基于曲线拟合的SIFT特征精确定位算法

Precise Feature Localization Algorithm of SIFT Based Curve fitting

尺度不变特征(SIFT,Scale Invariant Feature Transform)算法由特征提取、特征描述、特征匹配三部分构成。SIFT特征点是在高斯二阶差分层提取的局部极值点,并利用尺度空间函数的二阶泰勒级数展开,将局部极值精确定位至亚像素级,Hessian矩阵剔除弱边缘响应的点。但由于泰勒级数展开的函数形式以及Hessian矩阵均需要利用图像信号的导数信息,原算法利用差分近似代替微分,产生一定的误差。这里算法利用最小二乘拟合出10参数的三维二次曲线,直接对曲线函数求导来精确定位和弱边缘剔除,实验结果表明,相对于经典SIFT,这里算法具有更高的稳定性。

SIFT（Scale Invariant Feature Transform） algorithm is mainly composed of three parts including SFIT feature extraction, feature description, feature descriptor matching, and among them, SIFT feature extraction is gained by obtaining the extreme point by pixel in different scales of DOG, and by using Taylor expansion of the scale-space function, the accurate key point is located to sub-pixel level and the edge response eliminated. However, the curve guide function is gained by difference instead of derivative, so some deviation would be produced. The algorithm proposed in this paper could fit out 10 parameters of three dimensional quadratic curve by least-square, and with curve function derivation, implement accurate positioning and eliminate the edge response. Experiment result shows that this algorithm compared with SIFT, is of fairly high stability.