Trifocal Relative Pose from Lines at Points and its Efficient Solution

We present a new minimal problem for relative pose estimation mixing point features with lines incident at points observed in three views and its efficient homotopy continuation solver. We demonstrate the generality of the approach by analyzing and solving an additional problem with mixed point and line correspondences in three views. The minimal problems include correspondences of (i) three points and one line and (ii) three points and two lines through two of the points which is reported and analyzed here for the first time. These are difficult to solve, as they have 216 and - as shown here - 312 solutions, but cover important practical situations when line and point features appear together, e.g., in urban scenes or when observing curves. We demonstrate that even such difficult problems can be solved robustly using a suitable homotopy continuation technique and we provide an implementation optimized for minimal problems that can be integrated into engineering applications. Our simulated and real experiments demonstrate our solvers in the camera geometry computation task in structure from motion. We show that new solvers allow for reconstructing challenging scenes where the standard two-view initialization of structure from motion fails.Comment: This material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while most authors were in residence at Brown University's Institute for Computational and Experimental Research in Mathematics -- ICERM, in Providence, R

Linear Global Translation Estimation with Feature Tracks

This paper derives a novel linear position constraint for cameras seeing a common scene point, which leads to a direct linear method for global camera translation estimation. Unlike previous solutions, this method deals with collinear camera motion and weak image association at the same time. The final linear formulation does not involve the coordinates of scene points, which makes it efficient even for large scale data. We solve the linear equation based on $L_1$ norm, which makes our system more robust to outliers in essential matrices and feature correspondences. We experiment this method on both sequentially captured images and unordered Internet images. The experiments demonstrate its strength in robustness, accuracy, and efficiency.Comment: Changes: 1. Adopt BMVC2015 style; 2. Combine sections 3 and 5; 3. Move "Evaluation on synthetic data" out to supplementary file; 4. Divide subsection "Evaluation on general data" to subsections "Experiment on sequential data" and "Experiment on unordered Internet data"; 5. Change Fig. 1 and Fig.8; 6. Move Fig. 6 and Fig. 7 to supplementary file; 7 Change some symbols; 8. Correct some typo

Robust Multiple-View Geometry Estimation Based on GMM

Given three partially overlapping views of the scene from which a set of point or line correspondences have been extracted, 3D structure and camera motion parameters can be represented by the trifocal tensor, which is the key to many problems of computer vision on three views. Unlike in conventional typical methods, the residual value is the only rule to eliminate outliers with large value, we build a Gaussian mixture model assuming that the residuals corresponding to the inliers come from Gaussian distributions different from that of the residuals of outliers. Then Bayesian rule of minimal risk is employed to classify all the correspondences using the parameters computed from GMM. Experiments with both synthetic data and real images show that our method is more robust and precise than other typical methods because it can efficiently detect and delete the bad corresponding points, which include both bad locations and false matches

Metric 3D-reconstruction from Unordered and Uncalibrated Image Collections

In this thesis the problem of Structure from Motion (SfM) for uncalibrated and unordered image collections is considered. The proposed framework is an adaptation of the framework for calibrated SfM proposed by Olsson-Enqvist (2011) to the uncalibrated case. Olsson-Enqvist's framework consists of three main steps; pairwise relative rotation estimation, rotation averaging, and geometry estimation with known rotations. For this to work with uncalibrated images we also perform auto-calibration during the first step. There is a well-known degeneracy for pairwise auto-calibration which occurs when the two principal axes meet in a point. This is unfortunately common for real images. To mitigate this the rotation estimation is instead performed by estimating image triplets. For image triplets the degenerate congurations are less likely to occur in practice. This is followed by estimation of the pairs which did not get a successful relative rotation from the previous step. The framework is successfully applied to an uncalibrated and unordered collection of images of the cathedral in Lund. It is also applied to the well-known Oxford dinosaur sequence which consists of turntable motion. Image pairs from the turntable motion are in a degenerate conguration for auto-calibration since they both view the same point on the rotation axis

Control de robots móviles mediante visión omnidireccional utilizando la geometría de tres vistas

