, from multiple unlabeled point sets(represented by finite-mixture models), and registering them nonrigidly to this emerging mean shape. This algorithm avoids the correspondence problem by minimizing the Jensen-Shannon (JS) divergence between the point sets represented as finite mixtures of Gaussian densities.

Aperture optimization in emission imaging using ideal observers for joint detection and localization.

For the familiar 2-class detection problem (signal present/absent), ideal observers have been applied to optimization of pinhole and collimator parameters in planar emission imaging. Given photon noise and background and signal variabilities, such experiments show how to optimize an aperture to maximize detectability of the signal. Here, we consider a fundamentally different, more realistic task in which the observer is required to both detect and localize a signal.

Joint-MAP Bayesian tomographic reconstruction with a gamma-mixture prior.

We address the problem of Bayesian image reconstruction with a prior that captures the notion of a clustered intensity histogram. The problem is formulated in the framework of a joint-MAP (maximum a posteriori) estimation with the prior PDF modeled as a mixture-of-gammas density. This prior PDF has appealing properties, including positivity enforcement.