Pointwise mutual information - Revision history

en>Alejandro edera: /* Definition */

2015-01-10T13:53:31Z

Definition

← Older revision		Revision as of 15:53, 10 January 2015
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	~~The writer~~ is ~~called Wilber Pegues~~. ~~One of~~ the ~~issues she enjoys most is canoeing and she~~'~~s been performing it for quite a while~~. ~~Ohio is exactly where my home is but my husband desires us~~ to ~~transfer. He is an info officer~~.<br><br>~~Also visit~~ my ~~website ... love psychics;~~ [http://~~kjhkkb~~.~~net~~/xe/~~notice/374835~~ http://~~kjhkkb~~.~~net~~],		Friends contact him Royal. Bookkeeping is what he does. Bottle tops gathering is the only pastime his wife doesn't approve of. Some time in the past he selected to reside in Idaho.<br><br>Here is my webpage [http://112.217.168.194/onsesang/xe/index.php?document_srl=10158&mid=comm_info01 http://112.217.168.194/]

en>Kku: cite

2014-02-19T17:31:45Z

cite

← Older revision		Revision as of 19:31, 19 February 2014
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	~~{{One source\|date=July 2009}}~~		The writer is called Wilber Pegues. One of the issues she enjoys most is canoeing and she's been performing it for quite a while. Ohio is exactly where my home is but my husband desires us to transfer. He is an info officer.<br><br>Also visit my website ... love psychics; [http://kjhkkb.net/xe/notice/374835 http://kjhkkb.net],

	~~In [[optics]], '''Grassmann's law'''~~ is ~~an empirical result about human color perception: that chromatic sensation can be described in terms of an effective stimulus consisting of [[linear]] combinations of different light colors~~. ~~It was discovered by [[Hermann Grassmann]].~~

	~~== Statement ==~~

	~~[[File:Grassman color circle 1853.png\|right\|thumb\|Grassman expressed his law with respect to a circular arrangement~~ of ~~spectral colors in this 1853 illustration.<ref>{{cite book \| title = Hermann Günther Grassmann (1809-1877): visionary mathematician, scientist~~ and ~~neohumanist scholar : papers from~~ a ~~sesquicentennial conference~~
	~~\| authors = Hermann Grassmann, Gert Schubring~~
	~~\| publisher = Springer~~
	~~\| year = 1996~~
	~~\| isbn = 978-0-7923-4261-8~~
	~~\| page = 78~~
	~~\| url = http://books~~.~~google.com/books?id=PUifpzKWhLkC&printsec=frontcover&dq=grassman%27s+second+law+color+linear&as_brr=3&ei=HQg9SqDGLpDOlQT7mpW6BQ~~
	~~}}</ref>]]~~

	~~An early statement of law, attributed to Grassmann,~~ is~~:<ref>{{cite book~~
	~~\| title = A text-book of physiology: normal and pathological. For students and practitioners of medicine~~
	~~\| author = Winfield Scott Hall~~
	~~\| publisher = Lea Brothers & Co~~
	~~\| year = 1905~~
	~~\| page = 624~~
	~~\| url = http://books.google.com/books?id=HPVwAAAAIAAJ&pg=PA624&dq=%22grassman%27s+law%22+color&as_brr=1&ei=fH08SpHNPITOlQS4wpG6BQ~~
	~~}}</ref>~~

	~~{{cquote\|~~
	~~If two simple~~ but ~~non-complementary spectral colors be mixed with each other, they give rise~~ to ~~the color sensation which may be represented by a color in the spectrum lying between both and mixed with a certain quantity of white~~.
	}}

	~~== Modern interpretation ==~~

	~~If a test color~~ is ~~the combination of two other colors, then in a matching experiment based on mixing primary light colors,~~ an ~~observer's matching value of each primary will be the sum of the matching values for each of the other test colors when viewed separately~~.

	~~In other words, if beam 1 and 2 are the initial colors, and the observer chooses~~ <~~math~~>~~(R_1,G_1,B_1)~~<~~/math~~> as the strengths of the primaries that match beam 1 and <math>(R_2,G_2,B_2)</math> as the strengths of the primaries that match beam 2, then if the two beams were combined, the matching values will be the sums of the components. ~~Precisely, they will be <math>(R,G,B)</math>, where~~:

	~~:<math>R= R_1+R_2\,<~~/~~math>~~
	~~:<math>G= G_1+G_2\,<~~/~~math>~~
	~~:<math>B= B_1+B_2\,<~~/~~math>~~

	~~Grassmann's law can be expressed in general form by stating that for a given color with a [[Spectral density\|spectral power distribution]] <math>I(\lambda)<~~/~~math> the RGB coordinates are given by:~~

	~~:<math>R= \int_0^\infty I(\lambda)\,\bar r(\lambda)\,d\lambda<~~/~~math>~~
	:~~<math>G= \int_0^\infty I(\lambda)\,\bar g(\lambda)\,d\lambda<~~/~~math>~~
	~~:<math>B= \int_0^\infty I(\lambda)\,\bar b(\lambda)\,d\lambda<~~/~~math>~~

	~~Observe that these are linear in <math>I</math>; the functions <math>\bar r(\lambda), \bar g(\lambda), \bar b(\lambda)</math> are the [[color matching function]]s with respect to the chosen primaries~~.

	~~== See also ==~~

	* [[Color space]]
	* [[CIE 1931 color space]]

	~~== References ==~~

	~~{{reflist}}~~

	~~[[Category:Color]]~~
	~~[[Category:Visual system]~~]

en>Nnbbb: /* Chain-rule for pmi */ corrected a symbol swap typo in the statement of the result. the derivation was fine.

