Search

Moment invariants are well-established and effective shape descriptors for image classification. In this report, we introduce a package for R-language, named IM, that implements the calculation of moments for images and allows the reconstruction of images from moments within an object-oriented framework. Several types of moments may be computed using the IM library, including discrete and continuous Chebyshev, Gegenbauer, Legendre, Krawtchouk, dual Hahn, generalized pseudo-Zernike, Fourier-Mellin, and radial harmonic Fourier moments. In addition, custom bivariate types of moments can be calculated using combinations of two different types of polynomials. A method of polar transformation of pixel coordinates is used to provide an approximate invariance to rotation for moments that are orthogonal over a rectangle. The different types of polynomials used to calculate moments are discussed in this report, as well as comparisons of reconstruction and running time. Examples of image classification using image moments are provided., Comment: Apr 2014, technical report

Let $R$ be an algebra essentially of finite type over a field $k$ and let $\Omega_k(R)$ be its module of K\"ahler differentials over $k$. If $R$ is a homogeneous complete intersection and $\mathrm{char}(k)=0$, we prove that $\Omega_k(R)$ is of linear type whenever its Rees algebra is Cohen-Macaulay and locally at every homogeneous prime $\mathfrak{p}$ the embedding dimension of $R_{\mathfrak{p}}$ is at most twice its dimension., Comment: 9 pages