2,503 research outputs found
How round is a protein? Exploring protein structures for globularity using conformal mapping.
We present a new algorithm that automatically computes a measure of the geometric difference between the surface of a protein and a round sphere. The algorithm takes as input two triangulated genus zero surfaces representing the protein and the round sphere, respectively, and constructs a discrete conformal map f between these surfaces. The conformal map is chosen to minimize a symmetric elastic energy E S (f) that measures the distance of f from an isometry. We illustrate our approach on a set of basic sample problems and then on a dataset of diverse protein structures. We show first that E S (f) is able to quantify the roundness of the Platonic solids and that for these surfaces it replicates well traditional measures of roundness such as the sphericity. We then demonstrate that the symmetric elastic energy E S (f) captures both global and local differences between two surfaces, showing that our method identifies the presence of protruding regions in protein structures and quantifies how these regions make the shape of a protein deviate from globularity. Based on these results, we show that E S (f) serves as a probe of the limits of the application of conformal mapping to parametrize protein shapes. We identify limitations of the method and discuss its extension to achieving automatic registration of protein structures based on their surface geometry
A Metric for genus-zero surfaces
We present a new method to compare the shapes of genus-zero surfaces. We
introduce a measure of mutual stretching, the symmetric distortion energy, and
establish the existence of a conformal diffeomorphism between any two
genus-zero surfaces that minimizes this energy. We then prove that the energies
of the minimizing diffeomorphisms give a metric on the space of genus-zero
Riemannian surfaces. This metric and the corresponding optimal diffeomorphisms
are shown to have properties that are highly desirable for applications.Comment: 33 pages, 8 figure
Quasiconvex Programming
We define quasiconvex programming, a form of generalized linear programming
in which one seeks the point minimizing the pointwise maximum of a collection
of quasiconvex functions. We survey algorithms for solving quasiconvex programs
either numerically or via generalizations of the dual simplex method from
linear programming, and describe varied applications of this geometric
optimization technique in meshing, scientific computation, information
visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure
Automatic landmark annotation and dense correspondence registration for 3D human facial images
Dense surface registration of three-dimensional (3D) human facial images
holds great potential for studies of human trait diversity, disease genetics,
and forensics. Non-rigid registration is particularly useful for establishing
dense anatomical correspondences between faces. Here we describe a novel
non-rigid registration method for fully automatic 3D facial image mapping. This
method comprises two steps: first, seventeen facial landmarks are automatically
annotated, mainly via PCA-based feature recognition following 3D-to-2D data
transformation. Second, an efficient thin-plate spline (TPS) protocol is used
to establish the dense anatomical correspondence between facial images, under
the guidance of the predefined landmarks. We demonstrate that this method is
robust and highly accurate, even for different ethnicities. The average face is
calculated for individuals of Han Chinese and Uyghur origins. While fully
automatic and computationally efficient, this method enables high-throughput
analysis of human facial feature variation.Comment: 33 pages, 6 figures, 1 tabl
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