# A New Approach to Border Irregularity Assessment with Application in Skin Pathology
## 1 Introduction  
Over the past several decades, there has been a significant increase in the incidence rate and mortality caused by skin cutaneous melanoma, the most aggressive and dangerous skin cancer, among Caucasian populations worldwide [1]. Nowadays, melanoma is responsible for about 70% of skin cancer-related deaths in the United States and in Australia [2; 3]. Since no effective treatment of melanoma in advanced stages has been developed so far, its early diagnosis has become an extremely important issue. When detected early, melanoma is treatable in nearly all cases with a simple surgical excision [4]. The gold standard in skin melanoma diagnosis is the histopathological examination--the microscopic examination of tissue in order to study the manifestations of disease [5]. Other forms of examination, such as dermatoscopy, are useful for screening, but their diagnostic confidence is inferior to the histopathological examination. The epidermal area (Figure 1) is a particularly important target of examination when diagnosing skin conditions, especially for nearly all types of cancer. Its morphometric and cytologic features are key factors considered when grading a skin tissue [6; 7]. The histopathological criteria currently used in the diagnosis of melanoma consist of the analysis of numerous features, such as: lesion's asymmetry, morphometric features of epidermis, proliferation patterns of single melanocytes, cytological atypia, mitoses, and necrosis [7; 8]. The main criteria related to the morphometry of epidermal component are: uniformity and symmetry of epidermal thickness along the lesion, and elongation and thickening of rete ridges [7; 8]. Rete ridges (retes) are downward projections of the epidermis between the underlying connective tissue (Figure 2). The epidermal thickness is measuring along its sections between bases of adjacent retes, orthogonally to the main axis of the epidermal base. The epidermis main axis is a centerline of the epidermis base, i.e., the epidermal region with retes passed over. Figure 3 shows a comparison of a typical epidermal morphometry in benign and malignant lesions. Although traditionally pathologists examined histopathological slides under a light microscope, quantitative analysis of a large volume of specimen is a laborious and difficult task. Moreover, since pathologists make the diagnosis based on their personal clinical experience, it is often subjective and leads to intra- and inter-observer variability [9; 10]. These issues may be addressed by developing automatic image analysis methods, which will provide reliable and reproducible results. Figure 1: A whole slide image (WSI) of a typical skin preparation contains three main tissue layers: epidermis, dermis and adipose tissue. Figure 3: Structure comparison of the epidermal component: (**a**) melanoma in situ—effacement of rete ridges, irregular epidermal thickness; (**b**) junctional dysplastic nevus—uniformly elongated rete ridges, regular epidermal thickness. Figure 2: The epidermis (marked with the solid line) may have a non-trivial morphometry, with a number of rete ridges (some of them are marked with an arrow). In our study we propose a novel method for automatic determination of the location, base width, length, and height of border irregularities (projections) and demonstrate its application to the detection of retes in a segmented epidermis. These information can be used to develop complex indexes describing the epidermal morphometry, which would help improve the accuracy of diagnostic algorithms for skin conditions (e.g., using cognitive analysis techniques [11; 12]).