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Multiview geometry for general camera models
 PROCEEDINGS OF THE 2005 IEEE COMPUTER SOCIETY CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR’05)  VOLUME 1
, 2005
"... We consider calibration and structure from motion tasks for a previously introduced, highly general imaging model, where cameras are modeled as possibly unconstrained sets of projection rays. This allows to describe most existing camera types (at least for those operating in the visible domain), in ..."
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Cited by 34 (4 self)
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We consider calibration and structure from motion tasks for a previously introduced, highly general imaging model, where cameras are modeled as possibly unconstrained sets of projection rays. This allows to describe most existing camera types (at least for those operating in the visible domain), including pinhole cameras, sensors with radial or more general distortions, catadioptric cameras (central or noncentral), etc. Generic algorithms for calibration and structure from motion tasks (pose and motion estimation and 3D point triangulation) are outlined. The foundation for a multiview geometry of noncentral cameras is given, leading to the formulation of multiview matching tensors, analogous to the fundamental matrices, trifocal and quadrifocal tensors of perspective cameras. Besides this, we also introduce a natural hierarchy of camera models: the most general model has unconstrained projection rays whereas the most constrained model dealt with here is the central model, where all rays pass through a single point.
The Raxel Imaging Model and RayBased Calibration
, 2005
"... An imaging model provides a mathematical description of correspondence between points in a scene and in an image. The dominant imaging model, perspective projection, has long been used to describe traditional cameras as well as the human eye. We propose an imaging model which is flexible enough to r ..."
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Cited by 26 (3 self)
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An imaging model provides a mathematical description of correspondence between points in a scene and in an image. The dominant imaging model, perspective projection, has long been used to describe traditional cameras as well as the human eye. We propose an imaging model which is flexible enough to represent an arbitrary imaging system. For example using this model we can describe systems using fisheye lenses or compound insect eyes, which violate the assumptions of perspective projection. By relaxing the requirements of perspective projection, we give imaging system designers greater freedom to explore systems which meet other requirements such as compact size and wide field of view. We formulate our model by noting that all imaging systems perform a mapping from incoming scene rays to photosensitive elements on the image detector. This mapping can be conveniently described using a set of virtual sensing elements called raxels. Raxels include geometric, radiometric and optical properties. We present a novel ray based calibration method that uses structured light patterns to extract the raxel parameters of an arbitrary imaging system. Experimental results for perspective as well as nonperspective imaging systems are included.
Learning General Optical Flow Subspaces for Egomotion Estimation and Detection of Motion Anomalies
"... This paper deals with estimation of dense optical flow and egomotion in a generalized imaging system by exploiting probabilistic linear subspace constraints on the flow. We deal with the extended motion of the imaging system through an environment that we assume to have some degree of statistical r ..."
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Cited by 14 (4 self)
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This paper deals with estimation of dense optical flow and egomotion in a generalized imaging system by exploiting probabilistic linear subspace constraints on the flow. We deal with the extended motion of the imaging system through an environment that we assume to have some degree of statistical regularity. For example, in autonomous ground vehicles the structure of the environment around the vehicle is far from arbitrary, and the depth at each pixel is often approximately constant. The subspace constraints hold not only for perspective cameras, but in fact for a very general class of imaging systems, including catadioptric and multipleview systems. Using minimal assumptions about the imaging system, we learn a probabilistic subspace constraint that captures the statistical regularity of the scene geometry relative to an imaging system. We propose an extension to probabilistic PCA (Tipping and Bishop, 1999) as a way to robustly learn this subspace from recorded imagery, and demonstrate its use in conjunction with a sparse optical flow algorithm. To deal with the sparseness of the input flow, we use a generative model to estimate the subspace using only the observed flow measurements. Additionally, to identify and cope with image regions that violate subspace constraints, such as moving objects, objects that violate the depth regularity, or gross flow estimation errors, we employ a perpixel Gaussian mixture outlier process. We demonstrate results of finding the optical flow subspaces and employing them to estimate dense flow and to recover camera motion for a variety of imaging systems in several different environments. 1.
Structure and Motion from Scene Registration
"... We propose a method for estimating the 3D structure and the dense 3D motion (scene flow) of a dynamic nonrigid 3D scene, using a camera array. The core idea is to use a dense multicamera array to construct a novel, dense 3D volumetric representation of the 3D space where each voxel holds an estimat ..."
