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.
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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
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| <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.
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Filter
Linear
| A linear Gaussian filter with <math>\sigma=2</math> attenuates extrema without introducing new ones. But blurring may be a problem.
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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.
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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.
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scaleB=2;
Y2=SIVND_m(X,scaleB,'o');
