## 1 Introduction  
Lung cancer is the most common cause of death among all cancers worldwide. To cope with this serious situation, mass screening for lung cancer has been widely performed by simple X-ray films with sputum cytological tests. However, it is known that the accuracy of this method is not sufficient for early detection of lung cancer. Therefore, a lung cancer screening system by computed tomography (CT) for mass screening is proposed [1]. This system improves the accuracy of cancer detection considerably, but has one problem that the number of the images is increased to over dozens of slice sections per patient from one X-ray film [2]. It is difficult for a radiologist to interpret all the images in a limited time. In order to make the system more practical, it is necessary to build a computer-aided diagnosis (CAD) system[3] that automatically detects abnormal regions suspected to comprise pulmonary nodules that are the major radiographic indicators of lung cancers, and informs a radiologist about their positions in CT scans as a second opinion.  
There are many works for pulmonary nodule detection. [PERSON] _et al._[4] proposed the \"Quoit filter\" which was one of mathematical morphological image filters. [PERSON] _et al._[5] applied multiple gray level thresholding for initial detection and reduced false positives (FPs) using a Fisher linear discriminant classifier and a quadratic classifier. A template-matching technique [6] was used by [PERSON] _et al._ Another template-matching technique [14] was proposed by [PERSON] _et al._[PERSON] _et al._[7] detected nodule candidates using the divergence of normalized gradients or mean curvature features in a feature-selective classifier [8]. [PERSON] _et al._[9] compared four classifiers: a neural network, a support vector machine, naive Bayes and logistic regression. The random forest was performed for classification [10] by [PERSON] _et al._[PERSON] _et al._[11] used multiple thresholding and rule-based pruning to detect nodule candidates and then used a genetic-programming-based classifier to categorize nodules and non nodules. [PERSON] _et al._[12] proposed a detection method based on local shape information and local intensity dispersion information. [PERSON] _et al._[13] developed patient-specific models using patient's baseline image data for segmentation. A surface normal overlap method based on a statistical shape model [15] was proposed by [PERSON] _et al._[PERSON] _et al._[16] characterized suspicious regions with the iris filter output. [PERSON] _et al._[17] reduced false positives by a classification system based on artificial neural networks. [PERSON] _et al._[18] applied massive training artificial neural network (MTANN) for false positive reduction.  
In this paper, we propose a nodule detection method based on three novel filters and an appearance-based clustering technique. First, a radial suppression filter that suppresses voxel values in radial directions is applied to eliminate extra regions in the volumes of interest (VOIs). Next, a moment-of-inertia filter that regards voxel intensities as mass is applied to the VOIs so as to emphasize the differences in intensity distributions between nodules and blood vessels. Excessive emphases caused in the integument regions of blood vessels are compensated by a center displacement filter based on the parallel-axis theorem in the physics. Finally, false positives are reduced by an appearance-based two-step k-means clustering technique. The proposed method is evaluated using a publicly available CT dataset.