Quantification of body composition plays an important role in many clinical and research applications. Radiologic imaging techniques such as Dual-energy X-ray absorptiometry (DXA), magnetic resonance imaging (MRI), and computed tomography (CT) imaging make accurate quantification of the body composition possible. However, most current imaging-based methods need human interaction to quantify multiple tissues. When dealing with whole-body images of many subjects, interactive methods become impractical. This paper presents an automated, efficient, accurate, and practical body composition quantification method for low-dose CT images. Our method, named automatic anatomy recognition body composition analysis (AAR-BCA), aims to quantify four tissue components in body torso (BT) - subcutaneous adipose tissue (SAT), visceral adipose tissue (VAT), bone tissue, and muscle tissue - from CT images of given whole-body positron emission tomography/computed tomography (PET/CT) acquisitions. AAR-BCA consists of three key steps - modeling BT with its ensemble of key objects from a population of patient images, recognition or localization of these objects in a given patient image I, and delineation and quantification of the four tissue components in I guided by the recognized objects. In the first step, from a given set of patient images and the associated delineated objects, a fuzzy anatomy model of the key object ensemble, including anatomic organs, tissue regions, and tissue interfaces, is built where the objects are organized in a hierarchical order. The second step involves recognizing, or finding roughly the location of, each object in any given whole-body image I of a patient following the object hierarchy and guided by the built model. The third step makes use of this fuzzy localization information of the objects and the intensity distributions of the four tissue components, already learned and encoded in the model, to optimally delineate in a fuzzy manner and quantify these components. All parameters in our method are determined from training datasets. Thirty-eight low-dose CT images from different subjects are tested in a fivefold cross-validation strategy for evaluating AAR-BCA with a 23-15 train-test dataset division. For BT, over all objects, AAR-BCA achieves a false-positive volume fraction (FPVF) of 3.7% and false-negative volume fraction (FNVF) of 3.8%. Notably, SAT achieves both a FPVF and FNVF under 3%. For bone tissue, it achieves a FPVF and a FNVF both under 3.5%. For VAT tissue, the FNVF of 4.8% is higher than for other objects and so also for muscle (4.7%). The level of accuracy for the four tissue components in individual body subregions mostly remains at the same level as for BT. The processing time required per patient image is under a minute. Motivated by applications in cancer and systemic diseases, our goal in this paper was to seek a practical method for body composition quantification which is automated, accurate, and efficient, and works on BT in low-dose CT. The proposed AAR-BCA method toward this goal can quantify four tissue components including SAT, VAT, bone tissue, and muscle tissue in the body torso with under 5% overall error. All needed parameters can be automatically estimated from the training datasets.