A Theory of Phase Singularities for Image Representation and its Applications to Object Tracking and Image Matching

Abstract

This paper studies phase singularities (PSs) for image representation. We show that PSs calculated with Laguerre-Gauss filters contain important information and provide a useful tool for image analysis. PSs are invariant to image translation and rotation. We introduce several invariant features to characterize the core structures around PSs and analyze the stability of PSs to noise addition and scale change. We also study the characteristics of PSs in a scale space, which lead to a method to select key scales along phase singularity curves. We demonstrate two applications of PSs: object tracking and image matching. In object tracking, we use the iterative closest point algorithm to determine the correspondences of PSs between two adjacent frames. The use of PSs allows us to precisely determine the motions of tracked objects. In image matching, we combine PSs and scale-invariant feature transform (SIFT) descriptor to deal with the variations between two images and examine the proposed method on a benchmark database. The results indicate that our method can find more correct matching pairs with higher repeatability rates than some well-known methods.

Software and Hardware Implementations of Stereo Matching

“…In stereo matching, PS is estimated by convolving images with complex filters. Compared with SIFT method, PS-based approaches have the advantage of robustness against variations in luminance and imbalance between stereo image sensors at the cost of higher computing resource requirements [63,64]. Combines PS with SIFT, which can get higher repeatability rates.…”

Position measurement of linear motor mover based on image spectrum energy

“…To improve measurement accuracy and anti-interference, a fence image selection method that is based on image spectrum energy is proposed in this study. The spectrum energy value of the target source image is introduced into the image anti-interference evaluation function, and the phase singularity method [27,28] is used to calculate the displacement of the linear motor mover.…”

Measurement of in-plane displacements using the phase singularities generated by directional wavelet transforms of speckle pattern images

“…Recently, the introduction of a complex signal associated with SI has established a new point of view. The complex signal is obtained by vortex filtering the speckle pattern intensity, which generates phase singularities invariant to in-plane translations and rotations [4]. Therefore, this pseudophase information was used as a turning point with respect to the usual practice of speckle digital correlation, establishing a new method called optical vortex metrology (OVM).…”