Hyperbolic geometry for colour metrics

Hyperbolic geometry for colour metrics.

It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., co...

Hyperbolic Geometry

A computational framework for colour metrics and colour space transforms

An object-oriented computational framework for the transformation of colour data and colour metric tensors is presented. The main idea of the design is to represent the transforms between spaces as compositions of objects from a class hierarchy providing the methods for both the transforms themselves and the corresponding Jacobian matrices. In this way, new colour spaces can be implemented on t...

Hyperbolic-type metrics

The article is a status report on the contemporary research of hyperbolic-type metrics, and considers progress in the study of the classes of isometryand bilipschitz mappings with respect to some of the presented metrics. Also, the Gromov hyperbolicity question is discussed.

Metrics for Image Retrieval by Colour Content

We consider a functional-analytic setting for querying large image databases by colour content, in which the colour distributions (histograms), describing the colour content of an image, are probability measures on the colour space C. The Kantorovich distance turns out to be among the most relevant metrics on the space of colour distributions. We study the colour histogram space equipped with a...