1. An apparatus for detecting a plurality of arms and hands by using a three-dimensional (3D) image, the apparatus comprising: an image input unit configured to acquire a 3D image of an object; an arm detecting unit configured to detect one or more component-unit candidate regions of the object in the 3D image, and detect one or more arm regions by using arm detection feature information, extracted from each of the candidate regions, and a pattern recognition algorithm; and a hand detecting unit configured to calculate a position of a hand and a position of a wrist in each of the arm regions detected by the arm detecting unit, and detect a hand region by using the position of the hand and the position of the wrist.