A study of three-dimensional curvatures and curvatures of four-dimensional hypersurface for analyzing pulmonary nodules on high-resolution CT images

Abstract

In differential diagnosis for the purpose of distinguishing between benign and malignant small pulmonary nodules in high-resolution CT images, the internal structural features of the nodule provide important clues. The purpose of this paper is to give a quantitative representation of the internal structure of the nodules and to present a method based on the curvature, which has properties independent of the direction and position of observation. Curvature calculations for three-dimensional surfaces and the four-dimensional hypersurfaces are conventional procedures for calculating the curvature from three-dimensional gray-level images. However, the relationship among the features based on these curvatures has not been analyzed. Consequently, this paper proposes feature parameters of gray-level structure based on the curvature of a four-dimensional surface. Using artificial gray-level images, the relation between the feature parameters of the three-dimensional surface curvature and the four-dimensional hypersurface curvature is analyzed. It is shown that subtle details of gray-level structure can be represented by using the proposed method. The method is applied to the analysis of actual small pulmonary nodules. The identified properties of the gray-level structure of the nodule are compared to those derived by using the conventional method, and it is shown that the proposed method is promising for the analysis of more detailed gray-level structure. © 2005 Wiley Periodicals, Inc. Syst Comp Jpn, 36(10): 16–29, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20178