One dimensional sieve applied to images - Revision history

AndrewBangham: /* Now what about scale-space?. */

2014-06-22T21:55:14Z

Now what about scale-space?.

← Older revision		Revision as of 22:55, 22 June 2014
Line 42:		Line 42:
	The 'm'-sieve preserves scale-space so no new extrema (light regions) are formed as we move to increasing scales.<br>		The 'm'-sieve preserves scale-space so no new extrema (light regions) are formed as we move to increasing scales.<br>
	\|width="50%"\| Right Panel. A ''Gaussian'' filter bank also preserves scale-space as shown by Witkin 1986.<br>		\|width="50%"\| Right Panel. A ''Gaussian'' filter bank also preserves scale-space as shown by Witkin 1986.<br>
	(Babaud et. al. 1986 "The uniqueness of the Gaussian kernel ...")<ref>Babaud, Jean; Witkin, Andrew P.; Baudin, Michel; Duda, Richard O., "Uniqueness of the Gaussian Kernel for Scale-Space Filtering," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.PAMI-8, no.1, pp.26,33, Jan. 1986 doi: 10.1109/TPAMI.1986.4767749</ref>		(Babaud et. al. 1986 "The uniqueness of the Gaussian kernel ...")<ref>Babaud, Jean; Witkin, Andrew P.; Baudin, Michel; Duda, Richard O., "Uniqueness of the Gaussian Kernel for Scale-Space Filtering," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.PAMI-8, no.1, pp.26,33, Jan. 1986 doi: 10.1109/TPAMI.1986.4767749</ref>==References==
			<references />

	\|}		\|}

AndrewBangham: /* Using granules to represent the data segment. */

2014-06-22T21:53:49Z

Using granules to represent the data segment.

← Older revision		Revision as of 22:53, 22 June 2014
Line 51:		Line 51:
	\|width="50%"\| [[Image:Siv4 test granules.png\|400px\|'o' non-linear filter (sieve)]]		\|width="50%"\| [[Image:Siv4 test granules.png\|400px\|'o' non-linear filter (sieve)]]
	\|}		\|}
	An alternative is to treat the granularity domain in the manner of wavelets and concentrate the useful information by summing the 'energy' within the granules (fragment) along each scale to produce a histogram the equivalent of a local power spectrum ~~which~~ can be further simplified into, say, ~~six~~ logarithmically spaced scale-bands. ~~Similarly, the phase~~. To be useful, ~~both probably~~ should be normalised c.f. the ~~cepstrum and ?~~		An alternative is to treat the granularity domain in the manner of wavelets and concentrate the useful information by summing the 'energy' within the granules (in the signal fragment) along each scale to produce a histogram the equivalent of a local power spectrum. This can be further simplified into, say, twenty logarithmically spaced scale-bands. These two steps lose information (but hopefully concentrate useful components). To be useful, granularity spectrum should be normalised. One way is to compute the equivalent of the cepstrum. Similarly, the phase.

AndrewBangham: /* Using granules to represent the data segment. */

2014-06-22T21:48:45Z

Using granules to represent the data segment.

Show changes

AndrewBangham: /* Using granules to represent the data segment. */

2014-06-22T21:33:39Z

Using granules to represent the data segment.

← Older revision		Revision as of 22:33, 22 June 2014
Line 48:		Line 48:
	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"
	\|- valign="top"		\|- valign="top"
	\|width="50%"\| Another heat-map. The plot is an alternative view of the left Panel above. This time showing the features (at each scale) that are peeled off (removed) by increasing scale sieve filters. The color map is 'jet' to make the features more visible. We call these features granules. It is possible to imagine a 'tree' representation of these granules.		\|width="50%"\| Another heat-map. The plot is an alternative view of the left Panel above. This time showing the features (at each scale) that are peeled off (removed) by increasing scale sieve filters. The color map is 'jet' to make the features more visible. We call these features granules. It is possible to imagine a 'tree' representation of these granules ([[One_dimensional_sieve_introduction#Tracing_the_granules_through_scale-space_identifies_candidate_MSER.27s \| see here for the connection with MSER's.]])
	\|width="50%"\| [[Image:Siv4 test granules.png\|400px\|'o' non-linear filter (sieve)]]		\|width="50%"\| [[Image:Siv4 test granules.png\|400px\|'o' non-linear filter (sieve)]]
	\|}		\|}

AndrewBangham: /* Using granules as a signature for the data segment. */

2014-06-22T18:45:26Z

Using granules as a signature for the data segment.

← Older revision		Revision as of 19:45, 22 June 2014
Line 45:		Line 45:
	\|}		\|}

	====<span style="color:navy">Using ''granules'' ~~as a signature for~~ the data segment. </span>====		====<span style="color:navy">Using ''granules'' to represent the data segment. </span>====
	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"
	\|- valign="top"		\|- valign="top"

AndrewBangham: /* Using granules as a signature for the data segment. */

2014-06-22T18:42:28Z

Using granules as a signature for the data segment.

