where D and its derivatives are evaluated at the candidate keypoint and formula_23 is the offset from this point. The location of the extremum, formula_24, is determined by taking the derivative of this function with respect to formula_25 and setting it to zero. If the offset formula_24 is larger than formula_27 in any dimension, then that's an indication that the extremum lies closer to another candidate keypoint. In this case, the candidate keypoint is changed and the interpolation performed instead about that point. Otherwise the offset is added to its candidate keypoint to get the interpolated estimate for the location of the extremum. A similar subpixel determination of the locations of scale-space extrema is performed in the real-time implementation based on hybrid pyramids developed by Lindeberg and his co-workers.