Closed Curve approximation is a technique to approximate a digital planar curve with piece straight line segments. The terminating point of a candidate line segment is known as pseudo point. By detecting good choice of the pseudo point on the digital planar one may be able to visibly recognize the shape of the curve. The techniques analyzed in this paper makes closed curve approximation by deleting the redundant pseudo high high curvature points and retains the real pseudo high curvature point. This paper makes an attempt to summarize the deficiency of the closed curve approximation techniques under geometric invariance and the response for the noisy curve.