A Scale - Invariant Feature Point Extractor In Logarithmic Polar Coordinate System And Its Application In Image Matching

The currently widely-used scale-invariant feature transform (SIFT) algorithm and its improved algorithms are based on the Difference-of-Gaussian (DoG) function in the Cartesian space when performing keypoint detection and description. However, the DoG function causes the loss of the high-frequency image information, which leads to the sharp decline of matching performances along with the increasing of image deformation. According to the former research on images in the log-polar space, the present study formulates a new algorithm for detecting and describing blob points, corner points and edge points in the log-polar space which can completely reserve the image information so as to overcome the aforementioned faults of the SIFT algorithm and its improved algorithms. The algorithm employed in the present study converts the round image block which centers on the sample point in the Cartesian space into a rectangular image block in the log-polar space and performs keypoint detection and description based on the derived rectangular image block in the log-polar space. When performing keypoint detection, The algorithm proposed uses a window with constant width which moves along the logtr axis of the radial gradient image in the log-polar space of the sample point to calculate the character scales of the sample point. If a sample point is defined as a keypoint, the algorithm proposed will carry on keypoint description at the location of the character scale with the local maximum window response. The descriptor is a 192-dimensioned vector which is based on the magnitude and orientation of the grayscale gradient of the rectangular image block in the log-polar space. And it is invariant to the changes such as scale, orientation and intensity. According to the performance evaluation indices put forward by K. Mikolajczyk, we intend to make a comparison among the SIFT algorithm, the speeded up robust feature (SURF) algorithm, the Harris-Laplace algorithm and the algorithm proposed by the present study using the the Institut National de Recherche en Informatique et en Automatique (INRIA) dataset. The result demonstrates that compared with the SIFT algorithm, the SURF algorithm and the Harris-Laplace algorithm, the algorithm employed in the present study shows the significant advantages in the performance evaluation indices such as correspondences, repeatability, correct matches and matching score. In the last part of the present study, we give some examples of applications of the algorithm proposed in our study based on the random sample consensus (RANSAC) algorithm and iterative closest point (ICP) algorithm.