This paper presents a heuristic approach to approximate a two-dimensional planar shape using a thick-edged polygonal representation based on some optimal criteria. The optimal criteria primarily focus on derivation of minimal thickness for an edge of the polygonal shape representation to handle noisy contour. Vertices of the shape-approximating polygon are extracted through a heuristic exploration using a digital geometric approach in order to find optimally thick-line to represent a discrete curve. The merit of such strategies depends on how efficiently a polygon having minimal number of vertices can be generated with modest computational complexity as a meaningful representation of a shape without loss of significant visual characteristics. The performance of the proposed frame- work is comparable to the existing schemes based on extensive empirical study with standard data set.