Differential Geometry Based Vector Fields for Characterizing Surrounding Structures of Pulmonary Nodules

Yoshiki Kawata, Noboru Niki, Hironobu Ohmatsu, Masahiko Kusumoto, Ryutaro Kakinuma, Kensaku Mori, Hiroyuki Nishiyama, Kenji Eguchi, Masahiro Kaneko, Noriyuki Moriyama

Abstract: This paper presents a scheme to analyze surrounding structures of pulmonary nodules by using differential geometry based vector fields. In this scheme the differential characteristics such as the principal curvatures and directions are computed from the differential values of the isointensity surfaces. Each voxel in the nodule surrounding is described in terms of shape index and curvedness derived from the principal curvatures. Two vector fields are formed from the directions of the maximum principal curvatures of nodule surrounding and gradient vectors of nodule surface, respectively. The gradient vector field is computed by diffusing the gradient vector on the nodule surface. The regions corresponding to the cylindrical or conic figures which are similar to vessel and plural images are segmented by the shape index and curvedness values. Then, the relationship between the segmented regions and the nodule is evaluated by the inner product of the direction of the maximum principal curvature and the gradient vector. We demonstrate the feasibility of the scheme to classify benign and malignant nodules.