The LoG characteristic scale: a consistent measurement of lung nodule size in CT imaging

Nodule growth as observed in computed tomography (CT) scans acquired at different times is the primary feature to malignancy of indeterminate small lung nodules. In this paper, we propose the estimation of nodule size through a scale-space representation which needs no segmentation and has high intra- and inter-operator reproducibility. Lung nodules usually appear in CT images as blob-like patterns and can be analyzed in the scale-space by Laplacian of Gaussian ( LoG ) kernels. For each nodular pattern the LoG scale-space signature was computed and the related characteristic scale adopted as measurement of nodule size. Both in vitro and in vivo validation of LoG characteristic scale were carried out. In vitro validation was done by 40 nondeformable phantoms and 10 deformable phantoms. A close relationship between the characteristic scale and the equivalent diameter, i.e., the diameter of the sphere having the same volume of nodules, (Pearson correlation coefficient was 0.99) and, for nodules undergoing little deformations (obtained at constant volume), small variability of the characteristic scale was observed. The in vivo validation was performed on low and standard-dose CT scans collected from the ITALUNG screening trial (86 nodules) and from the LIDC public data set (89 solid nodules and 40 part-solid nodules or ground-glass opacities). The Pearson correlation coefficient between characteristic scale and equivalent diameter was 0.83-0.93 for ITALUNG and 0.68-0.83 for LIDC data set. Intra- and inter-operator reproducibility of characteristic scale was excellent: on a set of 40 lung nodules of ITALUNG data, two radiologists produced identical results in repeated measurements. The scan-rescan variability of the characteristic scale was also investigated on 86 two-year-stable solid lung nodules (each one observed, on average, in four CT scans) identified in the ITALUNG screening trial: a coefficient of repeatability of about 0.9 mm was observed. Experimental evidence supports the clinical use of the LoG characteristic scale to measure nodule size in CT imaging.