1. An ultrasonic imaging apparatus comprising: an ultrasonic probe configured to repeatedly acquire an ultrasonic image signal at intervals of a predetermined time period in an elevational direction; and at least one processor configured to: generate reference volume data and target volume data by using the repeatedly acquired ultrasonic image signal, detect a reference voxel of the generated reference volume data and a corresponding target voxel of the generated target volume data, and generate a displacement vector that relates to the detected reference voxel and the detected target voxel, and generate at least one piece of intermediate volume data with respect to the reference volume data and the target volume data by using the generated displacement vector, wherein the at least one processor is further configured to detect the target voxel of the target volume data by using voxel values of all contiguous voxels of the reference voxel contained in the reference volume data.