scholarly journals A global approach for image orientation using Lie algebraic rotation averaging and convex L∞ minimisation

2014 ◽  
Vol XL-3 ◽  
pp. 265-272
Author(s):  
M. Reich ◽  
C. Heipke
Keyword(s):  
Synthetic Data ◽  
Optimal Solution ◽  
Bundle Adjustment ◽  
Essential Matrix ◽  
Initial Values ◽  
Step Procedure ◽  
Robust Least Squares ◽  
Rotation Parameters ◽  
Image Pairs ◽  
Image Orientation

In this paper we present a new global image orientation approach for a set of multiple overlapping images with given homologous point tuples which is based on a two-step procedure. The approach is independent on initial values, robust with respect to outliers and yields the global minimum solution under relatively mild constraints. The first step of the approach consists of the estimation of global rotation parameters by averaging relative rotation estimates for image pairs (these are determined from the homologous points via the essential matrix in a pre-processing step). For the averaging we make use of algebraic group theory in which rotations, as part of the special orthogonal group <i>SO(3)</i>, form a Lie group with a Riemannian manifold structure. This allows for a mapping to the local Euclidean tangent space of <i>SO(3)</i>, the Lie algebra. In this space the redundancy of relative orientations is used to compute an average of the absolute rotation for each image and furthermore to detect and eliminate outliers. In the second step translation parameters and the object coordinates of the homologous points are estimated within a convex <i>L</i><sub>&infin;</sub> optimisation, in which the rotation parameters are kept fixed. As an optional third step the results can be used as initial values for a final bundle adjustment that does not suffer from bad initialisation and quickly converges to a globally optimal solution. We investigate our approach for global image orientation based on synthetic data. The results are compared to a robust least squares bundle adjustment. In this way we show that our approach is independent of initial values and more robust against outliers than a conventional bundle adjustment.

scholarly journals CONVEX IMAGE ORIENTATION FROM RELATIVE ORIENTATIONS

2016 ◽  
Vol III-3 ◽  
pp. 107-114 ◽  
Author(s):  
M. Reich ◽  
C. Heipke
Keyword(s):  
State Of The Art ◽  
Synthetic Data ◽  
Homogeneous System ◽  
Bundle Adjustment ◽  
Semidefinite Program ◽  
Critical Aspect ◽  
Benchmark Data ◽  
Least Squares Adjustment ◽  
Image Orientation ◽  
Orientation Parameters

In this paper we propose a novel workflow for the estimation of global image orientations given relative orientations between pairs of overlapping images. Our approach is convex and independent on initial values. First, global rotations are estimated in a relaxed semidefinite program (SDP) and refined in an iterative least squares adjustment in the tangent space of SO(3). A critical aspect is the handling of outliers in the relative orientations. We present a novel heuristic graph based approach for filtering the relative rotations that outperforms state-of-the-art robust rotation averaging algorithms. In a second part we make use of point-observations, tracked over a set of overlapping images and formulate a linear homogeneous system of equations to transfer the scale information between triplets of images, using estimated global rotations and relative translation directions. The final step consists of refining the orientation parameters in a robust bundle adjustment. The proposed approach handles outliers in the homologous points and relative orientations in every step of the processing chain. We demonstrate the robustness of the procedure on synthetic data. Moreover, the performance of our approach is illustrated on real world benchmark data.

scholarly journals CONVEX IMAGE ORIENTATION FROM RELATIVE ORIENTATIONS

2016 ◽  
Vol III-3 ◽  
pp. 107-114
Author(s):  
M. Reich ◽  
C. Heipke
Keyword(s):  
State Of The Art ◽  
Synthetic Data ◽  
Homogeneous System ◽  
Bundle Adjustment ◽  
Semidefinite Program ◽  
Critical Aspect ◽  
Benchmark Data ◽  
Least Squares Adjustment ◽  
Image Orientation ◽  
Orientation Parameters

In this paper we propose a novel workflow for the estimation of global image orientations given relative orientations between pairs of overlapping images. Our approach is convex and independent on initial values. First, global rotations are estimated in a relaxed semidefinite program (SDP) and refined in an iterative least squares adjustment in the tangent space of SO(3). A critical aspect is the handling of outliers in the relative orientations. We present a novel heuristic graph based approach for filtering the relative rotations that outperforms state-of-the-art robust rotation averaging algorithms. In a second part we make use of point-observations, tracked over a set of overlapping images and formulate a linear homogeneous system of equations to transfer the scale information between triplets of images, using estimated global rotations and relative translation directions. The final step consists of refining the orientation parameters in a robust bundle adjustment. The proposed approach handles outliers in the homologous points and relative orientations in every step of the processing chain. We demonstrate the robustness of the procedure on synthetic data. Moreover, the performance of our approach is illustrated on real world benchmark data.

scholarly journals Decision Support Tool for Offshore Wind Farm Vessel Routing under Uncertainty

