One dimensional sieve introduction: Difference between revisions

From BanghamLab
Jump to navigation Jump to search
Line 1: Line 1:
[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</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.
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.
{| border="0" cellpadding="5" cellspacing="5"    3D extrema thumb.gif
{| border="0" cellpadding="5" cellspacing="5"    3D extrema thumb.gif

Revision as of 10:17, 15 November 2013

Return to MSERs and extrema

1D Signals to MSERs and granules

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.

AAMToolbox Consider a signal, <math>X</math>
X=getData('PULSES3WIDE')
>blue  X=0 5 5 0 0 1 1 4 3 3 2 2 1 2 2 2 1 0 0 0 1 1 0 3 2 0 0 0 6 0 0
<math>X</math> has three one-sample-wide maxima (<math>M^1_8</math> , <math>M^1_{24}</math> , <math>M^1_{29}</math> ), two two-sample-wide maxima (<math>M^2_{14}</math> , <math>M^2_{21}</math>) some of which, when removed, will persist as larger scale maxima, e.g. <math>M^1_{24}</math> will become two samples wide as the peak is clipped off. IllustrateSIV 1 02.png

Filter

Linear

A linear Gaussian filter with <math>\sigma=2</math> attenuates extrema without introducing new ones. But blurring may be a problem. Gaussian filtered
h=fspecial('Gaussian',9,2);
Y=conv(X,(h(5,:)/sum(h(5,:))),'same');

Non-linear

A low-pass 'o' sieve scale 1 (non-linear filter underpinning the MSER algorithm) can remove scale 1 maxima. The result is shown in red, extrema at <math>M^1_8</math> , <math>M^1_{24}</math> , <math>M^1_{29}</math> have been removed. There is no blur. The remaining signal is unchanged. 'o' non-linear filter (sieve)
scaleA=1;
Y1=SIVND_m(X,scaleA,'o');
Scale 2 maxima are removed next using the 'o' sieve scale 2. The result is shown in green. Extrema at <math>M^2_{14}</math> , <math>M^2_{21}</math> have been removed. Still no blur and what remains is unchanged. 'o' non-linear filter (sieve)
scaleB=2;
Y2=SIVND_m(X,scaleB,'o');