On the Subspace of Image Gradient Orientations

We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing intensities with gradient orientations and the $\ell_2$ norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Our scheme requires the eigen-decomposition of a covariance matrix and is as computationally efficient as standard $\ell_2$ PCA. We demonstrate some of its favorable properties on robust subspace estimation

A minimalistic approach to appearance-based visual SLAM

This paper presents a vision-based approach to SLAM in indoor / outdoor environments with minimalistic sensing and computational requirements. The approach is based on a graph representation of robot poses, using a relaxation algorithm to obtain a globally consistent map. Each link corresponds to a relative measurement of the spatial relation between the two nodes it connects. The links describe the likelihood distribution of the relative pose as a Gaussian distribution. To estimate the covariance matrix for links obtained from an omni-directional vision sensor, a novel method is introduced based on the relative similarity of neighbouring images. This new method does not require determining distances to image features using multiple view geometry, for example. Combined indoor and outdoor experiments demonstrate that the approach can handle qualitatively different environments (without modification of the parameters), that it can cope with violations of the “flat floor assumption” to some degree, and that it scales well with increasing size of the environment, producing topologically correct and geometrically accurate maps at low computational cost. Further experiments demonstrate that the approach is also suitable for combining multiple overlapping maps, e.g. for solving the multi-robot SLAM problem with unknown initial poses

ShapeFit and ShapeKick for Robust, Scalable Structure from Motion

We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers. When pairwise directions represent scaled relative positions between pairs of views (estimated for instance with epipolar geometry) our method can be used for location recovery, that is the determination of relative pose up to a single unknown scale. For this task, our method yields performance comparable to the state-of-the-art with an order of magnitude speed-up. Our proposed numerical framework is flexible in that it accommodates other approaches to location recovery and can be used to speed up other methods. These properties are demonstrated by extensively testing against state-of-the-art methods for location recovery on 13 large, irregular collections of images of real scenes in addition to simulated data with ground truth

Robust Camera Location Estimation by Convex Programming

$3$D structure recovery from a collection of $2$D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation part, which can be formulated as the inverse problem of estimating $n$ locations $\mathbf{t}_1, \mathbf{t}_2, \ldots, \mathbf{t}_n$ in $\mathbb{R}^3$ from noisy measurements of a subset of the pairwise directions $\frac{\mathbf{t}_i - \mathbf{t}_j}{\|\mathbf{t}_i - \mathbf{t}_j\|}$, are sensitive to outliers in direction measurements. In this paper, we firstly provide a complete characterization of well-posed instances of the location estimation problem, by presenting its relation to the existing theory of parallel rigidity. For robust estimation of camera locations, we introduce a two-step approach, comprised of a pairwise direction estimation method robust to outliers in point correspondences between image pairs, and a convex program to maintain robustness to outlier directions. In the presence of partially corrupted measurements, we empirically demonstrate that our convex formulation can even recover the locations exactly. Lastly, we demonstrate the utility of our formulations through experiments on Internet photo collections.Comment: 10 pages, 6 figures, 3 table

A flexible space-variant anisotropic regularisation for image restoration with automated parameter selection

We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian distribution. The highly flexible variational structure of the corresponding regulariser encodes several free parameters which hold the potential for faithfully modelling the local geometry in the image and describing local orientation preferences. For an automatic estimation of such parameters, we design a robust maximum likelihood approach and report results on its reliability on synthetic data and natural images. For the numerical solution of the corresponding image restoration model, we use an iterative algorithm based on the Alternating Direction Method of Multipliers (ADMM). A suitable preliminary variable splitting together with a novel result in multivariate non-convex proximal calculus yield a very efficient minimisation algorithm. Several numerical results showing significant quality-improvement of the proposed model with respect to some related state-of-the-art competitors are reported, in particular in terms of texture and detail preservation

Stability effects on results of diffusion tensor imaging analysis by reduction of the number of gradient directions due to motion artifacts: an application to presymptomatic Huntington's disease.

In diffusion tensor imaging (DTI), an improvement in the signal-to-noise ratio (SNR) of the fractional anisotropy (FA) maps can be obtained when the number of recorded gradient directions (GD) is increased. Vice versa, elimination of motion-corrupted or noisy GD leads to a more accurate characterization of the diffusion tensor. We previously suggest a slice-wise method for artifact detection in FA maps. This current study applies this approach to a cohort of 18 premanifest Huntington's disease (pHD) subjects and 23 controls. By 2-D voxelwise statistical comparison of original FA-maps and FA-maps with a reduced number of GD, the effect of eliminating GD that were affected by motion was demonstrated.We present an evaluation metric that allows to test if the computed FA-maps (with a reduced number of GD) still reflect a "true" FA-map, as defined by simulations in the control sample. Furthermore, we investigated if omitting data volumes affected by motion in the pHD cohort could lead to an increased SNR in the resulting FA-maps.A high agreement between original FA maps (with all GD) and corrected FA maps (i.e. without GD corrupted by motion) were observed even for numbers of eliminated GD up to 13. Even in one data set in which 46 GD had to be eliminated, the results showed a moderate agreement