This paper reviews, implements and compares two corner detection algorithms for mining corner points on the generic shapes. These corner detectors detect corners by using combination of one rectangle (R) and two ellipses (EE). These algorithms have been used with different combinations: REE and EER together with different parameter settings in their descriptions. REE and EER combinations slide along the boundary of the shape and record number of boundary points in each rectangle and ellipses. REE and EER setup represent both local and global views of the image outlines and present natural corner detection methodologies to detect and mine all true corners accurately. A comparative study demonstrates the superiority of the REE and EER over some of the existing algorithms.