Metric (mathematics)

About: Metric (mathematics) is a research topic. Over the lifetime, 42617 publications have been published within this topic receiving 836571 citations. The topic is also known as: distance function & metric.

Optimal triangulation and quadric-based surface simplification

Abstract: Many algorithms for reducing the number of triangles in a surface model have been proposed, but to date there has been little theoretical analysis of the approximations they produce. Previously we described an algorithm that simplifies polygonal models using a quadric error metric. This method is fast and produces high quality approximations in practice. Here we provide some theory to explain why the algorithm works as well as it does. Using methods from differential geometry and approximation theory, we show that in the limit as triangle area goes to zero on a differentiable surface, the quadric error is directly related to surface curvature. Also, in this limit, a triangulation that minimizes the quadric error metric achieves the optimal triangle aspect ratio in that it minimizes theL2 geometric error. This work represents a new theoretical approach for the analysis of simplification algorithms. © 1999 Elsevier Science B.V. All rights reserved.

HSME: Hypersphere Manifold Embedding for Visible Thermal Person Re-Identification

Abstract: Person Re-identification(re-ID) has great potential to contribute to video surveillance that automatically searches and identifies people across different cameras. Heterogeneous person re-identification between thermal(infrared) and visible images is essentially a cross-modality problem and important for night-time surveillance application. Current methods usually train a model by combining classification and metric learning algorithms to obtain discriminative and robust feature representations. However, the combined loss function ignored the correlation between classification subspace and feature embedding subspace. In this paper, we use Sphere Softmax to learn a hypersphere manifold embedding and constrain the intra-modality variations and cross-modality variations on this hypersphere. We propose an end-to-end dualstream hypersphere manifold embedding network(HSMEnet) with both classification and identification constraint. Meanwhile, we design a two-stage training scheme to acquire decorrelated features, we refer the HSME with decorrelation as D-HSME. We conduct experiments on two crossmodality person re-identification datasets. Experimental results demonstrate that our method outperforms the state-of-the-art methods on two datasets. On RegDB dataset, rank-1 accuracy is improved from 33.47% to 50.85%, and mAP is improved from 31.83% to 47.00%.

Proximity Matching Using Fixed-Queries Trees

Abstract: We present a new data structure, called the fixed-queries tree, for the problem of finding all elements of a fixed set that are close, under some distance function, to a query element. Fixed-queries trees can be used for any distance function, not necessarily even a metric, as long as it satisfies the triangle inequality. We give an analysis of several performance parameters of fixed-queries trees and experimental results that support the analysis. Fixed-queries trees are particularly efficient for applications in which comparing two elements is expensive.

Fréchet ChemNet Distance: A Metric for Generative Models for Molecules in Drug Discovery

Abstract: The new wave of successful generative models in machine learning has increased the interest in deep learning driven de novo drug design. However, method comparison is difficult because of various flaws of the currently employed evaluation metrics. We propose an evaluation metric for generative models called Frechet ChemNet distance (FCD). The advantage of the FCD over previous metrics is that it can detect whether generated molecules are diverse and have similar chemical and biological properties as real molecules.