Abstract
In this paper, a new geometric structure of projective invariants is proposed. Compared with the traditional invariant calculation method based on 3D reconstruction, this method is comparable in the reliability of invariant calculation. According to this method, the only thing needed to find out is the geometric relationship between 3D points and 2D points, and the invariant can be obtained by using a single frame image. In the method based on 3D reconstruction, the basic matrix of two images is estimated first, and then, the 3D projective invariants are calculated according to the basic matrix. Therefore, in terms of algorithm complexity, the method proposed in this paper is superior to the traditional method. In this paper, we also study the projection transformation from a 3D point to a 2D point in space. According to this relationship, the geometric invariant relationships of other point structures can be easily derived, which have important applications in model-based object recognition. At the same time, the experimental results show that the eight-point structure invariants proposed in this paper can effectively describe the essential characteristics of the 3D structure of the target, without the influence of view, scaling, lighting, and other link factors, and have good stability and reliability.
Highlights
E recognition of 3D objects by a computer is to describe the features of the object by extracting the points of interest in the image and to recognize the object according to these features
Mathematical Problems in Engineering its invariant has been a widespread concern and promotion [17,18,19], but the previous calculation of the point, line, curve feature invariant requires that the extracted elements are coplanar, but the reality is that most of the elements obtained are not in a plane; the previous methods have great limitations. In view of this kind of present situation, based on the theory of Conformal Geometric Algebra (CGA), this paper proposes an eight-point geometric structure invariant in three-dimensional space, which has the following advantages
Six, and sevenpoint structure invariants, the calculation of invariants based on point features and line features is relatively accurate and easy; second, the calculation of the invariant only needs a single frame image, which avoids the calculation of the fundamental matrix between multiple images and camera calibration, compared with the invariant obtained by using multiple frames, and is simple and convenient; the invariants of other geometric structures can be deduced by using the algorithm proposed in this paper, and it is beneficial to find more invariants of unknown structures, which shows that the invariant algorithm proposed in this paper has good generality and simplicity
Summary
E recognition of 3D objects by a computer is to describe the features of the object by extracting the points of interest in the image and to recognize the object according to these features. Mathematical Problems in Engineering its invariant has been a widespread concern and promotion [17,18,19], but the previous calculation of the point, line, curve feature invariant requires that the extracted elements are coplanar, but the reality is that most of the elements obtained are not in a plane; the previous methods have great limitations In view of this kind of present situation, based on the theory of Conformal Geometric Algebra (CGA), this paper proposes an eight-point geometric structure invariant in three-dimensional space, which has the following advantages. We use the algorithm of this paper to calculate the invariants of the spatial six-point structure proposed by Zhu et al. Zhu et al designed a geometric structure that intersects two planes α, β in 3D space, taking two points C, D, E, and F at the intersection line AB and beyond the intersection line on the two planes. We use the Harris and Piersol [19] corner detection algorithm to extract the points that need to be used in the experiment
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