101 research outputs found
Landmark-Guided Elastic Shape Analysis of Spherically-Parameterized Surfaces
No full textWe argue that full surface correspondence (registration) and optimal deformations (geodesics) are two related problems and propose a framework that solves them simultaneously. We build on the Riemannian shape analysis of anatomical and star-shaped surfaces of Kurtek et al. and focus on articulated complex shapes that undergo elastic deformations and that may contain missing parts. Our core contribution is the re-formulation of Kurtek et al.'s approach as a constrained optimization over all possible re-parameterizations of the surfaces, using a sparse set of corresponding landmarks. We introduce a landmark-constrained basis, which we use to numerically solve this optimization and therefore establish full surface registration and geodesic deformation between two surfaces. The length of the geodesic provides a measure of dissimilarity between surfaces. The advantages of this approach are: (1) simultaneous computation of full correspondence and geodesic between two surfaces, given a sparse set of matching landmarks (2) ability to handle more comprehensive deformations than nearly isometric, and (3) the geodesics and the geodesic lengths can be further used for symmetrizing 3D shapes and for computing their statistical averages. We validate the framework on challenging cases of large isometric and elastic deformations, and on surfaces with missing parts. We also provide multiple examples of averaging and symmetrizing 3D models.Computer Graphics Foru
Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data
No full textMathematical and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observation regimes. Our ability to do this relies on the specification of strongly informative prior models over the amplitude component of function variability. We provide two strategies for this critical choice: a data-driven approach that defines an empirical basis for the amplitude subspace based on available training data, and a shape-restricted approach when the relative location and number of local extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to separately model amplitude and phase variability inherent in functional data. We emphasize the importance of uncertainty quantification and visualization of these two components as they provide complementary information about the estimated functions. We validate the proposed framework using simulation studies, and real applications to estimation of fractional anisotropy profiles based on diffusion tensor imaging measurements, growth velocity functions and bone mineral density curves.No embarg
Elastic shape matching of parameterized surfaces using square root normal fields
No full textAbstract. In this paper we define a new methodology for shape anal-ysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameter-ized surfaces. The main advantages of this metric are twofold. First, it provides a natural interpretation of elastic shape deformations that are being quantified. Second, this metric is invariant under the action of the reparameterization group. We also introduce a novel representation of surfaces termed square root normal fields or SRNFs. This representation is convenient for shape analysis because, under this representation, a reduced version of the general elastic metric becomes the simple L2 met-ric. Thus, this transformation greatly simplifies the implementation of our framework. We validate our approach using multiple shape analysis examples for quadrilateral and spherical surfaces. We also compare the current results with those of Kurtek et al. [1]. We show that the proposed method results in more natural shape matchings, and furthermore, has some theoretical advantages over previous methods.
Growth curve registration for evaluating salinity tolerance in barley
No full textBackground: Smarthouses capable of non-destructive, high-throughput plant phenotyping collect large amounts of data that can be used to understand plant growth and productivity in extreme environments. The challenge is to apply the statistical tool that best analyzes the data to study plant traits, such as salinity tolerance, or plant-growthrelated traits. Results: We derive family-wise salinity sensitivity (FSS) growth curves and use registration techniques to summarize growth patterns of HEB-25 barley families and the commercial variety, Navigator. We account for the spatial variation in smarthouse microclimates and in temporal variation across phenotyping runs using a functional ANOVA model to derive corrected FSS curves. From FSS, we derive corrected values for family-wise salinity tolerance, which are strongly negatively correlated with Na but not significantly with K, indicating that Na content is an important factor affecting salinity tolerance in these families, at least for plants of this age and grown in these conditions. Conclusions: Our family-wise methodology is suitable for analyzing the growth curves of a large number of plants from multiple families. The corrected curves accurately account for the spatial and temporal variations among plants that are inherent to high-throughput experiments.Rui Meng, Stephanie Saade, Sebastian Kurtek, Bettina Berger, Chris Brien, Klaus Pillen, Mark Tester and Ying Sun
A geometric approach to pairwise Bayesian alignment of functional data using importance sampling
No full textA comprehensive statistical framework for elastic shape analysis of 3D faces
No full textInternational audienceWe develop a comprehensive statistical framework for analyzing shapes of 3D faces. In particular, we adapt a recent elastic shape analysis framework to the case of hemispherical surfaces, and explore its use in a number of processing applications. This framework provides a parameterization-invariant, elastic Riemannian metric, which allows the development of mathematically rigorous tools for statistical analysis. Specifically, this paper describes methods for registration, comparison and deformation, averaging, computation of covariance and summarization of variability using principal component analysis, random sampling from generative shape models, symmetry analysis, and expression and identity classification. An important aspect of this work is that all tasks are preformed under a unified metric, which has a natural interpretation in terms of bending and stretching of one 3D face to align it with another. We use a subset of the BU-3DFE face dataset, which contains varying magnitudes of expression
Bayesian sensitivity analysis with the Fisher–Rao metric
No full textWe propose a geometric framework to assess sensitivity of Bayesian procedures to modelling assumptions based on the nonparametric Fisher–Rao metric. While the framework is general, the focus of this article is on assessing local and global robustness in Bayesian procedures with respect to perturbations of the likelihood and prior, and on the identification of influential observations. The approach is based on a square-root representation of densities, which enables analytical computation of geodesic paths and distances, facilitating the definition of naturally calibrated local and global discrepancy measures. An important feature of our approach is the definition of a geometric ϵ-contamination class of sampling distributions and priors via intrinsic analysis on the space of probability density functions. We demonstrate the applicability of our framework to generalized mixed-effects models and to directional and shape data
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