← Older revision		Revision as of 19:42, 22 June 2014
Line 48:		Line 48:
	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"
	\|- valign="top"		\|- valign="top"
	\|width="50%"\| Another heat-map. The plot is an alternative view of the left Panel above. This time showing the features (at each scale) that are peeled off (removed) by increasing scale sieve filters. The color map is 'jet' to make the features~~, we~~ call ~~them~~ granules~~, more obvious~~. It is possible to imagine a 'tree' representation of these granules.		\|width="50%"\| Another heat-map. The plot is an alternative view of the left Panel above. This time showing the features (at each scale) that are peeled off (removed) by increasing scale sieve filters. The color map is 'jet' to make the features more visible. We call these features granules. It is possible to imagine a 'tree' representation of these granules.
	\|width="50%"\| [[Image:Siv4 test granules.png\|400px\|'o' non-linear filter (sieve)]]		\|width="50%"\| [[Image:Siv4 test granules.png\|400px\|'o' non-linear filter (sieve)]]
	\|}		\|}

AndrewBangham: /* Now think about scale-space. */

2014-06-22T18:41:04Z

Now think about scale-space.

← Older revision		Revision as of 19:41, 22 June 2014
Line 36:		Line 36:

	====<span style="color:navy">Now think about '''scale-space'''. </span>====		====<span style="color:navy">Now think about '''scale-space'''. </span>====
	[[Image:Siv4 test 5.png\|~~500px~~\|center\|'m' non-linear filter (sieve) compared to Gaussian filter]]		[[Image:Siv4 test 5.png\|400px\|center\|'m' non-linear filter (sieve) compared to Gaussian filter]]
	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"
	\|- valign="top"		\|- valign="top"
Line 44:		Line 44:
	(Babaud et. al. 1986 "The uniqueness of the Gaussian kernel ...")<ref>Babaud, Jean; Witkin, Andrew P.; Baudin, Michel; Duda, Richard O., "Uniqueness of the Gaussian Kernel for Scale-Space Filtering," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.PAMI-8, no.1, pp.26,33, Jan. 1986 doi: 10.1109/TPAMI.1986.4767749</ref>		(Babaud et. al. 1986 "The uniqueness of the Gaussian kernel ...")<ref>Babaud, Jean; Witkin, Andrew P.; Baudin, Michel; Duda, Richard O., "Uniqueness of the Gaussian Kernel for Scale-Space Filtering," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.PAMI-8, no.1, pp.26,33, Jan. 1986 doi: 10.1109/TPAMI.1986.4767749</ref>
	\|}		\|}

	====<span style="color:navy">Using ''granules'' as a signature for the data segment. </span>====		====<span style="color:navy">Using ''granules'' as a signature for the data segment. </span>====
	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"

AndrewBangham: /* Now think about scale-space. */

2014-06-22T18:40:00Z

Now think about scale-space.

← Older revision		Revision as of 19:40, 22 June 2014
Line 44:		Line 44:
	(Babaud et. al. 1986 "The uniqueness of the Gaussian kernel ...")<ref>Babaud, Jean; Witkin, Andrew P.; Baudin, Michel; Duda, Richard O., "Uniqueness of the Gaussian Kernel for Scale-Space Filtering," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.PAMI-8, no.1, pp.26,33, Jan. 1986 doi: 10.1109/TPAMI.1986.4767749</ref>		(Babaud et. al. 1986 "The uniqueness of the Gaussian kernel ...")<ref>Babaud, Jean; Witkin, Andrew P.; Baudin, Michel; Duda, Richard O., "Uniqueness of the Gaussian Kernel for Scale-Space Filtering," Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.PAMI-8, no.1, pp.26,33, Jan. 1986 doi: 10.1109/TPAMI.1986.4767749</ref>
	\|}		\|}
			====<span style="color:navy">Using ''granules'' as a signature for the data segment. </span>====
	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"
	\|- valign="top"		\|- valign="top"

AndrewBangham: /* Repeat over scales 0 to 15 */

2014-06-22T18:38:01Z

Repeat over scales 0 to 15

← Older revision		Revision as of 19:38, 22 June 2014
Line 55:		Line 55:
	\|- valign="top"		\|- valign="top"
	\|width="50%"\| Increasing the scale (towards the front) removes extrema of increasing length. The algorithm cannot create new maxima (it is an 'o' sieve) it is, therefore, scale-space preserving.		\|width="50%"\| Increasing the scale (towards the front) removes extrema of increasing length. The algorithm cannot create new maxima (it is an 'o' sieve) it is, therefore, scale-space preserving.
	\|[[Image:Replacement IllustrateSIV 1 07.png\|400px\|'o' non-linear filter (sieve)]]		\|width="50%"\| [[Image:Replacement IllustrateSIV 1 07.png\|400px\|'o' non-linear filter (sieve)]]
	\|}		\|}
	YY=ones([length(X),1+maxscale]);		YY=ones([length(X),1+maxscale]);

AndrewBangham: /* 'siv4.mex' implemenation applies the m-sieve to a vector or column wise to a matrix */

2014-06-22T18:37:38Z

'siv4.mex' implemenation applies the m-sieve to a vector or column wise to a matrix

← Older revision		Revision as of 19:37, 22 June 2014
Line 11:		Line 11:
	{\| border="0" cellpadding="5" cellspacing="5"		{\| border="0" cellpadding="5" cellspacing="5"
	\|- valign="top"		\|- valign="top"
	\|width="50%"\| The data has minima and maxima of different scales (lengths). In one dimension we measure pulse length using a ruler, measuring tape or whatever - but not frequency or Gaussian scale.		\|width="30%"\| The data has minima and maxima of different scales (lengths). In one dimension we measure pulse length using a ruler, measuring tape or whatever - but not frequency or Gaussian scale.
	\|[[Image:IllustrateSIV_1_02.png\|400px]]		\|width="50%"\| [[Image:IllustrateSIV_1_02.png\|400px]]
	\|}		\|}