One dimensional sieve introduction

Return to MSERs and extrema

1D Signals

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.

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.

Filter

Linear

A linear Gaussian filter with <math>\sigma=2</math> attenuates extrema without introducing new ones. But blurring may be a problem.

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.

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.