Errors-in-Variables Anisotropic Extended Orthogonal Procrustes Analysis

This letter presents a novel total least squares (TLS) solution of the anisotropic row-scaling Procrustes problem. The ordinary LS Procrustes approach finds the transformation parameters between origin and destination sets of observations minimizing errors affecting only the destination one. In this letter, we introduce the errors-in-variables model in the anisotropic Procrustes analysis problem and present a solution that can deal with the uncertainty affecting both sets of observations. The algorithm is applied to solve the image exterior orientation problem. Experiments show that the proposed TLS method leads to an accuracy in the parameters estimation that is higher than the one reached with the ordinary LS anisotropic Procrustes solution when the number of points, whose coordinates are known in both the image and the external systems, is small

Solving bundle block adjustment by generalized anisotropic Procrustes analysis

The paper presents a new analytical tool to solve the classical photogrammetric bundle block adjustment. The analytical model is based on the generalized extension of the anisotropic row-scaling Procrustes analysis, that has been recently proposed by the same authors to solve the image exterior orientation problem. The main advantage of the method is given by the fact that the problem solution does not require any approximate value of the unknown parameters, nor any linearization procedure. Moreover, the algorithm is exceedingly simple to describe and easy to implement. Empirical results indicate that a zero-information initialization of the iterative relaxation procedure leads almost always to the correct final least squares solution. Experiments confirm the accuracy of the proposed method, when compared to the results obtained by applying a classical photogrammetric bundle block adjustment

FAST AND RESISTANT PROCRUSTEAN BUNDLE ADJUSTMENT

In a recent paper (Fusiello and Crosilla, 2015) a Procrustean formulation of the bundle block adjustment has been presented, with a solution based on alternating least squares. This paper improves on it in two respects: it introduces a faster iterative scheme that minimizes the same cost function, thereby achieving the same accuracy, and makes the method resistant to rogue measures through iteratively reweighted least-squares. Empirical results confirm the effectiveness of these enhancements

The Morphometric Synthesis for landmarks and edge-elements in images

Over the last decade, techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry, and computer graphics have been combined in a coherent new system of tools for the biometric analysis of landmarks , or labelled points, along with the biological images in which they are seen. Multivariate analyses of samples for all the usual scientific purposes - description of mean shapes, of shape variation, and of the covariation of shape with size, group, or other causes or effects - may be carried out very effectively in the tangent space to David Kendall's shape space at the Procrustes average shape. For biometric interpretation of such analyses, we need a basis for the tangent space that is Procrustes-orthonormal, and we need graphics for visualizing mean shape differences and other segments and vectors there; both of these needs are managed by the thin-plate spline. The spline also links the biometrics of landmarks to deformation analysis of curves in the images from which the landmarks originally arose. This article reviews the principal tools of this synthesis in a typical study design involving landmarks and edge information from a microfossil.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75091/1/j.1365-3121.1995.tb00535.x.pd

Leveraging feature uncertainty in the PnP problem

Trabajo presentado a la 25th British Machine Vision Conference (BMVC), celebrada en Nottingham (UK) del 1 al 5 de septiembre de 2014.-- Este ítem (excepto textos e imágenes no creados por el autor) está sujeto a una licencia de Creative Commons: Attribution-NonCommercial-NoDerivs 3.0 Spain.We propose a real-time and accurate solution to the Perspective-n-Point (PnP) problem --estimating the pose of a calibrated camera from n 3D-to-2D point correspondences-- that exploits the fact that in practice the 2D position of not all 2D features is estimated with the same accuracy. Assuming a model of such feature uncertainties is known in advance, we reformulate the PnP problem as a maximum likelihood minimization approximated by an unconstrained Sampson error function, which naturally penalizes the most noisy correspondences. The advantages of this approach are clearly demonstrated in synthetic experiments where feature uncertainties are exactly known. Pre-estimating the features uncertainties in real experiments is, though, not easy. In this paper we model feature uncertainty as 2D Gaussian distributions representing the sensitivity of the 2D feature detectors to different camera viewpoints. When using these noise models with our PnP formulation we still obtain promising pose estimation results that outperform the most recent approaches.This work has been partially funded by Spanish government under projects DPI2011-27510, IPT-2012-0630-020000, IPT-2011-1015-430000 and CICYT grant TIN2012-39203; by the EU project ARCAS FP7-ICT-2011-28761; and by the ERA-Net Chistera project ViSen PCIN-2013-047.Peer Reviewe

Bi-temporal 3D active appearance models with applications to unsupervised ejection fraction estimation

