Recently Freed and Hopkins [11] proved that there is no parity anomaly in M-theory on pin+ manifolds in the low-energy field theory approximation, and they also developed an algebraic theory of cubic forms. Earlier Witten [33] proved the anomaly cancellation for spin manifolds by introducing the E8-bundle technique. Motivated by the cubic forms and the anomaly cancellation formulas of Witten-Freed-Hopkins, we give some new cubic forms on spin, spinc, spinω2 and orientable 12- manifolds respectively. We relate them to η-invariants when the manifolds are with boundary, and mod 2 indices on 10 dimensional characteristic submanifolds when the manifolds are spinc or spinω2 . Our method of producing these cubic forms is a combination of (generalized) Witten classes and the character of the basic representation of affine E8.

In this paper, we study some algebraic topology aspects of Stringc structures, more precisely, from the perspective of Whitehead tower and the perspective of the loop group of Spinc(n). We also extend the generalized Witten genera constructed for the first time by Chen et al. [J. Differential Geom. 88 (2011), pp. 1–40] to correspond to Stringc structures of various levels and give vanishing results for them.

The goal of urban building mesh simplification is to generate a compact representation of a building from a given mesh. Local smoothness and sharp contours of urban buildings are important features for converting unstructured data into solid models, which should be preserved during the simplification. In this paper, we present a general method to filter and simplify 3D building mesh models, capable of preserving piecewise planar structures and sharp features. Given a building mesh model, a mesh filtering technique is firstly designed to yield piecewise planar regions and extract crease contours. The planar regions are used to constrain the simplification of the mesh. Mesh decimation is achieved through a series of edge collapse operations, which uses regional structural constraints and local geometric error metrics to handle planar and non-planar areas respectively. The proposed method preserves the mesh structure with meaningful levels of detail while reducing the number of faces. The effectiveness of this method is evaluated on various building models generated from different observation scales, and the performance is validated by extensive comparisons to state-of-the-art techniques.

Forest above-ground biomass (AGB) can be estimated based on light detection and ranging (LiDAR) point clouds. This paper introduces an accurate and detailed quantitative structure model (AdQSM), which can estimate the AGB of large tropical trees. AdQSM is based on the reconstruction of 3D tree models from terrestrial laser scanning (TLS) point clouds. It represents a tree as a set of closed and complete convex polyhedra. We use AdQSM to model 29 trees of various species (total 18 species) scanned by TLS from three study sites (the dense tropical forests of Peru, Indonesia, and Guyana). The destructively sampled tree geometry measurement data is used as reference values to evaluate the accuracy of diameter at breast height (DBH), tree height, tree volume, branch volume, and AGB estimated from AdQSM. After AdQSM reconstructs the structure and volume of each tree, AGB is derived by combining the wood density of the specific tree species from destructive sampling. The AGB estimation from AdQSM and the post-harvest reference measurement data show a satisfying agreement. The coefficient of variation of root mean square error (CV-RMSE) and the concordance correlation coefficient (CCC) are 20.37% and 0.97, respectively. AdQSM provides accurate tree volume estimation, regardless of the characteristics of the tree structure, without major systematic deviations. We compared the accuracy of AdQSM and TreeQSM in modeling the volume of 29 trees. The tree volume from AdQSM is compared with the reference value, and the determination coefficient (R2), relative bias (rBias), and CV-RMSE of tree volume are 0.96, 6.98%, and 22.62%, respectively. The tree volume from TreeQSM is compared with the reference value, and the R2, relative Bias (rBias), and CV-RMSE of tree volume are 0.94, −9.69%, and 23.20%, respectively. The CCCs between the volume estimates based on AdQSM, TreeQSM, and the reference values are 0.97 and 0.96. AdQSM also models the branches in detail. The volume of branches from AdQSM is compared with the destructive measurement reference data. The R2, rBias, and CV-RMSE of the branches volume are 0.97, 12.38%, and 36.86%, respectively. The DBH and height of the harvested trees were used as reference values to test the accuracy of AdQSM’s estimation of DBH and tree height. The R2, rBias, and CV-RMSE of DBH are 0.94, −5.01%, and 9.06%, respectively. The R2, rBias, and CV-RMSE of the tree height were 0.95, 1.88%, and 5.79%, respectively. This paper provides not only a new QSM method for estimating AGB based on TLS point clouds but also the potential for further development and testing of allometric equations.

We introduce a novel approach for the polygonization of Multi-view Stereo (MVS) meshes of buildings, which results in compact and topologically valid models. The main characteristic of our method is structure awareness, i.e., the recovery and preservation of the initial mesh primitives and their adjacencies. Our proposed methodology consists of three main stages: (a) primitive detection via mesh segmentation, (b) encoding of primitive adjacencies into a graph, and (c) polygonization. Polygonization is based on the approximation of the original mesh with a candidate set of planar polygonal faces. On this candidate set, we apply a binary labelling formulation to select and assemble an optimal set of faces under hard constraints that ensure that the final model is both manifold and watertight. Experiments on various building models demonstrate that our simplification method can produce simpler representations for both closed and open building meshes. Furthermore, these representations highly conform to the initial structure and are ready to be used for spatial analysis. The source code of this work is freely available at https://github.com/VasileiosBouzas/MeshPolygonization.