Tie-Zone Watershed, Bottlenecks, and Segmentation Robustness Analysis

In a recent paper [1], a new type of watershed (WS) transform was introduced: the tie-zone watershed (TZWS). This region-based watershed transform does not depend on arbitrary implementation and provides a unique (and thereby unbiased) optimal solution. Indeed, many optimal solutions are sometimes possible when segmenting an image by WS. The TZWS assigns each pixel to a catchment basin (CB) if in all solutions it belongs to this CB. Otherwise, the pixel is said to belong to a tie-zone (TZ). An efficient algorithm computing the TZWS and based on the Image Foresting Transform (IFT) was also proposed. In this article, we define the new concept of "bottlenecks" in the watermerging paradigm. Intuitively, the bottlenecks are the first contact points between at least two different wave fronts. They are pixels in the image where different colored waters meet and tie and from which may begin, therefore, the tie-zones. They represent the origin points or the access of the tie-zones (regions that cannot be labeled without making arbitrary choices). If they are preferentially assigned to one or another colored water according to an arbitrary processing order, as occurs in most of watershed algorithm, an entire region (its influence zone - the "bottle"!) is conquered together. The bottlenecks play therefore an important role in the bias that could be introduced by a WS implementation. It is why we show in this paper that both tie-zones and bottlenecks analysis can be associated with the robustness of a segmentation.