A positioning method for the feature points of a target board image adopting singular value decomposition

Abstract This paper presents a positioning method to extract the feature points employing the singular value decomposition for a target board image as an example. In order to discriminate the feature points from the noises existing in the image, the image matrix is factorized into three matrices. The geometrical implication of the three matrices is interpreted by three transformations which are rotation, scaling, and another rotation. The singular values in the diagonal of the scaling matrix are arranged in descending order, which stands for the significance sequence of the image features. The smaller singular values are corresponding to the noises while the greater ones are considered as primary features. Therefore the new singular values matrix is defined by the modified original scaling matrix in which the smaller singular values are removed by a cutting point. The smoothing image is reconstructed by the two original rotation matrices and the new singular values matrix with the same arrangement. The latter detection procedure of the feature points adopts the Harris corner detection method to evaluate the singular value decomposition filter. The experiments are performed on the target images with the noise densities of 0.005, 0.01 and 0.02 respectively. Comparing with the traditional approach, the feature points on the target which are considered as the primary features are preserved by the filter. Moreover, the noises vanish in the images because they are unimportant details. The experiments prove that the outlined method has the potential to feature points positioning as well as appropriateness for the manufacture engineering and mechanical inspection.