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2190 ◽  
Author(s):  
Rafael Dawid ◽  
David McMillan ◽  
Matthew Revie
Keyword(s):  
Wind Farm ◽  
Real Life ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Decision Support Tool ◽  
Offshore Wind ◽  
Offshore Wind Farm ◽  
Support Tool ◽  
Trade Offs ◽  
The Impact

This paper for the first time captures the impact of uncertain maintenance action times on vessel routing for realistic offshore wind farm problems. A novel methodology is presented to incorporate uncertainties, e.g., on the expected maintenance duration, into the decision-making process. Users specify the extent to which these unknown elements impact the suggested vessel routing strategy. If uncertainties are present, the tool outputs multiple vessel routing policies with varying likelihoods of success. To demonstrate the tool’s capabilities, two case studies were presented. Firstly, simulations based on synthetic data illustrate that in a scenario with uncertainties, the cost-optimal solution is not necessarily the best choice for operators. Including uncertainties when calculating the vessel routing policy led to a 14% increase in the number of wind turbines maintained at the end of the day. Secondly, the tool was applied to a real-life scenario based on an offshore wind farm in collaboration with a United Kingdom (UK) operator. The results showed that the assignment of vessels to turbines generated by the tool matched the policy chosen by wind farm operators. By producing a range of policies for consideration, this tool provided operators with a structured and transparent method to assess trade-offs and justify decisions.

scholarly journals INTEGRATION OF A GENERALISED BUILDING MODEL INTO THE POSE ESTIMATION OF UAS IMAGES

2016 ◽  
Vol XLI-B1 ◽  
pp. 1057-1064 ◽  
Author(s):  
J. Unger ◽  
F. Rottensteiner ◽  
C. Heipke
Keyword(s):  
Pose Estimation ◽  
Image Sequence ◽  
Image Sequences ◽  
Bundle Adjustment ◽  
Unmanned Aerial System ◽  
Real Image ◽  
Building Model ◽  
Current State ◽  
Image Orientation

A hybrid bundle adjustment is presented that allows for the integration of a generalised building model into the pose estimation of image sequences. These images are captured by an Unmanned Aerial System (UAS) equipped with a camera flying in between the buildings. The relation between the building model and the images is described by distances between the object coordinates of the tie points and building model planes. Relations are found by a simple 3D distance criterion and are modelled as fictitious observations in a Gauss-Markov adjustment. The coordinates of model vertices are part of the adjustment as directly observed unknowns which allows for changes in the model. Results of first experiments using a synthetic and a real image sequence demonstrate improvements of the image orientation in comparison to an adjustment without the building model, but also reveal limitations of the current state of the method.

scholarly journals RobOMP: Robust variants of Orthogonal Matching Pursuit for sparse representations

2019 ◽  
Author(s):  
Carlos A Loza
Keyword(s):  
Mean Squared Error ◽  
Matching Pursuit ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Parameter Tuning ◽  
Weight Vector ◽  
Orthogonal Matching Pursuit ◽  
Main Mode ◽  
Observation Matrix ◽  
And Performance

Sparse coding aims to find a parsimonious representation of an example given an observation matrix or dictionary. In this regard, Orthogonal Matching Pursuit (OMP) provides an intuitive, simple and fast approximation of the optimal solution. However, its main building block is anchored on the minimization of the Mean Squared Error cost function (MSE). This approach is only optimal if the errors are distributed according to a Gaussian distribution without samples that strongly deviate from the main mode, i.e. outliers. If such assumption is violated, the sparse code will likely be biased and performance will degrade accordingly. In this paper, we introduce five robust variants of OMP (RobOMP) fully based on the theory of M-Estimators under a linear model. The proposed framework exploits efficient Iteratively Reweighted Least Squares (IRLS) techniques to mitigate the effect of outliers and emphasize the samples corresponding to the main mode of the data. This is done adaptively via a learned weight vector that models the distribution of the data in a robust manner. Experiments on synthetic data under several noise distributions and image recognition under different combinations of occlusion and missing pixels thoroughly detail the superiority of RobOMP over MSE-based approaches and similar robust alternatives. We also introduce a denoising framework based on robust, sparse and redundant representations that open the door to potential further applications of the proposed techniques. The five different variants of RobOMP do not require parameter tuning from the user and, hence, constitute principled alternatives to OMP.

scholarly journals ORIENTATION OF OBLIQUE AIRBORNE IMAGE SETS – EXPERIENCES FROM THE ISPRS/EUROSDR BENCHMARK ON MULTI-PLATFORM PHOTOGRAMMETRY

2016 ◽  
Vol XLI-B1 ◽  
pp. 185-191
Author(s):  
M. Gerke ◽  
F. Nex ◽  
F. Remondino ◽  
K. Jacobsen ◽  
J. Kremer ◽  
...  
Keyword(s):  
Digital Camera ◽  
Research Problem ◽  
Bundle Adjustment ◽  
Random Errors ◽  
Interest Points ◽  
Image Block ◽  
Point Matching ◽  
Camera Systems ◽  
Oblique Images ◽  
Image Orientation

