Adrian M. Peter

Maximum Likelihood Wavelet Density Estimation With Applications to Image and Shape Matching

Density estimation for observational data plays an integral role in a broad spectrum of applications, e.g., statistical data analysis and information-theoretic image registration. Of late, wavelet-based density estimators have gained in popularity due to their ability to approximate a large class of functions, adapting well to difficult situations such as when densities exhibit abrupt changes. The decision to work with wavelet density estimators brings along with it theoretical considerations (e.g., non-negativity, integrability) and empirical issues (e.g., computation of basis coefficients) that must be addressed in order to obtain a bona fide density. In this paper, we present a new method to accurately estimate a non-negative density which directly addresses many of the problems in practical wavelet density estimation. We cast the estimation procedure in a maximum likelihood framework which estimates the square root of the density , allowing us to obtain the natural non-negative density representation . Analysis of this method will bring to light a remarkable theoretical connection with the Fisher information of the density and, consequently, lead to an efficient constrained optimization procedure to estimate the wavelet coefficients. We illustrate the effectiveness of the algorithm by evaluating its performance on mutual information-based image registration, shape point set alignment, and empirical comparisons to known densities. The present method is also compared to fixed and variable bandwidth kernel density estimators.

Shape analysis using the Fisher-Rao Riemannian metric: unifying shape representation and deformation

We show that the Fisher-Rao Riemannian metric is a natural, intrinsic tool for computing shape geodesics. When a parameterized probability density function is used to represent a landmark-based shape, the modes of deformation are automatically established through the Fisher information of the density. Consequently, given two shapes parameterized by the same density model, the geodesic distance between them under the action of the Fisher-Rao metric is a convenient shape distance measure. It has the advantage of being an intrinsic distance measure and invariant to reparameterization. We first model shape landmarks using a Gaussian mixture model and then compute geodesic distances between two shapes using the Fisher-Rao metric corresponding to the mixture model. We illustrate our approach by computing Fisher geodesics between 2D corpus callosum shapes. Shape representation via the mixture model and shape deformation via the Fisher geodesic are hereby unified in this approach

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. When a parameterized probability density function is used to represent a landmark-based shape, the modes of deformation are automatically established through the information matrix of the density. We first show that given two shapes parameterized by Gaussian mixture models (GMMs), the well-known Fisher information matrix of the mixture model is also a Riemannian metric (actually, the Fisher-Rao Riemannian metric) and can therefore be used for computing shape geodesics. The Fisher-Rao metric has the advantage of being an intrinsic metric and invariant to reparameterization. The geodesic-computed using this metric-establishes an intrinsic deformation between the shapes, thus unifying both shape representation and deformation. A fundamental drawback of the Fisher-Rao metric is that it is not available in closed form for the GMM. Consequently, shape comparisons are computationally very expensive. To address this, we develop a new Riemannian metric based on generalized \phi-entropy measures. In sharp contrast to the Fisher-Rao metric, the new metric is available in closed form. Geodesic computations using the new metric are considerably more efficient. We validate the performance and discriminative capabilities of these new information geometry-based metrics by pairwise matching of corpus callosum shapes. We also study the deformations of fish shapes that have various topological properties. A comprehensive comparative analysis is also provided using other landmark-based distances, including the Hausdorff distance, the Procrustes metric, landmark-based diffeomorphisms, and the bending energies of the thin-plate (TPS) and Wendland splines.

Shape L’Âne rouge: Sliding wavelets for indexing and retrieval

Shape representation and retrieval of stored shape models are becoming increasingly more prominent in fields such as medical imaging, molecular biology and remote sensing. We present a novel framework that directly addresses the necessity for a rich and compressible shape representation, while simultaneously providing an accurate method to index stored shapes. The core idea is to represent point-set shapes as the square root of probability densities expanded in a wavelet basis. We then use this representation to develop a natural similarity metric that respects the geometry of these probability distributions, i.e. under the wavelet expansion, densities are points on a unit hypersphere and the distance between densities is given by the separating arc length. The process uses a linear assignment solver for non-rigid alignment between densities prior to matching; this has the connotation of ldquoslidingrdquo wavelet coefficients akin to the sliding block puzzle LpsilaAne Rouge. We illustrate the utility of this framework by matching shapes from the MPEG-7 data set and provide comparisons to other similarity measures, such as Euclidean distance shape distributions.

Research Directions for Engineering Big Data Analytics Software

Many software startups and research and development efforts are actively trying to harness the power of big data and create software with the potential to improve almost every aspect of human life. As these efforts continue to increase, full consideration needs to be given to the engineering aspects of big data software. Since these systems exist to make predictions on complex and continuous massive datasets, they pose unique problems during specification, design, and verification of software that needs to be delivered on time and within budget. But, given the nature of big data software, can this be done? Does big data software engineering really work? This article explores the details of big data software, discusses the main problems encountered when engineering big data software, and proposes avenues for future research.

