Nonlinear image labeling for multivalued segmentation

Abstract

We describe a framework for multivalued segmentation and demonstrate that some of the problems affecting common region-based algorithms can be overcome by integrating statistical and topological methods in a nonlinear fashion. We address the sensitivity to parameter setting, the difficulty with handling global contextual information, and the dependence of results on analysis order and on initial conditions. We develop our method within a theoretical framework and resort to the definition of image segmentation as an estimation problem. We show that, thanks to an adaptive image scanning mechanism, there is no need of iterations to propagate a global context efficiently. The keyword multivalued refers to a result property, which spans over a set of solutions. The advantage is twofold: first, there is no necessity for setting a priori input thresholds; secondly, we are able to cope successfully with the problem of uncertainties in the signal model. To this end, we adopt a modified version of fuzzy connectedness, which proves particularly useful to account for densitometric and topological information simultaneously. The algorithm was tested on several synthetic and real images. The peculiarities of the method are assessed both qualitatively and quantitatively.

Fuzzy connectedness and image segmentation

“…However, there was no indication in these works as to how this concept could be exploited to facilitate image segmentation. Dellepiane and Fontana [12], [13] and Udupa and Samarasekera [8], [14] were the first to suggest this use. Dellepiane et al utilized Rosenfeld's "degree of connectedness" to arrive at a segmentation method (to be discussed in Section IV).…”

An Automatic Segmentation Method for MRI Multiparametric Volumes

“…Fuzzy connectedness can be defined in in terms of "intensity connectedness" [21] or in terms of "affinity" [22]. They take into account both feature space information and contextual-spatial relationships among pixels.…”

“…where   Following the method described in [27] and [21], the above connectedness map is generated for the first seed point and all the subsequent ones.…”

Parallel fuzzy segmentation of multiple objects

“…Contrary to this, segmentation is a very challenging task for computers, and research in this field of computer science is prolific. Recently developed algorithms based on the concept of fuzzy connectedness have been shown to produce "good" results under various conditions of noise, texture and artifacts for a variety of imaging technologies [5,7,8,11,25]. Their applications include studies to segment automatically brain [28] and abdominal [29] MR images with the assistance of an atlas of their corresponding regions, to segment MR images even if corrupted by variation of the magnetic field [16], to segment vector-valued functions [11,30], to detect and quantify multiple sclerosis in MR images [13,24,26], to segment images produced by PET [3], to analyze the morphology of airway tree structures [12,15,22] and to segment datasets in electron tomography [9].…”