Washington Mio

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For analyzing shapes of planar, closed curves, we propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier(More)
We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments non-uniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape-preserving transformations. The elastic properties of the curves(More)
Using a differential-geometric treatment of planar shapes, we present tools for: 1) hierarchical clustering of imaged objects according to the shapes of their boundaries, 2) learning of probability models for clusters of shapes, and 3) testing of newly observed shapes under competing probability models. Clustering at any level of hierarchy is performed(More)
We develop a new framework for the quantitative analysis of shapes of planar curves. Shapes are modeled on elastic strings that can be bent, stretched or compressed at different rates along the curve. Shapes are treated as elements of a space obtained as the quotient of an infinite-dimensional Riemannian manifold of elastic curves by the action of a(More)
BACKGROUND How developmental mechanisms generate the phenotypic variation that is the raw material for evolution is largely unknown. Here, we explore whether variation in a conserved signaling axis between the brain and face contributes to differences in morphogenesis of the avian upper jaw. In amniotes, including both mice and avians, signals from the(More)
We introduce a class of spectral shape signatures constructed from symmetric functions on the eigenfunctions of the Laplacian exponentially weighted by their eigenvalues. Such a construction is motivated by problems that arise in the use of the eigenfunctions for shape comparison, such as indeterminacies in the choice of signs and the particular ordering in(More)
Registration of 3D surfaces is a critical step for shape analysis. Recent studies show that spectral representations based on intrinsic pairwise geodesic distances between points on surfaces are effective for registration and alignment due to their invariance under rigid transformations and articulations. Kernel functions are often applied to the pairwise(More)
Numerous lines of evidence point to a genetic basis for facial morphology in humans, yet little is known about how specific genetic variants relate to the phenotypic expression of many common facial features. We conducted genome-wide association meta-analyses of 20 quantitative facial measurements derived from the 3D surface images of 3118 healthy(More)
Quantitative analysis of gene expression domains and investigation of relationships between gene expression and developmental and phenotypic outcomes are central to advancing our understanding of the genotype–phenotype map. Gene expression domains typically have smooth but irregular shapes lacking homologous landmarks, making it difficult to analyze shape(More)