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Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2×2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these. Using amoeba structuring elements, we devise image-adaptive versions of both filter classes. Experiments demonstrate the favourable properties of the filters.
In this work, we propose a novel way for performing operations of mathematical morphology on color images. To this end, we convert pixelwise the rgb-values into symmetric 2x2 matrices. The new color space can be interpreted geometrically as a biconal color space structure. Motivated by the formulation of the fundamental morphological operations dilation and erosion in terms of partial differential equations (PDEs), we show how to define finite difference schemes making use of the matrix field formulation. The computation of a pseudo supremum and a pseudo infimum of three color matrices is a crucial step for setting up advanced PDE-based methods. We show that this can be achieved for our goal by an algebraic technique. We investigate our approach by dedicated experiments and confirm useful properties of the new PDE-based color morphology operations.
In this paper we are concerned with robust structure-preserving denoising filters for color images. We build on a recently proposed transformation from the RGB color space to the space of symmetric 2×2 matrices that has already been used to transfer morphological dilation and erosion concepts from matrix-valued data to color images. We investigate the applicability of this framework to the construction of color-valued median filters. Additionally, we introduce spatial adaptivity into our approach by morphological amoebas that offer excellent capabilities for structure-preserving filtering. Furthermore, we define color-valued amoeba M-smoothers as a generalization of the median-based concepts. Our experiments confirm that all these methods work well with color images. They demonstrate the potential of our approach to define color processing tools based on matrix field techniques.
In spite of significant advances in Shape from Shading (SfS) over the last years, it
is still a challenging task to design SfS approaches that are flexible enough to handle a
wide range of input scenes. In this paper, we address this lack of flexibility by proposing
a novel model that extends the range of possible applications. To this end, we consider
the class of modern perspective SfS models formulated via partial differential equations
(PDEs). By combining a recent spherical surface parametrisation with the advanced
non-Lambertian Oren-Nayar reflectance model, we obtain a robust approach that allows
to deal with an arbitrary position of the light source while being able to handle rough
surfaces and thus more realistic objects at the same time. To our knowledge, the resulting
model is currently the most advanced and most flexible approach in the literature on
PDE-based perspective SfS. Apart from deriving our model, we also show how the corresponding
set of sophisticated Hamilton-Jacobi equations can be efficiently solved by
a specifically tailored fast marching scheme. Experiments with medical real-world data
demonstrate that our model works in practice and that is offers the desired flexibility.