Characterization of micro-terrain features has been explored to detect convex and concave features in the terrain. The analysis of first and second derivatives of a function fitted to the terrain is a frequently used resource to describe terrain characteristics and to undertake GIS-based analysis for use in erosion models. Infinitesimal calculus is applied in this approach for the detection of gullies, based on their morphology and profile curvature, under the assumption that a gully represents a Relative Minimum (RM) with convex form. The algorithm is based on the analysis of the different profiles presented in a square kernel (with odd number of pixels), which is iterated over the full image (Digital Elevation Model). Four axes are drawn on this kernel (one vertical, one horizontal and two oblique) representing a row vector, a column vector and the two diagonal vectors of the kernel, respectively. Once these vectors are identified, a second-degree function is adjusted to each. According to the resultant functions, the first and second derivatives are calculated. A condition is stated to define a favorable case of gully candidate for each profile if four or three functions (profiles) present an RM (first derivative equal to zero and second derivative positive). Then a gully is assumed to exist within the kernel. For fewer than three local minima in a kernel, it is assumed that there is no gully in this window. The results are generated in .txt format, where the coordinates of the centroids of the original pixels from the TanDEM-X DEM are provided, along with the number of RMs found for the corresponding Kernel, of which they are the center.