The Application Of Partial Differential Equations In The Shape Recognition

Shape recognition, measuring the similarities between shapes via a certain metrical criteria, is really an important issue in the fields of computer vision and pattern recognition. Quantities of researching work, in the last decades, have been carrying out with many methods putting forwards, which have their respective restrictions for their individual specific applications.Thereinto, moment, featured by easy expression and convenient calculation, has been extensively used in shape recognition. The disadvantage of using invariant moment to describe shapes, however, is that it can only describe the holistic information of a shape and lacks partial description, which will not achieve a better discriminating results if using it. And that's why a new method of shape description is expected to come into being.Lena Gorelick etc., in 2006, proposed the Poisson equation-geometric moment Descriptor (PGD) that used the solution of the Poisson equation defined in the shape area to describe a shape and then to construct the characteristic functions of the effectively described parts and then gained PGD via the integration of using geometric moments, which has proved to be good in shape classification and retrieval experiments.This paper has made improvement for the shape description method mentioned above. To replace geometric moments instead, we adopted Legendre moments, Zernike moment invariants, and Orthogonal Fourier-Mellin moment invariants to integrate the characteristic functions that yielded Poisson equation-Legendre moment descriptor (PLD), Poisson-Zernike moment descriptors (PZD), and Poisson equation-Fourier-Mellin Moment Descriptors (PFD), which have gained better results on shape recognition and classification. In fact, Legendre moments, compared with the geometric moments, takes the orthogonal Legendre polynomials as its transformation Kernel that can make information integration more concise and accurate because its moments are independent from each other without data redundancy; and Zernike moments have orthogonality and translation, rotation and scale invariability as well and especially have more sensitivity over noise; the orthogonal Fourier-Mellin moments, however, have more advantages in describing the small-scale images in the fact that they have advantages of the two moments mentioned above.These three new descriptors presented in this paper have maintained the advantages of the Poisson equation-geometric moment descriptors that can not only represent the holistic features of a shape but also describe the partial features of the shape. Additionally, they have the combined advantages of the three moments that can describe a shape with more comprehensiveness and accuracy.