1. An apparatus for controlling automatic focus, comprising: (a) an imaging device; (b) a focus control element coupled to said imaging device and providing a focal range to said imaging device; (c) a computer processor coupled to said imaging device and said focus control element and configured for controlling said imaging device and associated focus control element; and (d) programming executable on said computer processor for carrying out an autofocusing process comprising: (i) capturing object images; (ii) performing a first depth estimation method on said images; (iii) performing a second depth estimation method on said images; (iv) selecting said first depth estimation method, or said second depth estimation method, based on comparing their results for use in focusing; (v) performing steps (i) through (iv) at multiple focus positions to arrive at an accurate depth estimation; (vi) adjusting focus with a focusing movement performed in response to said accurate depth estimation; and (vii) determining that a desired level of focus accuracy is obtained in response to computing a variance which reaches a value indicating sufficient confidence that a proper focus position has been attained.