Direct and inverse discrete Zernike transform.

Geometrically Invariant Image Watermarking Based on Feature Extraction and Zernike Transform

A robust and geometric invariant digital image watermarking scheme based on feature extraction and local Zernike transform is proposed in this paper. The Adaptive Harris Detector is proposed to extract feature patches for watermarking use. A local Zernike moments-based watermarking scheme is raised, where the watermarked patches can be obtained directly by inverse Zernike Transform. Each extrac...

Invariant Image Watermarking Using Harris Feature Extraction and Zernike Moments

A robust and geometric invariant digital image watermarking scheme based on feature extraction and local Zernike transform is proposed in this paper. The Adaptive Harris Detector is proposed to extract feature patches for watermarking use. A local Zernike moments-based watermarking scheme is raised, where the watermarked patches can be obtained directly by inverse Zernike Transform. Each extrac...

Numerical Solution of Volterra-Fredholm Integral Equations with The Help of Inverse and Direct Discrete Fuzzy Transforms and Collocation Technique

Computing Zernike polynomials of arbitrary degree using the discrete Fourier transform

The conventional representation of Zernike polynomials Rn (ρ) gives unacceptable numerical results for large values of the degree n. We present an algorithm for the computation of Zernike polynomials of arbitrary degree n. The algorithm has the form of a discrete Fourier (cosine) transform which comes with advantages over other methods in terms of computation time, accuracy and ease of implemen...

Bessel-zernike discrete variable representation basis.

The connection between the Bessel discrete variable basis expansion and a specific form of an orthogonal set of Jacobi polynomials is demonstrated. These so-called Zernike polynomials provide alternative series expansions of suitable functions over the unit interval. Expressing a Bessel function in a Zernike expansion provides a straightforward method of generating series identities. Furthermor...