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.

From Axial to Road-Centre Lines: A New Representation for Space Syntax and a New Model of Route Choice for Transport Network Analysis:

Abstract: Axial analysis is one of the fundamental components of space syntax. The space syntax community has suggested that it picks up qualities of configurational relationships between spaces not illuminated by other representations. However, critics have questioned the absolute necessity of axial lines to space syntax, as well as the exact definition of axial lines. Why not another representation? In particular, why not road-centre lines, which are easily available in many countries for use within geographical information systems? Here I propose that a recently introduced method of analysis, angular segment analysis, can marry axial and road-centre line representations, and in doing so reflect a cognitive model of how route choice decisions may be made. I show that angular segment analysis can be applied generally to road-centre line segments or axial segments, through a simple length- weighted normalisation procedure that makes values between the two maps comparable. I make comparative quantitative assessments for a real urban system, not just investigating angular analysis between axial and road-centre line networks, but also including more intuitive measures based on metric (or block) distances between locations. I show that the new angular segment analysis algorithm produces better correlation with observed vehicular flow than both standard axial analysis and metric distance measures. The results imply that there is no reason why space syntax inspired measures cannot be combined with transportation network analysis representations in order to create a new, cognitively coherent, model of movement in the city.

Automatic Parameter Selection for Denoising Algorithms Using a No-Reference Measure of Image Content

Abstract: Across the field of inverse problems in image and video processing, nearly all algorithms have various parameters which need to be set in order to yield good results. In practice, usually the choice of such parameters is made empirically with trial and error if no “ground-truth” reference is available. Some analytical methods such as cross-validation and Stein's unbiased risk estimate (SURE) have been successfully used to set such parameters. However, these methods tend to be strongly reliant on restrictive assumptions on the noise, and also computationally heavy. In this paper, we propose a no-reference metric Q which is based upon singular value decomposition of local image gradient matrix, and provides a quantitative measure of true image content (i.e., sharpness and contrast as manifested in visually salient geometric features such as edges,) in the presence of noise and other disturbances. This measure 1) is easy to compute, 2) reacts reasonably to both blur and random noise, and 3) works well even when the noise is not Gaussian. The proposed measure is used to automatically and effectively set the parameters of two leading image denoising algorithms. Ample simulated and real data experiments support our claims. Furthermore, tests using the TID2008 database show that this measure correlates well with subjective quality evaluations for both blur and noise distortions.

Autoencoding beyond pixels using a learned similarity metric

Abstract: We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder with a generative adversarial network we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. Moreover, we show that the method learns an embedding in which high-level abstract visual features (e.g. wearing glasses) can be modified using simple arithmetic.

MoverScore: Text Generation Evaluating with Contextualized Embeddings and Earth Mover Distance

Abstract: A robust evaluation metric has a profound impact on the development of text generation systems. A desirable metric compares system output against references based on their semantics rather than surface forms. In this paper we investigate strategies to encode system and reference texts to devise a metric that shows a high correlation with human judgment of text quality. We validate our new metric, namely MoverScore, on a number of text generation tasks including summarization, machine translation, image captioning, and data-to-text generation, where the outputs are produced by a variety of neural and non-neural systems. Our findings suggest that metrics combining contextualized representations with a distance measure perform the best. Such metrics also demonstrate strong generalization capability across tasks. For ease-of-use we make our metrics available as web service.