目的 当前国际流行的SIFT算法及其改进算法在检测与描述特征点时基于高斯差分函数,存在损失图像高频信息的缺陷,从而导致图像匹配时其性能随着图像变形的增加而出现急剧下降。针对SIFT算法及其改进算法的这一缺陷,本研究提出了一种新的无图像信息损失的、在对数极坐标系下的尺度不变特征点检测与描述算法。方法 本研究提出的尺度不变特征点检测与描述算法首先将直角坐标系下以采样点为中心的圆形图块转换为对数极坐标系下的矩形图块,并以此矩形图块为基础对采样点进行特征点检测与描述符提取;该算法使用固定宽度的窗口在采样点的对数极坐标径向梯度图像的log_t^r轴上进行移动以判断该点是否为特征点并计算该点的特征尺度,并在具有局部极大窗口响应的特征尺度位置处提取特征点的描述符。该算法的描述符基于对数极坐标系下的矩形图块的灰度梯度的幅值与角度,是一个192维向量,并具有对于尺度、旋转、光照等变化的不变性。结果 本研究采用INRIA数据组和Mikolajczyk提出的匹配性能指标对SIFT算法、SURF算法和提出的尺度不变特征点检测与描述算法进行比较。与SIFT算法和SURF算法相比,提出的尺度不变特征点检测与描述算法在对应点数、重复率、正确匹配点数和匹配率等方面均具有一定优势。结论 提出了一种基于对数极坐标系的图像匹配算法,即将直角坐标系下以采样点为中心的圆形图块转换为对数极坐标系下的矩形图块,这样在特征点的检测过程中,可以有效规避SIFT算法因为采用DoG函数而造成的高频信息损失;在描述符提取过程中,对数极坐标系可以有效地减少图像的变化量,从而提高了匹配性能。

Objective The internationally popular scale-invariant feature transform (SIFT) algorithm and its improved algorithms are based on the difference-of-Gaussian (DoG) function for keypoint detection and description. However, the DoG function causes high-frequency image information loss, which leads to a sharp decline in matching performances along with increased image deformation. According to previous research on images in log-polar space, a new algorithm for keypoint detection and description in log-polar space is developed in this study. The new algorithm can completely reserve image information to overcome the drawbacks of the SIFT algorithm and its improved algorithms. Method The algorithm employed in this study converts the round image block centered on the sample point in Cartesian space into a rectangular image block in log-polar space and performs keypoint detection and descriptor extraction based on the derived rectangular image block. When performing keypoint detection, the proposed algorithm utilizes a window with a constant width that moves along the log_t^r axis of the radial gradient image in the log-polar space of the sample point to determine whether a sample point is to be defined as a keypoint and to calculate the character scales of the sample point. When a sample point is defined as a keypoint, the proposed algorithm performs descriptor extraction in the location of the character scale with a local maximum window response. The descriptor is a 192-dimensional vector that is based on the magnitude and orientation of the grayscale gradient of the rectangular image block in the log-polar space; it is invariant to changes in scale, orientation, and intensity. Result The SIFT algorithm, the speeded up robust feature (SURF) algorithm, and the proposed algorithm are compared based on the Institut National de Recherche en Informatique et en Automatique dataset and the performance evaluation indices proposed by Mikolajczyk. Results demonstrate that compared with SIFT and SURF algorithms, the proposed algorithm has significant advantages in the performance evaluation indices, such as correspondences, repeatability, correct matchs, and matching score. Conclusion Classical image matching algorithms are based on Cartesian space; their matching performances for images with deformation, such as scale changing, are limited. This study formulates a new image matching algorithm based on log-polar space. First, the proposed algorithm converts the round image block centered on the sample point in Cartesian space into a rectangular image block in log-polar space. Thus, the proposed algorithm can effectively avoid high-frequency image information loss caused by the DoG function when performing keypoint detection. Second, the proposed algorithm extracts the descriptors of the keypoint based on the derived rectangular image block in log-polar space. This condition reduces the variance of images significantly. In sum, the proposed algorithm can significantly improve the performance of image matching by transforming an image in Cartesian space into one in log-polar space.