Steerable filtering using novel circular harmonic functions with application to edge detection

In this paper, we perform approximate steering of the elongated 2D Hermite-Gauss functions with respect to rotations and provide a compact analytical expressions for the related basis functions. A special notation introduced here considerably simplifies the derivation and unifies the cases of even and odd indices. The proposed filters are applied to edge detection. Quantitative analysis shows a performance increase of about 12.5% in terms of the Pratt’s figure of merit with respect to the well-established Gaussian gradient proposed earlier.

CLOSED FORM OF THE STEERED ELONGATED HERMITE-GAUSS WAVELETS

We provide a closed form, both in the spatial and in the frequency domain, of a family of wavelets which arise from steering elongated Hermite-Gauss filters. These wavelets have interesting mathematical properties, as they form new dyadic families of eigenfunctions of the 2D Fourier transform, and generalize the well known Laguerre-Gauss harmonics. A special notation introduced here greatly simplifies our proof and unifies the cases of even and odd orders. Applying these wavelets to edge detection increases the performance of about 12.5% with respect to standard methods, in terms of the Pratt’s figure of merit, both for noisy and noise-free input images

CMA – a comprehensive Bioconductor package for supervised classification with high dimensional data

For the last eight years, microarray-based class prediction has been a major topic in statistics, bioinformatics and biomedicine research. Traditional methods often yield unsatisfactory results or may even be inapplicable in the p > n setting where the number of predictors by far exceeds the number of observations, hence the term “ill-posed-problem”. Careful model selection and evaluation satisfying accepted good-practice standards is a very complex task for inexperienced users with limited statistical background or for statisticians without experience in this area. The multiplicity of available methods for class prediction based on high-dimensional data is an additional practical challenge for inexperienced researchers. In this article, we introduce a new Bioconductor package called CMA (standing for “Classification for MicroArrays”) for automatically performing variable selection, parameter tuning, classifier construction, and unbiased evaluation of the constructed classifiers using a large number of usual methods. Without much time and effort, users are provided with an overview of the unbiased accuracy of most top-performing classifiers. Furthermore, the standardized evaluation framework underlying CMA can also be beneficial in statistical research for comparison purposes, for instance if a new classifier has to be compared to existing approaches. CMA is a user-friendly comprehensive package for classifier construction and evaluation implementing most usual approaches. It is freely available from the Bioconductor website at http://bioconductor.org/packages/2.3/bioc/html/CMA.html