# A New Approach to Border Irregularity Assessment with Application in Skin Pathology
## 4 Discussion  
In this article we proposed a method for automatic determination of the location, width, length, and height of border irregularities (projections) and demonstrated its application in measuring morphometry of retes in a segmented epidermis. The main axis of the analyzed region and the approximated location of projections along that axis are determined by analyzing the skeleton of that region obtained using an augmented Fast Marching Method. The main axis is determined by finding such a path in an undirected graph spanned on the skeleton of the region which satisfies a joint criterion of the length and distance from the region's \"outer\" edge. Points on the region border being candidate nodes for endpoints of projection bases, i.e., points located in centers of border protrusions, are identified by finding prominent peaks the curvature of the region border filtered using a combination of a simple averaging filter and a low-pass filter. Projection roots are then matched with appropriate candidates according to geometric criteria, such as: the relative orientation of a \"projection root-candidate node\" vector with respect to the orientation of a given projection, and the distance between a node and the root. Since some projections contain multiple tips whereas others are partially joined with their neighboring projections, we perform a post-processing step and either merge or split the affected segmented projections. Finally, we measure the morphometry (width, length and height) of individual projections. We tested our method on a set of 25 skin whole slide images (WSIs) of common melanocytic lesions. For each image an experienced dermatopathologist manually prepared the ground truth consisting of the epidermis segmentation (the analyzed region) as well as information about individual retes (i.e., downward projections of the epidermis between the underlying connective tissue)--the approximated location of its base endpoints and its length. Experimental results show that the proposed method yields promising results. In total, 825 out of 992 (83%) manually segmented retes were detected correctly and the \"strict\" Jaccard similarity coefficient for the task of detecting rete ridges was 0.798. Most errors were caused by the misdetection of micro-retes (false negatives) and by treating skin appendages as retes (false positives). The relative error of width and height estimates is on average \(\pm\)20% and \(\pm\)16%, respectively. Our method has a tendency to rather over- than underestimate values of those morphometric parameters. In a follow-up study we plan to use the outcome of this method to develop complex indexes describing the epidermal morphometry (variations in epidermal thickness as well as changes in elongation of retes along the lesion) and assess their usefulness for diagnosing skin melanocytic lesions. Pathologists, based on their clinical experience, conjectured that there exist relationships between certain types of distortions and skin conditions, for instance: atrophy of basal epidermal unit is often sighted in melanomas, whereas uniform elongation of retes tends to indicate a benign lesion [7; 8]. Figure 30: The three main limitations of the proposed method: (**a**) the algorithm incorrectly takes long retes at the end of the lesion as part of the main axis (the main axis is marked blue, whereas the proper ending of the main axis is marked green); (**b**) long retes which do not grow approximately perpendicularly into dermis, but rather are joined with the epidermal plate in multiple places along their boundary (as rete #3), will usually be split by the algorithm as if they were series of short retes fused together (the actual split is marked red, whereas the proper split is marked green); (**c**) our method fails to identify the rete base for a group retes fused near the epidermal plate if total width of such a group is too large (as it is the case for the group #2). However, no detailed criteria were formulated so far and we intend to fill this void.