A corner is defined as the junction point of two or more stright line edges. Corners are special features in a image. They are of great use in computing the optical flow and structure from motion. In this paper, we report an optimal corner detector which uses a mathematical model for a corner. An optimal gray tone corner detector is derived for a restricted case of corners, i.e., corners made by lines which are symmetric about a horizontal axis. The resultant corner detector is described by the product of the sine in x and an exponential in the y direction in a portion of the mask and by the product of two sines in x and y directions in the remaining portion. It is then generalized to include any corner of an arbitrary angle and orientation. This results in an approximation of all corners by a total of twelve major types. It is observed that all the twelve masks can actually be configured with four smaller sub-masks, and this results in a significant reduction in the computations. The computations are further reduced by using the separability of masks. Results for synthetic and real scenes are reported.