Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations \(U:\mathbb {R}^{d} \rtimes S^{d...

Retinal images provide early signs of diabetic retinopathy, glaucoma, and hypertension. These signs can be investigated based on microaneurysms or smaller vessels. The diagnostic biomarkers are the change of vessel widths and angles especially at junctions, which are investigated using the vessel segmentation or tracking. Vessel paths may also be interrupted; crossings and...

Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices. We present some existing results of the theory of regularisation in this novel framework, where errors are represented as bounds by means of the appropriate partial order. We apply the theory to diffusion tensor imaging, where correct noise modelling...

Robust measures are introduced for methods to determine statistically uncorrelated or also statistically independent components spanning data measured in a way that does not permit direct separation of these underlying components. Because of the nonlinear nature of the proposed methods, iterative methods are presented for the optimization of merit functions, and local convergence...

We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation seminorm and \(\mathrm {L}^{p}\) norms. A unified well-posedness analysis is presented and a detailed study of the one-dimensional model is performed, by computing exact solutions for the...

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of...

Using the Kullback–Leibler divergence we provide a simple statistical measure which uses only the covariance matrix of a given set to verify whether the set is an ellipsoid. Similar measure is provided for verification of circles and balls. The new measure is easily computable, intuitive, and can be applied to higher dimensional data. Experiments have been performed to illustrate...

One of the approaches in diffusion tensor imaging is to consider a Riemannian metric given by the inverse diffusion tensor. Such a metric is used for geodesic tractography and connectivity analysis in white matter. We propose a metric tensor given by the adjugate rather than the previously proposed inverse diffusion tensor. The adjugate metric can also be employed in the...

The performance of matching and object recognition methods based on interest points depends on both the properties of the underlying interest points and the choice of associated image descriptors. This paper demonstrates advantages of using generalized scale-space interest point detectors in this context for selecting a sparse set of points for computing image descriptors for...

We develop a framework for polynomial regression on Riemannian manifolds. Unlike recently developed spline models on Riemannian manifolds, Riemannian polynomials offer the ability to model parametric polynomials of all integer orders, odd and even. An intrinsic adjoint method is employed to compute variations of the matching functional, and polynomial regression is accomplished...

To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem P curve of minimizing \(\int _{0}^{\ell} \sqrt{\xi^{2} +\kappa^{2}(s)} {\rm d}s \) for a planar curve having fixed initial and final positions and directions. Here κ(s) is the curvature of the curve with free total length ℓ. This problem comes from a model of...

We propose a novel skeleton-based approach to gait recognition using our Skeleton Variance Image. The core of our approach consists of employing the screened Poisson equation to construct a family of smooth distance functions associated with a given shape. The screened Poisson distance function approximation nicely absorbs and is relatively stable to shape boundary perturbations...

In this paper we introduce an integrative approach towards color texture classification and recognition using a supervised learning framework. Our approach is based on Generalized Learning Vector Quantization (GLVQ), extended by an adaptive distance measure, which is defined in the Fourier domain, and adaptive filter kernels based on Gabor filters. We evaluate the proposed...