SIFT Keypoints

The Scale-Invariant Feature Transform (SIFT) [4] algorithm provides a robust method for extracting distinctive features from images that are invariant to rotation, scale and distortion. In order to identify invariant keypoints that can be repeatably found in multiple views of varying scale and rotation, local extrema are detected in Gauss-filtered difference images.

SIFT算法的实质可以归为在不同尺度空间上查找关键点（特征点）的问题。所谓关键点，就是一些十分突出的点，这些点不会因光照条件的改变而消失，比如角点、边缘点、暗区域的亮点以及亮区域的暗点，既然两幅图像中有相同的景物， 那么使用某种方法分别提取各自的稳定点，这些点之间就会有相互对应的匹配点。而在SIFT中，关键点是在不同尺度空间的图像下检测出的具有方向信息的局部极值点。涉及到的最重要的两步是：1.构建尺度空间 2.关键点检测

G(x,y,σ)=12πσ2e−(x2+y2)/(2σ2)
L(x,y,σ)=G(x,y,σ)∗I(x,y)

1）对图像做高斯平滑
2）对图像做降采样（减小计算量）。

LoG算子和DoG算子only相差常数系数，而这并不会改变极值点的位置。因此我们在DoG算子中求得极值点就是LoG算子的极值点，也正是我们需要的关键点。而DoG在计算上只需相邻尺度高斯平滑后图像相减，因此简化了计算！

1. SIFT的matlab程序，非常详细  http://www.vlfeat.org/~vedaldi/code/sift.html
2. SIFT tutorial http://www.aishack.in/2010/05/sift-scale-invariant-feature-transform/
3. 一个非常详细ppt教程，可用作教学http://wenku.baidu.com/view/53021cf24693daef5ef73daf.html
4. D. Lowe, “Object recognition from local scale-invariant features,” in the proceedings of the Seventh IEEE International Conference on Computer Vision, vol. 2, pp. 1150–1157 (1999).

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