Distance and Similarity Measures. Furht, B., editor In Encyclopedia of Multimedia, pages 188–189. Springer US, 2008. 00000
Distance and Similarity Measures [link]Paper  abstract   bibtex   
DefinitionThe notion of distance or similarity between two color vectors is of paramount importance for the development of the vector processing techniques such as noise removal filters, edge detectors and image zoomers.Since each color vector is uniquely determined via its magnitude (length) and direction (orientation), the evaluation of the color vectors can be realized in the magnitude domain, the directional domain, or it can utilize both vectors' magnitude and direction [1–3].The most commonly used measure to quantify the distance between two color vectors χi = [xi1, xi2, xi3] and χj = [xj1, xj2, xj3], in the magnitude domain, is the generalized weighted Minkowski metric:d(xi,xj)=∥xi,xj∥L=c(∑3k=1ξk\textbarxik−xjk\textbarL)1/Ld(xi,xj)=∥xi,xj∥L=c(∑k=13ξk\textbarxik−xjk\textbarL)1/Ld(\\textbackslashrm \\textbackslashbf x\\_i ,\\textbackslashrm \\textbackslashbf x\\_j ) = \textbackslashleft\textbackslash\textbar \\\textbackslashrm \\textbackslashbf x\\_i ,\\textbackslashrm \\textbackslashbf x\\_j \ \textbackslashright\textbackslash\textbar_L = c\textbackslashleft( \\textbackslashsum\textbackslashnolimits_\k = 1\\textasciicircum3 \\textbackslashxi _k \textbackslashleft\textbar \x_\ik\ - x_\jk\ \ \textbackslashright\textbar\textasciicircumL \ \ \textbackslashright)\textasciicircum\1/L\where c is the non-negative scaling parameter denoting the measure of the overall discrimination power and the ...
@incollection{furht_distance_2008,
	title = {Distance and {Similarity} {Measures}},
	copyright = {©2008 Springer-Verlag},
	isbn = {978-0-387-74724-8 978-0-387-78414-4},
	url = {http://link.springer.com/referenceworkentry/10.1007/978-0-387-78414-4_306},
	abstract = {DefinitionThe notion of distance or similarity between two color vectors is of paramount importance for the development of the vector processing techniques such as noise removal filters, edge detectors and image zoomers.Since each color vector is uniquely determined via its magnitude (length) and direction (orientation), the evaluation of the color vectors can be realized in the magnitude domain, the directional domain, or it can utilize both vectors' magnitude and direction [1–3].The most commonly used measure to quantify the distance between two color vectors χi = [xi1, xi2, xi3] and χj = [xj1, xj2, xj3], in the magnitude domain, is the generalized weighted Minkowski metric:d(xi,xj)=∥xi,xj∥L=c(∑3k=1ξk{\textbar}xik−xjk{\textbar}L)1/Ld(xi,xj)=∥xi,xj∥L=c(∑k=13ξk{\textbar}xik−xjk{\textbar}L)1/Ld(\{{\textbackslash}rm \{{\textbackslash}bf x\}\}\_i ,\{{\textbackslash}rm \{{\textbackslash}bf x\}\}\_j ) = {\textbackslash}left{\textbackslash}{\textbar} \{\{{\textbackslash}rm \{{\textbackslash}bf x\}\}\_i ,\{{\textbackslash}rm \{{\textbackslash}bf x\}\}\_j \} {\textbackslash}right{\textbackslash}{\textbar}\_L = c{\textbackslash}left( \{{\textbackslash}sum{\textbackslash}nolimits\_\{k = 1\}{\textasciicircum}3 \{{\textbackslash}xi \_k {\textbackslash}left{\textbar} \{x\_\{ik\} - x\_\{jk\} \} {\textbackslash}right{\textbar}{\textasciicircum}L \} \} {\textbackslash}right){\textasciicircum}\{1/L\}where c is the non-negative scaling parameter denoting the measure of the overall discrimination power and the ...},
	language = {en},
	urldate = {2016-05-03},
	booktitle = {Encyclopedia of {Multimedia}},
	publisher = {Springer US},
	editor = {Furht, Borko},
	year = {2008},
	note = {00000},
	pages = {188--189}
}
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