Este trabajo trata acerca del control visual de robot móviles. Dentro de este campo tan amplio de investigación existen dos elementos a los que prestaremos especial atención: la visión omnidireccional y los modelos geométricos multi-vista. Las cámaras omnidireccionales proporcionan información angular muy precisa, aunque presentan un grado de distorsión significativo en dirección radial. Su cualidad de poseer un amplio campo de visión hace que dichas cámaras sean apropiadas para tareas de navegación robótica. Por otro lado, el uso de los modelos geométricos que relacionan distintas vistas de una escena permite rechazar emparejamientos erróneos de características visuales entre imágenes, y de este modo robustecer el proceso de control mediante visión. Nuestro trabajo presenta dos técnicas de control visual para ser usadas por un robot moviéndose en el plano del suelo. En primer lugar, proponemos un nuevo método para homing visual, que emplea la información dada por un conjunto de imágenes de referencia adquiridas previamente en el entorno, y las imágenes que toma el robot a lo largo de su movimiento. Con el objeto de sacar partido de las cualidades de la visión omnidireccional, nuestro método de homing es puramente angular, y no emplea información alguna sobre distancia. Esta característica, unida al hecho de que el movimiento se realiza en un plano, motiva el empleo del modelo geométrico dado por el tensor trifocal 1D. En particular, las restricciones geométricas impuestas por dicho tensor, que puede ser calculado a partir de correspondencias de puntos entre tres imágenes, mejoran la robustez del control en presencia de errores de emparejamiento. El interés de nuestra propuesta reside en que el método de control empleado calcula las velocidades del robot a partir de información únicamente angular, siendo ésta muy precisa en las cámaras omnidireccionales. Además, presentamos un procedimiento que calcula las relaciones angulares entre las vistas disponibles de manera indirecta, sin necesidad de que haya información visual compartida entre todas ellas. La técnica descrita se puede clasificar como basada en imagen (image-based), dado que no precisa estimar la localización ni utiliza información 3D. El robot converge a la posición objetivo sin conocer la información métrica sobre la trayectoria seguida. Para algunas aplicaciones, como la evitación de obstáculos, puede ser necesario disponer de mayor información sobre el movimiento 3D realizado. Con esta idea en mente, presentamos un nuevo método de control visual basado en entradas sinusoidales. Las sinusoides son funciones con propiedades matemáticas bien conocidas y de variación suave, lo cual las hace adecuadas para su empleo en maniobras de aparcamiento de vehículos. A partir de las velocidades de variación sinusoidal que definimos en nuestro diseño, obtenemos las expresiones analíticas de la evolución de las variables de estado del robot. Además, basándonos en dichas expresiones, proponemos un método de control mediante realimentación del estado. La estimación del estado del robot se obtiene a partir del tensor trifocal 1D calculado entre la vista objetivo, la vista inicial y la vista actual del robot. Mediante este control sinusoidal, el robot queda alineado con la posición objetivo. En un segundo paso, efectuamos la corrección de la profundidad mediante una ley de control definida directamente en términos del tensor trifocal 1D. El funcionamiento de los dos controladores propuestos en el trabajo se ilustra mediante simulaciones, y con el objeto de respaldar su viabilidad se presentan análisis de estabilidad y resultados de simulaciones y de experimentos con imágenes reales

Robust Estimation of Trifocal Tensors Using Natural Features for Augmented Reality Systems

Augmented reality deals with the problem of dynamically augmenting or enhancing the real world with computer generated virtual scenes. Registration is one of the most pivotal problems currently limiting AR applications. In this paper, a novel registration method using natural features based on online estimation of trifocal tensors is proposed. This method consists of two stages: offline initialization and online registration. Initialization involves specifying four points in two reference images respectively to build the world coordinate system on which a virtual object will be augmented. In online registration, the natural feature correspondences detected from the reference views are tracked in the current frame to build the feature triples. Then these triples are used to estimate the corresponding trifocal tensors in the image sequence by which the four specified points are transferred to compute the registration matrix for augmentation. The estimated registration matrix will be used as an initial estimate for a nonlinear optimization method that minimizes the actual residual errors based on the Levenberg-Marquardt (LM) minimization method, thus making the results more robust and stable. This paper also proposes a robust method for estimating the trifocal tensors, where a modified RANSAC algorithm is used to remove outliers. Compared with standard RANSAC, our method can significantly reduce computation complexity, while overcoming the disturbance of mismatches. Some experiments have been carried out to demonstrate the validity of the proposed approach