One dimensional sieve introduction - Revision history

AndrewBangham: /* Linear */

2014-01-03T15:55:32Z

Linear

← Older revision		Revision as of 15:55, 3 January 2014
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	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"
	\|- valign="top"		\|- valign="top"
	\|width="50%"\| A linear Gaussian filter with <math>\sigma=2</math> attenuates extrema without introducing new ones. The signal is simpler but has large scale information ~~been~~ more difficult to read ~~given the blurring.~~ \|[[Image:GaussianSmoothedSigma2.png\|350px\|Gaussian filtered]]		\|width="50%"\| A linear Gaussian filter with <math>\sigma=2</math> attenuates extrema without introducing new ones. The signal is simpler but has blurring made large scale information more difficult to read?
			\|[[Image:GaussianSmoothedSigma2.png\|350px\|Gaussian filtered]]
	\|}		\|}
	h=fspecial('Gaussian',9,2);		h=fspecial('Gaussian',9,2);

AndrewBangham: /* 1D Signals to MSERs and granules */

2014-01-03T15:54:08Z

1D Signals to MSERs and granules

← Older revision		Revision as of 15:54, 3 January 2014
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	[http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/MSER%27s_and_Connected_sets#One_dimensional_signals Return to MSERs and extrema]<br><br>		[http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/MSER%27s_and_Connected_sets#One_dimensional_signals Return to MSERs and extrema]<br><br>
	=<span style="color:Chocolate">1D Signals to MSERs and granules</span>=		=<span style="color:Chocolate">1D Signals to MSERs and granules</span>=
	Matlab function IllustrateSIV_1 illustrates how MSERs (maximally stable extremal regions) and sieves are related. We start with one dimensional signals before moving to two dimensional images and three dimensional volumes.		A Matlab function IllustrateSIV_1.m illustrates how MSERs (maximally stable extremal regions) and sieves are related. We start with one dimensional signals before moving to two dimensional images and three dimensional volumes.<br><br>
			The information lies in the pattern of pulses. Each pulse is characterised by a position, length (scale) and amplitude. The goal is to find maxima that persist over a number of scales - i.e. they are stable.<br><br>
	{\| border="0" cellpadding="5" cellspacing="5" 3D extrema thumb.gif		{\| border="0" cellpadding="5" cellspacing="5" 3D extrema thumb.gif
	\|- valign="top"		\|- valign="top"

AndrewBangham: /* Linear */

2014-01-03T15:50:52Z

Linear

← Older revision		Revision as of 15:50, 3 January 2014
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	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"
	\|- valign="top"		\|- valign="top"
	\|width="50%"\| A linear Gaussian filter with <math>\sigma=2</math> attenuates extrema without introducing new ones. ~~But~~ blurring ~~may be a problem~~.		\|width="50%"\| A linear Gaussian filter with <math>\sigma=2</math> attenuates extrema without introducing new ones. The signal is simpler but has large scale information been more difficult to read given the blurring. \|[[Image:GaussianSmoothedSigma2.png\|350px\|Gaussian filtered]]
	\|[[Image:GaussianSmoothedSigma2.png\|350px\|Gaussian filtered]]
	\|}		\|}
	h=fspecial('Gaussian',9,2);		h=fspecial('Gaussian',9,2);

AndrewBangham at 14:41, 20 November 2013

2013-11-20T14:41:07Z

← Older revision		Revision as of 14:41, 20 November 2013
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	{\| border="0" cellpadding="5" cellspacing="5" 3D extrema thumb.gif		{\| border="0" cellpadding="5" cellspacing="5" 3D extrema thumb.gif
	\|- valign="top"		\|- valign="top"
	\|width="20%"\| [[Image:IllustrateSIV_1_01_thumb.gif\|140px\|~~AAMToolbox~~]]		\|width="20%"\| <!-- [[Image:IllustrateSIV_1_01_thumb.gif\|140px\|IllustrateSIV 1 01 thumb]]-->
	\|'''Consider a signal''', <math>X</math><br>		\|'''Consider a signal''', <math>X</math><br>
	X=getData('PULSES3WIDE')		X=getData('PULSES3WIDE')

AndrewBangham: /* So far maxima. What about minima and more? */

2013-11-17T19:19:15Z

So far maxima. What about minima and more?

← Older revision		Revision as of 19:19, 17 November 2013
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	<span style="color:Chocolate">'''Which is better for finding 1D MSER's, 'o' or 'c'?'''</span>		<span style="color:Chocolate">'''Which is better for finding 1D MSER's, 'o' or 'c'?'''</span>
	*It depends on the data		*It depends on the data
	*Further alternative operators include 'M', 'N' and 'm'.		*Further alternative operators include 'M', 'N' and 'm' which might be better still (to be discussed elsewhere).
	\|[[Image:Illustrate_c_SIV_1_09.png\|400px\|'o' non-linear filter (sieve)]]		\|[[Image:Illustrate_c_SIV_1_09.png\|400px\|'o' non-linear filter (sieve)]]
	\|}		\|}

AndrewBangham: /* So far maxima. What about minima and more? */

2013-11-17T11:28:27Z

So far maxima. What about minima and more?

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 *invert the signal, process it, and invert it back.
 *OR, in this case, we could substitute a min for a max within SIVND_m.
 This implementation also maintains ''lists of both maxima and minima'' throughout because there can be value in using the combined operators M, N, m
          switch type

AndrewBangham: /* So far maxima. What about minima and more? */

2013-11-17T10:58:39Z

So far maxima. What about minima and more?

