1. A method of processing an ultrasound image, the method comprising: generating a plurality of two-dimensional (2D) ultrasound images from three-dimensional (3D) ultrasound volume data of an object to be diagnosed; generating a plurality of tissue edge images of an edge of at least one tissue component in the object to be diagnosed based on values of a plurality of pixels forming each of the 2D ultrasound images generated from the 3D ultrasound volume data; and generating a 2D ultrasound image from which a noise component has been removed by discriminating the edge of the at least one tissue component from a position of the noise component based on a difference between a similarity of the edge of the at least one tissue component in the tissue edge images and a similarity of the noise component in the tissue edge images.