Rapid and unsupervised quantitative analysis is of utmost importance to ensure clinical acceptance of many examinations using cardiac magnetic resonance imaging (MRI). We present a framework that aims at fulfilling these goals for the application of left ventricular ejection fraction estimation in four-dimensional MRI. The theoretical foundation of our work is the generative two-dimensional Active Appearance Models by Cootes et al., here extended to bi-temporal, three-dimensional models. Further issues treated include correction of respiratory induced slice displacements, systole detection, and a texture model pruning strategy. Cross-validation carried out on clinical-quality scans of twelve volunteers indicates that ejection fraction and cardiac blood pool volumes can be estimated automatically and rapidly with accuracy on par with typical inter-observer variability. \u

Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI

Detection and localisation of structural deformations using terrestrial laser scanning and generalised procrustes analysis

One of the most vital duties for engineers is to preserve life and nature by utilising safe designs that take into account environmental standards and monitoring the performance of structures against design criteria. Furthermore, monitoring can be used to determine any required maintenance of an important structure following a catastrophic event. Numerous different techniques and instruments can be employed for such a purpose with different requirements producing different results. For instance, some techniques need to embed sensors inside the building, such as Geotechnical Sensors. Others can offer high quality, but with a low point density and require fixed stations and targets, like Total Stations (TS). In such cases, the location of deformation tends to be known, such as in dams, bridges, and high-rise buildings. However, this is not always the case where it might be hard to expect deformation location as in the case of historic ruins where each part of the structure could be subject to deformation. The challenge in such case is to detect the deformation without any previous knowledge. Remote Sensing (RS) techniques, such as Digital Photogrammetry, Synthetic Aperture Radar (SAR), Interferometric Synthetic Aperture Radar (InSAR), and Terrestrial Laser Scanner (TLS) can be solutions for such an issue. Interestingly, many researchers are focusing on using TLS for monitoring owing to the great spatial resolution system can offer. However, there are three challenges in using TLS in monitoring: the first one is a huge amount of data and the difficulty of handling it; the second one is the difficulty of comparing between two epochs because observations of TLS are not repeatable; and the third issue is the noise which is attached to the data. The first problem is solved by segmentation and point structure while the second and the third ones still need more investigation, although some interesting researches have been done in this area. The aim of this research is to develop a new approach to detect and localise unpredictable deformation. It is based on TLS measurements and Generalised Procrustes Analysis (GPA) techniques to determine deformation vectors, while boxing structure and F-test are used to detect and localise deformation. In summary, after applying this approach, the whole concerned building is represented as parts, for each of which the displacement vector and the deformation probability are estimated. Ultimately, it is possible to monitor any part through different epochs. In addition, through this technique, it is possible to determine deformations - not just between two epochs, but for sequences of them. This can give more reliable results. Four validation experiments have been conducted. The first test was designed to assess the performance of the developed software and to fix some variables. Therefore, it was based on simulated data with controlled white noise, distributed according to the normal distribution, and simulated deformations. The results of this test revealed the success of the proposed algorithm to detect and to localise deformations. In addition, it showed the success when no deformations exist. Furthermore, optimistically, it could observe deformations with magnitude less than the noise level; however, the probability was only 40%. Correspondingly, real scan data with simulated deformations was used in the second test. The purpose of this test is to examine the performance of the proposed method in case of real errors budget. However, the short range of the test (about 10m), a featureless scanned area (wall only), and scanning from one position for all epochs (no need for registration) can reduce errors to a minimum. Results of this test showed the success of the proposed method to detect and localise deformations. Potentially, it can give indications for areas with deformations less than the noise level. Furthermore, results of the proposed method can be considered better than that of CloudCompare software. The third test was conducted to examine the performance of the proposed technique regarding different materials and textures. For this purpose, the Nottingham Geospatial Building (NGB) was selected with more extensive ranges (between 20-25 m). Similar to the second test, all measurements were taken from the same scanner position. To some extent, the proposed technique succeeded to detect and to localise deformations. However, the researcher does not recommend it for monitoring modern and complicated buildings, instead it has been developed for monitoring historic ruins. Finally, the proposed method was applied on the Bellmanpark Limekiln, Clitheroe, Lancashire monitoring project. This is a live project for Historic England and addresses a historic building that currently has some structural issues. The outcome of the proposed method revealed deformations in the faces South East (SE) and North East (NE). From examining these faces, three deformed areas were found: two in the face SE and one in the face NE, which might cause some cracks appeared in these faces. Alternatively, the CloudCompare software has been employed to detect deformation. Although results coincide with the proposed method for detected deformations, it cannot locate these deformations very well because it diffused over a wide area. In addition, it cannot determine actual directions of the deformations unlike the proposed method