In this paper, a new computer tomography (CT) lung nodule computer-aided detection (CAD) method is proposed for detecting both solid nodules and ground-glass opacity (GGO) nodules (part solid and nonsolid). This method consists of several steps. First, the lung region is segmented from the CT data using a fuzzy thresholding method. Then, the volumetric shape index map, which is based on local Gaussian and mean curvatures, and the "dot" map, which is based on the eigenvalues of a Hessian matrix, are calculated for each voxel within the lungs to enhance objects of a specific shape with high spherical elements (such as nodule objects). The combination of the shape index (local shape information) and "dot" features (local intensity dispersion information) provides a good structure descriptor for the initial nodule candidates generation. Antigeometric diffusion, which diffuses across the image edges, is used as a preprocessing step. The smoothness of image edges enables the accurate calculation of voxel-based geometric features. Adaptive thresholding and modified expectation-maximization methods are employed to segment potential nodule objects. Rule-based filtering is first used to remove easily dismissible nonnodule objects. This is followed by a weighted support vector machine (SVM) classification to further reduce the number of false positive (FP) objects. The proposed method has been trained and validated on a clinical dataset of 108 thoracic CT scans using a wide range of tube dose levels that contain 220 nodules (185 solid nodules and 35 GGO nodules) determined by a ground truth reading process. The data were randomly split into training and testing datasets. The experimental results using the independent dataset indicate an average detection rate of 90.2%, with approximately 8.2 FP/scan. Some challenging nodules such as nonspherical nodules and low-contrast part-solid and nonsolid nodules were identified, while most tissues such as blood vessels were excluded. The method's high detection rate, fast computation, and applicability to different imaging conditions and nodule types shows much promise for clinical applications.