Scale-space segmentation

There have been numerous research works in this area, out of which a few have now reached a state where they can be applied either with interactive manual intervention (usually with application to medical imaging) or fully automatically.

Koenderink[2] proposed to study how iso-intensity contours evolve over scales and this approach was investigated in more detail by Lifshitz and Pizer.

Gauch and Pizer[6] studied the complementary problem of ridges and valleys at multiple scales and developed a tool for interactive image segmentation based on multi-scale watersheds.

The use of stable image structures over scales has been furthered by Ahuja and his co-workers[10][11] into a fully automated system.

[13] Bijaoui and Rué [14] associate structures detected in scale-space above a minimum noise threshold into an object tree which spans multiple scales and corresponds to a kind of feature in the original signal.

A one-dimension example of scale-space segmentation. A signal (black), multi-scale-smoothed versions of it (red), and segment averages (blue) based on scale-space segmentation
The dendrogram corresponding to the segmentations in the figure above. Each "×" identifies the position of an extremum of the first derivative of one of 15 smoothed versions of the signal (red for maxima, blue for minima). Each "+" identifies the position that the extremum tracks back to at the finest scale. The signal features that persist to the highest scale (smoothest version) are evident as the tall structures that correspond to the major segment boundaries in the figure above.