Currently, the demand for larger screens and high-definition (HD) television-sets is rapidly increasing. To display standard definition (SD) video on high-resolution television sets, spatial up-scaling techniques are necessary to increase the resolution. One technique that makes this possible is linear up-scaling complemented by non-linear sharpness enhancement, such as Luminance Transient Improvement
(LTI). In this paper, three different two-dimensional (2D) implementations of the LTI algorithm are analyzed in terms of image quality and computational complexity. Results show that taking the local edge orientation into account is essential for obtaining high image quality. Furthermore, it is shown that the process of operating perpendicular to an edge can be replaced by a simplified alternative with a minimal loss of image quality.