Keypoint detection usually results in a large number of keypoints which are mostly clustered, redundant, and noisy. These keypoints often require special processing like Adaptive Non-Maximal Suppression (ANMS) to retain the most relevant ones. In this paper, we present three new efficient ANMS approaches which ensure a fast and homogeneous repartition of the keypoints in the image. For this purpose, a square approximation of the search range to suppress irrelevant points is proposed to reduce the computational complexity of the ANMS. To further speed up the proposed approaches, we also introduce a novel strategy to initialize the search range based on image dimension which leads to a faster convergence. An exhaustive survey and comparisons with already existing methods are provided to highlight the effectiveness and scalability of our methods and the initialization strategy. (c) 2018 Elsevier B.V. All rights reserved.