During the last decade the use of airborne multi camera systems increased significantly. The development in digital camera technology allows mounting several mid- or small-format cameras efficiently onto one platform and thus enables image capture under different angles. Those oblique images turn out to be interesting for a number of applications since lateral parts of elevated objects, like buildings or trees, are visible. However, occlusion or illumination differences might challenge image processing. From an image orientation point of view those multi-camera systems bring the advantage of a better ray intersection geometry compared to nadir-only image blocks. On the other hand, varying scale, occlusion and atmospheric influences which are difficult to model impose problems to the image matching and bundle adjustment tasks. In order to understand current limitations of image orientation approaches and the influence of different parameters such as image overlap or GCP distribution, a commonly available dataset was released. The originally captured data comprises of a state-of-the-art image block with very high overlap, but in the first stage of the so-called ISPRS/EUROSDR benchmark on multi-platform photogrammetry only a reduced set of images was released. In this paper some first results obtained with this dataset are presented. They refer to different aspects like tie point matching across the viewing directions, influence of the oblique images onto the bundle adjustment, the role of image overlap and GCP distribution. As far as the tie point matching is concerned we observed that matching of overlapping images pointing to the same cardinal direction, or between nadir and oblique views in general is quite successful. Due to the quite different perspective between images of different viewing directions the standard tie point matching, for instance based on interest points does not work well. How to address occlusion and ambiguities due to different views onto objects is clearly a non-solved research problem so far. In our experiments we also confirm that the obtainable height accuracy is better when all images are used in bundle block adjustment. This was also shown in other research before and is confirmed here. Not surprisingly, the large overlap of 80/80% provides much better object space accuracy – random errors seem to be about 2-3fold smaller compared to the 60/60% overlap. A comparison of different software approaches shows that newly emerged commercial packages, initially intended to work with small frame image blocks, do perform very well.

Multi-Objecitve Control of Dynamical Systems

1995 ◽  
Author(s):  
Petros Voulgaris
Keyword(s):  
Exact Solution ◽  
Duality Theory ◽  
Closed Loop ◽  
Finite Impulse Response ◽  
Optimal Solution ◽  
Standard Methods ◽  
Continuity Properties ◽  
Step Procedure ◽  
Quadratic Programming Problems ◽  
Finite Step

Abstract In this paper we consider the problem of minimizing the H2-norm of the closed loop map while maintaining its ℓ1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed loop maps. Utilizing duality theory, it is shown that the optimal solution is unique and has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the ℓ1-constraint are established.

scholarly journals A Grey Wolf Optimization-based Track-Before-Detect Method for Maneuvering Extended Target Detection and Tracking

Sensors ◽  
2019 ◽  
Vol 19 (7) ◽  
pp. 1577 ◽  
Author(s):  
Bo Yan ◽  
Xu Yang Zhao ◽  
Na Xu ◽  
Yu Chen ◽  
Wen Bo Zhao
Keyword(s):  
Target Detection ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Real Data ◽  
Grey Wolf ◽  
Grey Wolf Optimization ◽  
Detection And Tracking ◽  
Extended Target ◽  
Air Surveillance ◽  
Track Before Detect

A grey wolf optimization-based track-before-detect (GWO-TBD) method is developed for extended target detection and tracking. The aim of the GWO-TBD is tracking weak and maneuvering extended targets in a cluttered environment using the measurement points of an air surveillance radar. The optimal solution is the trajectory constituted by the points of an extended target. At the beginning of the GWO-TBD, the measurements of each scan are clustered into alternative sets. Secondly, closely sets are associated for tracklets. Each tracklet equals a candidate solution. Thirdly, the tracklets are further associated iteratively to find a better solution. An improved GWO algorithm is developed in the iteration for removal of unappreciated solution and acceleration of convergence. After the iteration of several generations, the optimal solution can be achieved, i.e. trajectory of an extended target. Both the real data and synthetic data are performed with the GWO-TBD and several existing algorithms in this work. Result infers that the GWO-TBD is superior to the others in detecting and tracking maneuvering targets. Meanwhile, much less prior information is necessary in the GWO-TBD. It makes the approach is engineering friendly.

scholarly journals Network Completion for Static Gene Expression Data

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Natsu Nakajima ◽  
Tatsuya Akutsu
Keyword(s):  
Gene Expression ◽  
Gene Expression Data ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Genetic Networks ◽  
Expression Data ◽  
Initial Network ◽  
Static Data ◽  
Normal Gene ◽  
Stationary Conditions

We tackle the problem of completing and inferring genetic networks under stationary conditions from static data, where network completion is to make the minimum amount of modifications to an initial network so that the completed network is most consistent with the expression data in which addition of edges and deletion of edges are basic modification operations. For this problem, we present a new method for network completion using dynamic programming and least-squares fitting. This method can find an optimal solution in polynomial time if the maximum indegree of the network is bounded by a constant. We evaluate the effectiveness of our method through computational experiments using synthetic data. Furthermore, we demonstrate that our proposed method can distinguish the differences between two types of genetic networks under stationary conditions from lung cancer and normal gene expression data.

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