We propose a new framework to reconstruct building details by automatically assembling 3D templates on coarse textured building models. In a preprocessing step, we generate an initial coarse model to approximate a point cloud computed using Structure from Motion and Multi View Stereo, and we model a set of 3D templates of facade details. Next, we optimize the initial coarse model to enforce consistency between geometry and appearance (texture images). Then, building details are reconstructed by assembling templates on the textured faces of the coarse model. The 3D templates are automatically chosen and located by our optimization-based template assembly algorithm that balances image matching and structural regularity. In the results, we demonstrate how our framework can enrich the details of coarse models using various data sets.

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A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying Gauss-Bonnet formula. Furthermore, the hyperbolic polyhedral metric with given curvature can be obtained using a discrete Yamabe flow with surgery. In particular, each hyperbolic polyhedral metric on a closed surface with negative Euler characteristic is discrete conformal to a unique hyperbolic metric.

The goal of this paper is to prove rigorous results for the behavior of genealogies in a one-dimensional long range biased voter model introduced by Hallatschek and Nelson [Theor. Pop. Biol. 73 (2008) 158–170]. The first step, which is easily accomplished using results of Mueller and Tribe [Probab. Theory Related Fields 102 (1995) 519–545], is to show that when space and time are rescaled correctly, our biased voter model converges to a Wright–Fisher SPDE. A simple extension of a result of Durrett and Restrepo [Ann. Appl. Probab. 18 (2008) 334–358] then shows that the dual branching coalescing random walk converges to a branching Brownian motion in which particles coalesce after an exponentially distributed amount of intersection local time. Brunet et al. [Phys. Rev. E (3) 76 (2007) 041104, 20] have conjectured that genealogies in models of this type are described by the Bolthausen–Sznitman coalescent, see [Proc. Natl. Acad. Sci. USA 110 (2013) 437–442]. However, in the model we study there are no simultaneous coalescences. Our third and most significant result concerns “tracer dynamics” in which some of the initial particles in the biased voter model are labeled. We show that the joint distribution of the labeled and unlabeled particles converges to the solution of a system of stochastic partial differential equations. A new duality equation that generalizes the one Shiga [In Stochastic Processes in Physics and Engineering (Bielefeld, 1986) (1988) 345–355 Reidel] developed for the Wright–Fisher SPDE is the key to the proof of that result.

The free boundary value problem in obstacle problem for von Krmn equations is studied. By using the method of complementarity analysis, Rockafellar's theory of duality is generalized to the nonlinear variational problems and a complementarity theory of obstacle problem for von Krmn plates is established. We prove that the uniqueness and existence of solution directly depend on a complementary gap function. Moreover, a generalized dual extreme principle is established. We prove that the nonlinear primal variational inequality problem is eventually equivalent to a semi-quadratic dual optimization problem defined on a statically admissible space. This equivalence can be used to develop an effective numerical method for solving nonlinear free boundary value problems.