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Cited by 10 (0 self)
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We propose a method for estimating the 3D structure and the dense 3D motion (scene flow) of a dynamic nonrigid 3D scene, using a camera array. The core idea is to use a dense multicamera array to construct a novel, dense 3D volumetric representation of the 3D space where each voxel holds an estimated intensity value and a confidence measure of this value. The problem of 3D structure and 3D motion estimation of a scene is thus reduced to a nonrigid registration of two volumes–hence the term ”Scene Registration”. Registering two dense 3D scalar volumes does not require recovering the 3D structure of the scene as a preprocessing step, nor does it require explicit reasoning about occlusions. From this nonrigid registration we accurately extract the 3D scene flow and the 3D structure of the scene, and successfully recover the sharp discontinuities in both time and space. We demonstrate the advantages of our method on a number of challenging synthetic and real data sets. 1.
S.B.: Plenoptic flow: Closedform visual odometry for light field cameras
 In: Proceedings, 2011 IEEE/RSJ international conference on intelligent robots and systems (IROS
, 2011
"... Abstract—Three closedform solutions are proposed for six degree of freedom (6DOF) visual odometry for light field cameras. The first approach breaks the problem into geometrically driven subproblems with solutions adaptable to specific applications, while the second generalizes methods from opti ..."
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Cited by 9 (7 self)
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Abstract—Three closedform solutions are proposed for six degree of freedom (6DOF) visual odometry for light field cameras. The first approach breaks the problem into geometrically driven subproblems with solutions adaptable to specific applications, while the second generalizes methods from optical flow to yield a more direct approach. The third solution integrates elements into a remarkably simple equation of plenoptic flow which is directly solved to estimate the camera’s motion. The proposed methods avoid feature extraction, operating instead on all measured pixels, and are therefore robust to noise. The solutions are closedform, computationally efficient, and operate in constant time regardless of scene complexity, making them suitable for realtime robotics applications. Results are shown for a simulated underwater survey scenario, and realworld results demonstrate good performance for a threecamera array, outperforming a stateoftheart stereo featuretracking approach. I.
Geolocalization using Skylines from OmniImages
"... We propose a novel method to accurately estimate the global position of a moving car using an omnidirectional camera and untextured 3D city models. The camera is oriented upwards to capture images of the immediate skyline, which is generally unique and serves as a fingerprint for a specific location ..."
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Cited by 8 (1 self)
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We propose a novel method to accurately estimate the global position of a moving car using an omnidirectional camera and untextured 3D city models. The camera is oriented upwards to capture images of the immediate skyline, which is generally unique and serves as a fingerprint for a specific location in a city. Our goal is to estimate global position by matching skylines extracted from omnidirectional images to skyline segments from coarse 3D city models. Our contributions include a sky segmentation algorithm for omnidirectional images using graph cuts and a novel approach for matching omniimage skylines to 3D models.
Eye Design in the Plenoptic Space of Light Rays
 In Proc. International Conference on Computer Vision
, 2003
"... Natural eye designs are optimized with regard to the tasks the eyecarrying organism has to perform for survival. This optimization has been performed by the process of natural evolution over many millions of years. Every eye captures a subset of the space of light rays. The information contained in ..."
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Cited by 3 (2 self)
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Natural eye designs are optimized with regard to the tasks the eyecarrying organism has to perform for survival. This optimization has been performed by the process of natural evolution over many millions of years. Every eye captures a subset of the space of light rays. The information contained in this subset and the accuracy to which the eye can extract the necessary information determines an upper limit on how well an organism can perform a given task. In this work we propose a new methodology for camera design. By interpreting eyes as sample patterns in light ray space we can phrase the problem of eye design in a signal processing framework. This allows us to develop mathematical criteria for optimal eye design, which in turn enables us to build the best eye for a given task without the trial and error phase of natural evolution. The principle is evaluated on the task of 3D egomotion estimation.
A hierarchy of cameras for 3D photography
 COMPUTER VISION AND IMAGE UNDERSTANDING
, 2004
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Minimal Solutions for Generic Imaging Models
"... A generic imaging model refers to a nonparametric camera model where every camera is treated as a set of unconstrained projection rays. Calibration would simply be a method to map the projection rays to image pixels; such a mapping can be computed using plane based calibration grids. However, exist ..."
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Cited by 2 (0 self)
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A generic imaging model refers to a nonparametric camera model where every camera is treated as a set of unconstrained projection rays. Calibration would simply be a method to map the projection rays to image pixels; such a mapping can be computed using plane based calibration grids. However, existing algorithms for generic calibration use more point correspondences than the theoretical minimum. It has been wellestablished that nonminimal solutions for calibration and structurefrommotion algorithms are generally noiseprone compared to minimal solutions. In this work we derive minimal solutions for generic calibration algorithms. Our algorithms for generally central cameras use 4 point correspondences in three calibration grids to compute the motion between the grids. Using simulations we show that our minimal solutions are more robust to noise compared to nonminimal solutions. We also show very accurate distortion correction results on fisheye images.