2013-12-06T15:26:52Z

Chain-rule for pmi: corrected a symbol swap typo in the statement of the result. the derivation was fine.

← Older revision		Revision as of 17:26, 6 December 2013
Line 1:		Line 1:
	~~Wilber Berryhill~~ is ~~the name his parents gave him and he completely digs~~ that ~~name. My spouse and I reside~~ in ~~Kentucky~~. ~~Since he~~ was ~~eighteen he's been operating as an information officer but he plans on altering it~~. ~~To perform lacross is some thing he would never give~~ [~~http~~:~~//www~~.~~familysurvivalgroup~~.~~com/easy~~-~~methods~~-~~planting~~-~~looking~~-~~backyard~~/ ~~live psychic reading] up~~.<br><br>~~my site~~: [http://~~www~~.~~article-galaxy~~.com/~~profile.php~~?a=~~143251 free psychic readings] psychic~~ (~~[http:~~//~~www~~.~~khuplaza.com~~/~~dent~~/~~14869889 Privacy of Data~~: ~~This tool is built-~~with ~~and~~ functions~~-in Client Side JavaScripting~~, ~~so only your computer will see or process your data input~~/~~output~~.~~a cool way to improve~~])		{{One source\|date=July 2009}}

			In [[optics]], '''Grassmann's law''' is an empirical result about human color perception: that chromatic sensation can be described in terms of an effective stimulus consisting of [[linear]] combinations of different light colors. It was discovered by [[Hermann Grassmann]].

			== Statement ==

			[[File:Grassman color circle 1853.png\|right\|thumb\|Grassman expressed his law with respect to a circular arrangement of spectral colors in this 1853 illustration.<ref>{{cite book \| title = Hermann Günther Grassmann (1809-1877): visionary mathematician, scientist and neohumanist scholar : papers from a sesquicentennial conference
			\| authors = Hermann Grassmann, Gert Schubring
			\| publisher = Springer
			\| year = 1996
			\| isbn = 978-0-7923-4261-8
			\| page = 78
			\| url = http://books.google.com/books?id=PUifpzKWhLkC&printsec=frontcover&dq=grassman%27s+second+law+color+linear&as_brr=3&ei=HQg9SqDGLpDOlQT7mpW6BQ
			}}</ref>]]

			An early statement of law, attributed to Grassmann, is:<ref>{{cite book
			\| title = A text-book of physiology: normal and pathological. For students and practitioners of medicine
			\| author = Winfield Scott Hall
			\| publisher = Lea Brothers & Co
			\| year = 1905
			\| page = 624
			\| url = http://books.google.com/books?id=HPVwAAAAIAAJ&pg=PA624&dq=%22grassman%27s+law%22+color&as_brr=1&ei=fH08SpHNPITOlQS4wpG6BQ
			}}</ref>

			{{cquote\|
			If two simple but non-complementary spectral colors be mixed with each other, they give rise to the color sensation which may be represented by a color in the spectrum lying between both and mixed with a certain quantity of white.
			}}

			== Modern interpretation ==

			If a test color is the combination of two other colors, then in a matching experiment based on mixing primary light colors, an observer's matching value of each primary will be the sum of the matching values for each of the other test colors when viewed separately.

			In other words, if beam 1 and 2 are the initial colors, and the observer chooses <math>(R_1,G_1,B_1)</math> as the strengths of the primaries that match beam 1 and <math>(R_2,G_2,B_2)</math> as the strengths of the primaries that match beam 2, then if the two beams were combined, the matching values will be the sums of the components. Precisely, they will be <math>(R,G,B)</math>, where:

			:<math>R= R_1+R_2\,</math>
			:<math>G= G_1+G_2\,</math>
			:<math>B= B_1+B_2\,</math>

			Grassmann's law can be expressed in general form by stating that for a given color with a [[Spectral density\|spectral power distribution]] <math>I(\lambda)</math> the RGB coordinates are given by:

			:<math>R= \int_0^\infty I(\lambda)\,\bar r(\lambda)\,d\lambda</math>
			:<math>G= \int_0^\infty I(\lambda)\,\bar g(\lambda)\,d\lambda</math>
			:<math>B= \int_0^\infty I(\lambda)\,\bar b(\lambda)\,d\lambda</math>

			Observe that these are linear in <math>I</math>; the functions <math>\bar r(\lambda), \bar g(\lambda), \bar b(\lambda)</math> are the [[color matching function]]s with respect to the chosen primaries.

			== See also ==

			* [[Color space]]
			* [[CIE 1931 color space]]

			== References ==

			{{reflist}}

			[[Category:Color]]
			[[Category:Visual system]]

en>Gjnaasaa: /* Definition */ Added clarification to avoid confusion

2012-04-06T09:10:46Z

Definition: Added clarification to avoid confusion

New page

Wilber Berryhill is the name his parents gave him and he completely digs that name. My spouse and I reside in Kentucky. Since he was eighteen he's been operating as an information officer but he plans on altering it. To perform lacross is some thing he would never give [http://www.familysurvivalgroup.com/easy-methods-planting-looking-backyard/ live psychic reading] up.<br><br>my site: [http://www.article-galaxy.com/profile.php?a=143251 free psychic readings] psychic ([http://www.khuplaza.com/dent/14869889 Privacy of Data: This tool is built-with and functions-in Client Side JavaScripting, so only your computer will see or process your data input/output.a cool way to improve])