A Wireless Sensor Networks' Analytics System for Predicting Performance in On-Demand Deployments

The need for advanced tools that provide efficient design of on-demand deployment of wireless sensor networks (WSN) is critical for meeting our nations demand for increased intelligence, reconnaissance, and surveillance. For practical applications, WSN deployments can be time consuming and error prone since they have the utmost challenge of guaranteeing connectivity and proper area coverage upon deployment. This creates an unmet demand for decision-support systems that help manage this complex process. This paper presents research to develop a system for predicting optimal deployments of WSN. Specifically, it presents results of image processing algorithms for terrain classification, results of modeling WSN signal propagation under different terrain conditions, results of optimization and visualization techniques for high-dimensional deployments, and system architecture for efficient integration and future deployment. Results show a feasible approach that can be used to automatically determine areas of high signal obstruction-which is essential to estimate obstruction parameters in simulations-and mapping of accurate WSN path-loss models to enhance the overall decision-making process during predeployment of large-scale WSN.

A new closed-form information metric for shape analysis

Shape matching plays a prominent role in the analysis of medical and biological structures. Recently, a unifying framework was introduced for shape matching that uses mixture-models to couple both the shape representation and deformation. Essentially, shape distances were defined as geodesics induced by the Fisher-Rao metric on the manifold of mixture-model represented shapes. A fundamental drawback of the Fisher-Rao metric is that it is NOT available in closed-form for the mixture model. Consequently, shape comparisons are computationally very expensive. Here, we propose a new Riemannian metric based on generalized phi-entropy measures. In sharp contrast to the Fisher-Rao metric, our new metric is available in closed-form. Geodesic computations using the new metric are considerably more efficient. Discriminative capabilities of this new metric are studied by pairwise matching of corpus callosum shapes. Comparisons are conducted with the Fisher-Rao metric and the thin-plate spline bending energy.

A support vector machine for terrain classification in on-demand deployments of wireless sensor networks

Terrain characteristics can significantly alter the quality of the results provided by the deployment methodology of large-scale wireless sensor networks. For example, transmissions between nodes that are heavily obstructed will require additional transmission power to establish connection between nodes. In some cases, heavily obstructed areas may prevent nodes from establishing a connection at all. Therefore, terrain analysis and classification of specific deployment areas should be incorporated in the methodology process for evaluation and optimization of the performance of wireless sensor networks upon deployment. Although there exists radio frequency (RF) models capable of modeling obstructions, such as vegetation, foliage, etc., automatic assignment of parameter values for these models may be troublesome, specifically in highly irregular deployments terrains, where proximity of poor and optimal conditions for signal propagation may be adjacent to each other. In these situations, parameter estimation for modeling terrain obstruction may result in overly optimistic or pessimistic results, causing characterizations or predictions that deviate from the true performance of the WSN once deployed. This paper presents the results of employing a support vector machine for automatic terrain classification. The approach can be used to automatically determine areas of high obstruction, which is essential to estimate obstruction parameters in simulations and enhancing the overall decision-making process during pre-deployment of large-scale and irregular deployment terrains.

Intelligent system for predicting wireless sensor network performance in on-demand deployments

The need for advanced tools that provide efficient design and planning of on-demand deployment of wireless sensor networks (WSN) is critical for meeting our nations demand for increased intelligence, reconnaissance, and surveillance in numerous safety-critical applications. For practical applications, WSN deployments can be time-consuming and error-prone, since they have the utmost challenge of guaranteeing connectivity and proper area coverage upon deployment. This creates an unmet demand for decision-support systems that help manage this complex process. This paper presents research-in-progress to develop an advanced decision-support system for predicting the optimal deployment of wireless sensor nodes within an area of interest. The proposed research will have significant impact on the future application of WSN technology, specifically in the emergency response, environmental quality, national security, and engineering education domains.

CASAIR: Content and Shape-Aware Image Retargeting and Its Applications

This paper proposes a novel image-retargeting algorithm that can retarget images to a large family of non-rectangular shapes. Specifically, we study image retargeting from a broader perspective that includes the content as well as the shape of an image, and the proposed content and shape-aware image-retargeting (CASAIR) algorithm is driven by the dual objectives of image content preservation and image domain transformation, with the latter defined by an application-specific target shape. The algorithm is based on the idea of seam segment carving that successively removes low-cost seam segments from the image to simultaneously achieve the two objectives, with the selection of seam segments determined by a cost function incorporating inputs from image content and target shape. To provide a complete characterization of shapes that can be obtained using CASAIR, we introduce the notion of bhv-convex shapes, and we show that bhv-convex shapes are precisely the family of shapes that can be retargeted to by CASAIR. The proposed algorithm is simple in both its design and implementation, and in practice, it offers an efficient and effective retargeting platform that provides its users with considerable flexibility in choosing target shapes. To demonstrate the potential of CASAIR for broadening the application scope of image retargeting, this paper also proposes a smart camera-projector system that incorporates CASAIR. In the context of ubiquitous display, CASAIR equips the camera-projector system with the capability of retargeting images online in order to maximize the quality and fidelity of the displayed images whenever the situation demands.