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The SIFT (Scale Invariant Feature Transform) algorithm is an approach for extracting distinctive invariant features from images. It is widely used in image matching. Since SIFT detector detects the extreme points through the whole scale space, it often selects keypoints that have no value and reduces the efficiency of the algorithm. This paper proposes a fast SIFT algorithm based on Sobel edge detector. Sobel edge detector is applied to generate an edge group scale space and SIFT detector detects the extreme point under the constraint of the edge group scale space. The experimental results show that the proposed algorithm decreases the redundancy of keypoints and speeds up the implementation while the matching rate between different images maintains at a high level. As the threshold of Sobel detector increases, number of keypoints decreases and matching rate gets higher.