Invariance is widely used in 3-D object recognition due to its good performance on change of viewpoint. A method of computing 3-D invariants of seven points from two images is presented, which can be used to achieve reliable recognition of a 3-D object and scene. Based on the matrix representation of the projective transformation between 3-D and 2-D points, geometric invariants are derived by the determinant ratios. First, the general ratiocination about invariants is represented. Second, the general method of deriving 3-D invariants from images is proposed. Simulation results on real images show that the derived invariants remain stable and are quite robust and accurate.

Most previous spatial methods to deblur rotary motion blur raise an overregularization problem in the solution of deconvolution. We construct a frequency domain framework to formulate the rotary motion blur. The well-conditioned frequency components are protected so as to avoid the overregularization. Then, Wiener filtering is applied to yield the optimal estimation of original pixels under different noise levels. The identifications of rotary motion parameters are also presented. To detect the rotary center, we develop a zero-interval searching method that works on the degraded pixel spectrum. This method is robust to noise. For the blur angle, it is iteratively calibrated by a novel divide-andconquer method, which possesses computational efficiency. Furthermore, this paper presents a shape-recognition and linear surface fitting method to interpolate missing pixels caused by circularly fetching. Experimental results illustrate the proposed algorithm outperforms spatial algorithms by up to 0.5-4 dB in the peak signal-to-noise ratio and the improvement of signal-to-noise ratio and prove the methods for missing pixel interpolation and parameter identifications effective.

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This paper constructs a frequency domain framework to deblur rotary degradation. The proposed method quantifies the rotary blur mechanism as frequency response and yields mean-square optimal estimation for original pixels under different noise levels. Then we present two methods to identify motion parameters. To detect correct rotary center, we propose a novel interval-searching method that works on the degraded pixel spectrum. The method is robust to noise. And a divide-conquer method is presented to iteratively calibrate the blur angle. Experimental results illustrate the frequency method outperforms spatial algorithms by up to 0.5 ~ 4 dB in Peak-Signal-Noise-Ratio (PSNR) and prove the methods for parameter identifications effective.