LRF-Net: Learning Local Reference Frames for 3D Local Shape Description and Matching

The local reference frame (LRF) acts as a critical role in 3D local shape description and matching. However, most of existing LRFs are hand-crafted and suffer from limited repeatability and robustness. This paper presents the first attempt to learn an LRF via a Siamese network that needs weak supervision only. In particular, we argue that each neighboring point in the local surface gives a unique contribution to LRF construction and measure such contributions via learned weights. Extensive analysis and comparative experiments on three public datasets addressing different application scenarios have demonstrated that LRF-Net is more repeatable and robust than several state-of-the-art LRF methods (LRF-Net is only trained on one dataset). In addition, LRF-Net can significantly boost the local shape description and 6-DoF pose estimation performance when matching 3D point clouds.Comment: 28 pages, 14 figure

Serendipity and Tensor Product Affine Pyramid Finite Elements

Using the language of finite element exterior calculus, we define two families of $H^1$-conforming finite element spaces over pyramids with a parallelogram base. The first family has matching polynomial traces with tensor product elements on the base while the second has matching polynomial traces with serendipity elements on the base. The second family is new to the literature and provides a robust approach for linking between Lagrange elements on tetrahedra and serendipity elements on affinely-mapped cubes while preserving continuity and approximation properties. We define shape functions and degrees of freedom for each family and prove unisolvence and polynomial reproduction results.Comment: Accepted to SMAI Journal of Computational Mathematic

Spatially Aware Dictionary Learning and Coding for Fossil Pollen Identification

We propose a robust approach for performing automatic species-level recognition of fossil pollen grains in microscopy images that exploits both global shape and local texture characteristics in a patch-based matching methodology. We introduce a novel criteria for selecting meaningful and discriminative exemplar patches. We optimize this function during training using a greedy submodular function optimization framework that gives a near-optimal solution with bounded approximation error. We use these selected exemplars as a dictionary basis and propose a spatially-aware sparse coding method to match testing images for identification while maintaining global shape correspondence. To accelerate the coding process for fast matching, we introduce a relaxed form that uses spatially-aware soft-thresholding during coding. Finally, we carry out an experimental study that demonstrates the effectiveness and efficiency of our exemplar selection and classification mechanisms, achieving $86.13\%$ accuracy on a difficult fine-grained species classification task distinguishing three types of fossil spruce pollen.Comment: CVMI 201

Pricing, Advertising, and Market Structure with Frictions

This paper develops a model of pricing and advertising in a matching environment with capacity constrained sellers and uncoordinated buyers. Sellers’ search intensity attracts buyers only probabilistically through costly informative advertisement. Equilibrium prices and profit maximizing advertising levels are derived and their properties analyzed. The model generates an inverted U-shape relationship between individual advertisement and market tightness which is robust to alternative advertising technologies. The well known empirical fact in the IO literature reflects the trade-off between price and market tightness matching effects. Finally, in this environment we can alleviate the discontinuity problem, allowing for unique symmetric equilibrium price to be derived.Directed searching; Advertising; Pricing; Market structure

Pricing, Advertising, and Market Structure with Frictions

This paper develops a model of pricing and advertising in a matching environment with capacity constrained sellers and uncoordinated buyers. Sellers' search intensity attracts buyers only probabilistically through costly informative advertisement. Equilibrium prices and profit maximizing advertising levels are derived and their properties analyzed. The model generates an inverted U-shape relationship between individual advertisement and market tightness which is robust to alternative advertising technologies. The well known empirical fact in the IO literature reflects the trade-off between price and market tightness-matching effects. Finally, in this environment we can alleviate the discontinuity problem, allowing for unique symmetric equilibrium price to be derived.Directed searching, Advertising, Pricing,Market structure

Stability of Reeb graphs under function perturbations: the case of closed curves

Reeb graphs provide a method for studying the shape of a manifold by encoding the evolution and arrangement of level sets of a simple Morse function defined on the manifold. Since their introduction in computer graphics they have been gaining popularity as an effective tool for shape analysis and matching. In this context one question deserving attention is whether Reeb graphs are robust against function perturbations. Focusing on 1-dimensional manifolds, we define an editing distance between Reeb graphs of curves, in terms of the cost necessary to transform one graph into another. Our main result is that changes in Morse functions induce smaller changes in the editing distance between Reeb graphs of curves, implying stability of Reeb graphs under function perturbations.Comment: 23 pages, 12 figure