Neutrosophic segmentation of breast lesions for dedicated breast computed tomography

Abstract

We proposed the neutrosophic approach for segmenting breast lesions in breast computed tomography (bCT) images. The neutrosophic set considers the nature and properties of neutrality (or indeterminacy). We considered the image noise as an indeterminate component while treating the breast lesion and other breast areas as true and false components. We iteratively smoothed and contrast-enhanced the image to reduce the noise level of the true set. We then applied one existing algorithm for bCT images, the RGI segmentation, on the resulting noise-reduced image to segment the breast lesions. We compared the segmentation performance of the proposed method (named as NS-RGI) to that of the regular RGI segmentation. We used 122 breast lesions (44 benign and 78 malignant) of 111 noncontrast enhanced bCT cases. We measured the segmentation performances of the NS-RGI and the RGI using the Dice coefficient. The average Dice values of the NS-RGI and RGI were 0.82 and 0.80, respectively, and their difference was statistically significant ([Formula: see text]). We conducted a subsequent feature analysis on the resulting segmentations. The classifier performance for the NS-RGI ([Formula: see text]) improved over that of the RGI ([Formula: see text], [Formula: see text]).

Keywords: CADx; breast CT; neutrosophy; quantitative feature analysis; segmentation.

Fig. 1

This diagram illustrates the procedures for the proposed neutrosophic image enhancement for bCT images. The algorithm transforms the bCT images into NS domain by assigning each voxel’s membership in true (foreground), false (background), and indeterminacy (noise) sets. After that, three operations iteratively smooth and enhance the NS image to increase the contrast between true (breast lesion) and false (other breast tissue) sets by isolating image noise. Once the changes in true, intermediate, and false sets are stabilized, the algorithm transforms the NS images back to create cleaned or enhanced bCT images.

Fig. 2

This figure illustrates how the proposed method enhances or cleans the given image for segmentation. (a)–(c) Input image in coronal, axial, and sagittal view. (d)–(f) Images in NS domain after one iteration. (g)–(i) Output image in coronal, axial, and sagittal view. (j)–(k) Segmentation results in coronal view for RGI and NS-RGI. It is clear that the NS method was able to clean the noise from the image, while retaining other information (e.g., lesion edge information) in the image, thus resulted in better segmentation.

Fig. 3

This diagram illustrates how we created NS-RGI and RGI cases for this study. For both NS-RGI and RGI cases, bCT images were first preprocessed. For NS-RGI cases, bCT images were cleaned or enhanced via the proposed NS enhancement and then the RGI segmentation algorithm was applied to the resulting enhanced images. For RGI cases, bCT images smoothed with $3\times 3\times 3$ cube to reduce the effect of the noise and then the RGI segmentation algorithm was applied on the smoothed images.

Fig. 4

This figure illustrates how mesh-subdivision improves the surface representation of small breast lesions less than 10 mm. (a) A small benign lesion with a maximum diameter of 4.6 mm. (b) The small lesion after the mesh-subdivision. One can see the improvement in the surface representation of the breast lesion, especially on spiculated margins.

Fig. 5

This figure shows the scatter plots for Dice values for the NS-RGI and RGI segmentation algorithms in terms of breast density. The diameters of circles in the plot are proportional to the maximum lesion diameter measured by the expert. For all density levels, the average Dice values of the NS-RGI segmentation algorithm were higher than those of the RGI cases, while only density level 2 showed a statistically significant difference. For cases with ${\text{Dice}}_{\mathrm{RGI}}$ higher than 0.7, ${\text{Dice}}_{\mathrm{NS}\text{-}\mathrm{RGI}}$ showed similar performances. For many cases with ${\text{Dice}}_{\mathrm{RGI}}$ less than 0.7, ${\text{Dice}}_{\mathrm{NS}\text{-}\mathrm{RGI}}$ showed improved segmentation performance. There were two cases (with asterisk marker) that ${\text{Dice}}_{\mathrm{NS}\text{-}\mathrm{RGI}}$ showed inferior segmentation performance than ${\text{Dice}}_{\mathrm{RGI}}$.

Fig. 6

This figure shows the cases (in coronal view) that NS-RGI showed lower segmentation performances (Dice value lower than 0.7), while RGI showed successful segmentation outcomes (Dice value higher than 0.7). The breast density level of first (a and b) and second (c and d) row lesions are levels 3 and 4, respectively. Left column subimages (a and c) are the bCT cases without NS enhancement and right column subimages (b and d) are those with NS enhancement. As the lesions (highlighted as green outline) are connected with breast parenchymal tissue, the NS enhancement incorrectly includes the neighboring parenchymal tissue as foreground, and therefore it kept applying the enhancement operations to the case. The resulting segmentation outcome (b and d) from NS-RGI showed leaked boundary compared to those of RGI.