← Older revision		Revision as of 10:58, 17 November 2013
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	The filter (sieve) that finds maxima is a connect-set ''opening'' ('o' sieve). A 'c' sieve finds the connected-set closing, or minima. To work with minima we could:		The filter (sieve) that finds maxima is a connect-set ''opening'' ('o' sieve). A 'c' sieve finds the connected-set closing, or minima. To work with minima we could:
	*invert the signal, process it, and invert it back.		*invert the signal, process it, and invert it back.
	*OR we could substitute a ~~mini~~ for a max:		*OR, in this case, we could substitute a min for a max within SIVND_m.
	if type=='o'		This implementation also maintains ''lists of both maxima and minima'' throughout because there can be value in using the combined operators M, N, m
	v=~~min~~(~~deltas~~);		switch type
	~~elseif type~~=='c'		case {'o'} % opening, merge all maximal runs of less than scale with their nearest value
	v=~~max~~(~~deltas~~);		data=ND_connected_set_merging(data,scale,type,verbose);
	~~end~~		case {'c'} % closing, merge all minima runs of less than scale with their nearest value
	~~Actually~~, ~~the SIVND_m.~~m ~~implementation uses the latter. It also maintains~~ ''~~lists of both maxima and minima~~'~~' throughout.~~		data=ND_connected_set_merging(data,scale,type,verbose);
			case {'C'} % closing, invert-open-invert
			data.workArray=uint8(-double(data.workArray)+256);
			data.value=uint8(-double(data.value)+256);
			data=ND_connected_set_merging(data,scale,'o',verbose);
			data.workArray=uint8(-double(data.workArray)+256);
			data.value=uint8(-double(data.value)+256);
			case 'M' % Open close
			data=ND_connected_set_merging(data,scale,'o',verbose);
			data=ND_connected_set_merging(data,scale,'c',verbose);
			case 'N' % Close open
			data=ND_connected_set_merging(data,scale,'c',verbose);
			data=ND_connected_set_merging(data,scale,'o',verbose);
			case 'm' % recursive median
			data=ND_connected_set_rmedian(data,scale,'m',verbose);
			otherwise
			error('type not recognised it should be (m, o, c, C, M or N)');
			end

AndrewBangham: /* So far maxima. What about minima and more? */

2013-11-17T10:51:44Z

So far maxima. What about minima and more?

← Older revision		Revision as of 10:51, 17 November 2013
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	=<span style="color:Chocolate">So far '''''maxima'''''. What about ''minima'' and more?</span>=		=<span style="color:Chocolate">So far '''''maxima'''''. What about ''minima'' and more?</span>=
	'''~~Which is the~~ ''~~most stable~~''?'''~~<br><br>~~		The filter (sieve) that finds maxima is a connect-set ''opening'' ('o' sieve). A 'c' sieve finds the connected-set closing, or minima. To work with minima we could:
	~~This is a pragmatic judgement. Parameters might include~~		*invert the signal, process it, and invert it back.
	~~#how stable over scale~~ (~~length~~)		*OR we could substitute a mini for a max:
	~~#amplitude~~ (~~value or level~~)		if type=='o'
	~~#a vector~~ of ~~amplitude over scale~~		v=min(deltas);
	~~#proximity to others~~		elseif type=='c'
			v=max(deltas);
			end
			Actually, the SIVND_m.m implementation uses the latter. It also maintains ''lists of both maxima and minima'' throughout.

AndrewBangham: /* We have candidate 1D MSER's */

2013-11-17T10:41:32Z

We have candidate 1D MSER's

← Older revision		Revision as of 10:41, 17 November 2013
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	=<span style="color:Chocolate">We have candidate 1D MSER's</span>=		=<span style="color:Chocolate">We have candidate 1D MSER's</span>=
	'''Which is the ''most stable''?'''<br><br>		<span style="color:SaddleBrown">'''Which is the ''most stable''?'''<br><br>
	This is a pragmatic judgement. Parameters might include		This is a pragmatic judgement. Parameters might include</span>
	#how stable over scale (length)		#<span style="color:SaddleBrown">how stable over scale (length)</span>
	#amplitude (value or level)		#<span style="color:SaddleBrown">amplitude (value or level)</span>
	#a vector of amplitude over scale		#<span style="color:SaddleBrown">a vector of amplitude over scale</span>
	#proximity to others		#<span style="color:SaddleBrown">proximity to others</span>

	=<span style="color:Chocolate">So far '''''maxima'''''. What about ''minima'' and more?</span>=		=<span style="color:Chocolate">So far '''''maxima'''''. What about ''minima'' and more?</span>=
	'''Which is the ''most stable''?'''<br><br>		'''Which is the ''most stable''?'''<br><br>

AndrewBangham: /* We have candidate 1D MSER's */

2013-11-17T10:40:21Z

We have candidate 1D MSER's

← Older revision		Revision as of 10:40, 17 November 2013
Line 94:		Line 94:

	=<span style="color:Chocolate">We have candidate 1D MSER's</span>=		=<span style="color:Chocolate">We have candidate 1D MSER's</span>=
			'''Which is the ''most stable''?'''<br><br>
			This is a pragmatic judgement. Parameters might include
			#how stable over scale (length)
			#amplitude (value or level)
			#a vector of amplitude over scale
			#proximity to others
			=<span style="color:Chocolate">So far '''''maxima'''''. What about ''minima'' and more?</span>=
	'''Which is the ''most stable''?'''<br><br>		'''Which is the ''most stable''?'''<br><br>
	This is a pragmatic judgement. Parameters might include		This is a pragmatic judgement. Parameters might include