Similarity detection of rational space curves

Abstract

We provide an algorithm to check whether two rational space curves are related by a similarity. The algorithm exploits the relationship between the curvatures and torsions of two similar curves, which is formulated in a computer algebra setting. Helical curves, where curvature and torsion are proportional, need to be distinguished as a special case. The algorithm is easy to implement, as it involves only standard computer algebra techniques, such as greatest common divisors and resultants, and Gröbner basis for the special case of helical curves. Details on the implementation and experimentation carried out using the computer algebra system Maple 18 are provided.

[Retracted] Remote Judgment Method of Painting Image Style Plagiarism Based on Wireless Network Multitask Learning

“…In the formula, IR represents the discrimination rate, DR represents the number of plagiarism incidents of the identified painting image, and S represents the number of actual painting image incidents. In order to verify the performance of the method proposed in this paper, we do the experiment as well as with the other five methods proposed in References [5][6][7][8][9], and the results of IR-FIR are shown in Figure 5.…”

“…According to the obtained maximum singular value, the convolutional layer parameters are normalized, so that the entire discriminant network meets 1-Lipschitz continuity. Reference [7] proposes to recognize similar parts from multiple execution trajectories of multithreaded programs under the same input and abstract behavior motifs that are not easily affected by thread interleaving to realize plagiarism detection for multithreaded programs. This method captures the dynamic execution trajectory of the program.…”

Approximate symmetries of planar algebraic curves with inexact input

“…Then the goal is to decide whether two given geometric objects are related by some (projective, affine, similar, or isometric) transformation and in the affirmative case to detect all such equivalences. These problems are often addressed in papers coming from applied fields like Computer Aided Geometric Design, Pattern Recognition or Computer Vision, see [2][3][4] for the exhaustive list of references. In fields like Patter Recognition or Computer Vision especially the problem of detecting similarity is essential because objects must be recognized regardless of their position and scale.…”

“…One can find several papers focused on the detection and computation of symmetries and some equivalences of curves, see e.g. [5][6][7][8], or a recent sequence of papers [2,3,[9][10][11]. Lately, the problem of deterministically computing the symmetries of a given planar algebraic curve, implicitly defined, and the problem of deterministically checking whether or Figure 1: A curve with the rotational symmetry with the center at the origin and the angle 2π/5 (blue) and its perturbation which does not possess any symmetry (red).…”

Recognition of complex polynomial Bezier curves under similarity transformations

“…For Bézier curves, rational curves and implicit algebraic curves, detecting whether two plane curves are similar by an orientation preserving similarity transformation is important. (see [11][12][13][14][15][16][17][18][19]).…”