1. An apparatus for forming a 3-dimensional (3D) ultrasound image, comprising: a generation unit configured to generate a binarization image of a 2D ultrasound image to generate a surface curved line of a target object on the 2D ultrasound image and automatically generate a region of interest (ROI) box for the target object on the 2D ultrasound image by moving bounds of the ROI box to pixels closest to the surface curved line; a first determination unit configured to calculate a mean square error value between a predetermined standard histogram for a 2D ultrasound image of the target object and a histogram for a 2D ultrasound image within the ROI box, and determine whether the ROI box is suitably generated for a display of the target object therewithin based on the calculation result; a detection unit configured to detect a contour of the target object in the ROI box; and a formation unit configured to form the 3D ultrasound image by rendering volume data existing in the detected contour.