A Scalable Fluctuating Distance Field: An Application to Tumor Shape Analysis

Tumor growth involves highly complicated processes and complex dynamics, which typically lead to deviation of tumor shape from a compact structure. In order to quantify the tumor shape variations in a follow-up scenario, a shape registration based on a scalable fluctuating shape field is described. In the earlier work of fluctuating distance fields (Tari and Genctav, J Math Imaging Vis 1–18, 2013; Tari, Fluctuating distance fields, parts, three-partite skeletons. In: Innovations for shape analysis. Springer, Berlin/New York, pp 439–466, 2013), the shape field consists of positive and negative values whose zero crossing separates the central and the peripheral volumes of a silhouette. We add a non-linear constraint upon the original fluctuating field idea in order to introduce a “fluctuation scale”, which indicates an assumption about peripherality. This provides the induction of an hierarchy hypothesis onto the field. When fixed, the field becomes robust for scale changes for analysis of correspondence. We utilize the scalable fluctuating field first in segmentation of the protruded regions in a tumor, which are significant for the radiotherapy planning and assessment procedures. Furthermore, the unique information encoded in the shape field is utilized as an underlying shape representation for follow-up registration applications. The representation performance of the scalable field for a fixed ‘fluctuation scale’ is demonstrated in comparison to the conventional distance transform approach for the registration problem.