Objectives: Recent advances in three-dimensional (3D) display technology have contributed significantly to society, particularly in the increasing use of stereoscopic characters. For example, 3D text information is utilized in digital signage. However, research on 3D characters is limited and discussion on the safety and comfort of 3D technology is lacking. According to the 3D Consortium Safety Guidelines in Japan, a comfortable visual parallax with 3D images is less than ±1.0°. However, 3D text must be shown in front of its associated content in order for it to be displayed simultaneously with that content. Methods: We carried out an experiments to verify the permissive limits of cognition in subjects regarding the parallax of 3D images. In the experiment, 94 subjects aged 18 to 81 viewed a 3D flat Maltess cross image having no depth and projected outward from a screen at a large parallax of 1.0° to 6.0°. Results: Eighty-six percent of the subjects recognized the 3D flat image even when it protruded at a 2.0° parallax. These subjects viewed the image comfortably and without visual problems. Conclusions: This study concludes that people can cognitively recognize a 3D telop at a 2.0° parallax without feeling fatigued.