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We propose a linearization based method to recognize two parameter polynomial implicit curves C(x, y): xi× yj - B × xk × yl - A = 0 in digital images. In this representation space, a pixel is associated with convex polygons and the recognition problem is addressed using a line stabbing solution together with linear programming. We extend the use of this method to the segmentation of a multi-scale digital contour with two parameter functions. The problem is thus the following: given a set of pixel $S$ with an associated size, which is the set of two parameter polynomial functions and their definition interval which crosses each pixel of S. In this paper, we use the 0-Flake model but the method can also be applied to the 1-Flake model.