Display apparatus and method of determining air touch using the same and method of displaying three dimensional image using the same

A display device includes a display panel, a first camera, a second camera, and a distance measuring unit. The first camera and the second camera are adjacent to the display panel. The distance measuring unit recognizes a position of a body part of an observer and the distance to the body part from the display panel based on a first image of the first camera and a second image of the second camera. Therefore, the air touch can be recognized, and the display quality of the three-dimensional stereoscopic image can be improved. [Reference numerals] (300) Display panel driving unit; (500) Distance measuring unit