Modified Rodrigues parameters (MRPs) are triplets in \({\mathbb {R}}^3\) bijectively and rationally mapped to quaternions through stereographic projection. We present here a compelling case for MRPs as a minimal degree-of-freedom parameterization of orientation through novel solutions to prominent problems in the fields of 3D vision and computer graphics. In our primary ...

This paper proposes a basic structured light system for pose estimation. It consists of a circular laser pattern and a camera rigidly attached to the laser source. We develop a geometric modeling that allows to efficiently estimate the pose at scale of the system, relative to a reference plane onto which the pattern is projected. Three different robust estimation strategies, ...

We examine the orthographic-n-point problem (OnP), which extends the perspective-n-point problem to telecentric cameras. Given a set of 3D points and their corresponding 2D points under orthographic projection, the OnP problem is the determination of the pose of the 3D point cloud with respect to the telecentric camera. We show that the OnP problem is equivalent to the unbalanced ...

A new and robust mapping approach is proposed entitled mapping forests (MFs) for computer vision applications based on regression transformations. Mapping forests relies on learning nonlinear mappings deduced from pairs of source and target training data, and improves the performance of mappings by enabling nonlinear transformations using forests. In contrast to previous ...

We propose a state estimation approach for functional magnetic resonance imaging (fMRI). In state estimation, time-dependent image reconstruction problem is modeled by separate state evolution and observation models, and the objective is to estimate the time series of system states, given the models and the time-dependent measurement data. Our method computes the state estimates by ...

We will in this paper present methods and algorithms for estimating two-view geometry based on an orthographic camera model. We use a previously neglected nonlinear criterion on rigidity to estimate the calibrated essential matrix. We give efficient algorithms for estimating it minimally (using only three point correspondences), in a least squares sense (using four or more point ...

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex relaxation for a certain set of graph-based multiclass data segmentation models involving a graph total variation term, region homogeneity ...

In order to detect salient lines in spherical images, we consider the problem of minimizing the functional \(\int \limits _0^l \mathfrak {C}(\gamma (s)) \sqrt{\xi ^2 + k_g^2(s)} \, \mathrm{d}s\) for a curve \(\gamma \) on a sphere with fixed boundary points and directions. The total length l is free, s denotes the spherical arclength, and \(k_g\) denotes the geodesic curvature of ...

When designing and developing scale selection mechanisms for generating hypotheses about characteristic scales in signals, it is essential that the selected scale levels reflect the extent of the underlying structures in the signal. This paper presents a theory and in-depth theoretical analysis about the scale selection properties of methods for automatically selecting local ...

We propose several variants of the primal–dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates, \(O(1{/}N^2)\) with respect to initialisation and O(1 / N) with respect to the dual sequence, and the residual part of the primal sequence. We ...

The field of high dynamic range imaging addresses the problem of capturing and displaying the large range of luminance levels found in the world, using devices with limited dynamic range. In this paper we present a novel tone mapping algorithm that is based on K-means clustering. Using dynamic programming we are able to not only solve the clustering problem efficiently, but also ...

Mathematical morphology is a theory with applications in image processing and analysis. This paper presents a quantale-based approach to color morphology based on the CIELab color space in spherical coordinates. The novel morphological operations take into account the perceptual difference between color elements by using a distance-based ordering scheme. Furthermore, the novel ...

We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost based on a Huber-regularised TV seminorm. Differentiability properties of the solution operator are verified and a first-order ...

Some basic properties of a slightly generalized version of the scale-invariant rank operator are given, and it is shown how this operator can be used to create a nearly scale-invariant generalization of path openings that is robust to noise. Efficient algorithms are given for sequences and directed acyclic graphs with binary values, as well as sequences with real (greyscale) ...

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 ...

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 is ...

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 ...