Disambiguating flat spots in discrete scalar fields

We consider 2D scalar fields sampled on a regular grid. When the gradient is low relative to the resolution of the dataset’s range, the signal may contain flat spots: connected areas where all points share the same value. Flat spots hinder certain analyses, such as topological characterization or drainage network computations. We present an algorithm to determine a symbolic slope inside flat spots and consistently place a minimal set of critical points, in a way that is less biased than state-of-the-art methods. We present experimental results on both synthetic and real data, demonstrating how our method provides a more plausible positioning of critical points and a better recovery of the Morse–Smale complex.