Three-dimensional conditional random field for the dermal-epidermal junction segmentation

Abstract

The segmentation of the dermal-epidermal junction (DEJ) in in vivo confocal images represents a challenging task due to uncertainty in visual labeling and complex dependencies between skin layers. We propose a method to segment the DEJ surface, which combines random forest classification with spatial regularization based on a three-dimensional conditional random field (CRF) to improve the classification robustness. The CRF regularization introduces spatial constraints consistent with skin anatomy and its biological behavior. We propose to specify the interaction potentials between pixels according to their depth and their relative position to each other to model skin biological properties. The proposed approach adds regularity to the classification by prohibiting inconsistent transitions between skin layers. As a result, it improves the sensitivity and specificity of the classification results.

Keywords: biomedical imaging; in vivo microscopy; machine learning; reflectance confocal microscopy.

Fig. 1

Examples of different DEJ patterns. The circular rings pattern in (a) provides an easy identification of the DEJ compared to the uncertain one in (b). However, the latter one is the most frequent, especially on the cheeks.

Fig. 2

Three-dimensional CRF modelization. The set of nodes in gray and in white belong to two different en-face sections. The edge potentials of each en-face sections ${\psi }_{jk}$ [Eq. (3)] are learned at each depth. Edge potentials between en-face sections ${\psi }_{ij}$ [Eq. (3)] impose biological transition constraints.

Fig. 3

Laplacian variance and distance to the closest minimum for a pixel between 20 and $120\mu \mathrm{m}$. The blue line represents the Laplacian variance at coordinates $(i,j)$ at all depths. The dashed vertical lines mark the position of the minimum of the Laplacian variance. The red line corresponds to the distance to the closest minimum.

Fig. 4

Segmentations at depth $d$: epidermis (red), uncertain (yellow), dermis (blue). (a) Annotated image at depth $d$, (b) RF at depth $d$, (c) ${\mathrm{CRF}}_{2\text{-}\mathrm{D}}$ at depth $d$, (d) ${\mathrm{CRF}}_{3\text{-}\mathrm{D}\mathrm{Sym}}$ at depth $d$, and (e) ${\mathrm{CRF}}_{3\text{-}\mathrm{D}\mathrm{Asym}}$ at depth $d$. The addition of constraints into the CRF model improves the accuracy of the segmentation.

Fig. 5

Segmentations at depth $d+1$. (a) Annotated image at depth $d+1$, (b) RF at depth $d+1$, (c) ${\mathrm{CRF}}_{2\text{-}\mathrm{D}}$ at depth $d+1$, (d) ${\mathrm{CRF}}_{3\text{-}\mathrm{D}\mathrm{Sym}}$ at depth $d+1$, and (e) ${\mathrm{CRF}}_{3\text{-}\mathrm{D}\mathrm{Asym}}$ at depth $d+1$. Inconsistent transitions exist between depth $d$ and $d+1$. One can notice the misclassification obtained by RF and ${\mathrm{CRF}}_{2\text{-}\mathrm{D}}$. The use of ${\mathrm{CRF}}_{3\text{-}\mathrm{D}\mathrm{Asym}}$ provides a coherent segmentation.

Fig. 6

Visual appearance of the transition from the epidermis to the uncertain area, which corresponds to the epidermal lower boundary. Notice that the aged DEJ (b) appears flatter than the young DEJ (a), as expected. Colors encode the depth.