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233
Catadioptric Omnidirectional Camera,”
- Proc. IEEE Conf. on Comp. Vis. Patt. Recog.,
, 1997
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A Theory of Single-Viewpoint Catadioptric Image Formation
- International Journal of Computer Vision
, 1999
"... Conventional video cameras have limited fields of view which make them restrictive for certain applications in computational vision. A catadioptric sensor uses a combination of lenses and mirrors placed in a carefully arranged configuration to capture a much wider field of view. One important design ..."
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Cited by 236 (12 self)
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Conventional video cameras have limited fields of view which make them restrictive for certain applications in computational vision. A catadioptric sensor uses a combination of lenses and mirrors placed in a carefully arranged configuration to capture a much wider field of view. One important design goal for catadioptric sensors is choosing the shapes of the mirrors in a way that ensures that the complete catadioptric system has a single effective viewpoint. The reason a single viewpoint is so desirable is that it is a requirement for the generation of pure perspective images from the sensed images. In this paper, we derive the complete class of single-lens single-mirror catadioptric sensors that have a single viewpoint. We describe all of the solutions in detail, including the degenerate ones, with reference to many of the catadioptric systems that have been proposed in the literature. In addition, we derive a simple expression for the spatial resolution of a catadioptric sensor in te...
Vision-based Navigation and Environmental Representations with an Omni-d-d Camera
- IEEE Transactions on Robotics and Automation
, 2000
"... This paper proposes a method for the visual-based navigation of a mobile robot in indoor environments, using a single omni-directional (catadioptric) camera. The geometry of the catadioptric sensor and the method used to obtain a bird's eye (orthographic) view of the ground plane are presented. ..."
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Cited by 123 (17 self)
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This paper proposes a method for the visual-based navigation of a mobile robot in indoor environments, using a single omni-directional (catadioptric) camera. The geometry of the catadioptric sensor and the method used to obtain a bird's eye (orthographic) view of the ground plane are presented. This representation significantly simplifies the so to navigation protiok by eliminating any perspective effects. The nature of each navigation task is taken into account when designing the required navigation skills and environmental representation. We propose two main navigation mo dalities: Topological Navigation and Visual Path Following. To po lok Navigatio is used fo traveling lo distances and do es no require knowledge of the exact position of the robot but rather, a qualitative position of the took map. The navigation process combines appearance based methods and visual servorv up oso environmental features. Visual Path Following is required for local, very precise navigation fo e.g.do o traversal,do cking. The robot is contro to fo w a pre-specified p...
A general imaging model and a method for finding its parameters
- In Proc. ICCV
, 2001
"... Linear perspective projection has served as the dominant imaging model in computer vision. Recent developments in image sensing make the perspective model highly restrictive. This paper presents a general imaging model that can be used to represent an arbitrary imaging system. It is observed that al ..."
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Cited by 117 (3 self)
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Linear perspective projection has served as the dominant imaging model in computer vision. Recent developments in image sensing make the perspective model highly restrictive. This paper presents a general imaging model that can be used to represent an arbitrary imaging system. It is observed that all imaging systems perform a mapping from incoming scene rays to photo-sensitive 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 calibration method that uses structured light patterns to extract the raxel parameters of an arbitrary imaging system. Experimental results for perspective as well as non-perspective imaging systems are included. 1
Catadioptric Projective Geometry
- INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2001
"... Catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera. Central catadioptric sensors are the class of these devices having a single effective viewpoint. In this paper, we propose a unifying model for the projective geometry induced by ..."
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Cited by 116 (16 self)
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Catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera. Central catadioptric sensors are the class of these devices having a single effective viewpoint. In this paper, we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications. We show that a central catadioptric projection is equivalent to a two-step mapping via the sphere. The second step is equivalent to a stereographic projection in the case of parabolic mirrors. Conventional lens-based perspective cameras are also central catadioptric devices with a virtual planar mirror and are, thus, covered by the unifying model. We prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images (conics). It turns out that planar and parabolic mirrors build a dual catadioptric projection pair. As a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system.
Geometric Properties of Central Catadioptric Line Images and their Application in Calibration
- IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—In central catadioptric systems, lines in a scene are projected to conic curves in the image. This work studies the geometry of the central catadioptric projection of lines and its use in calibration. It is shown that the conic curves where the lines are mapped possess several projective in ..."
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Cited by 80 (9 self)
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Abstract—In central catadioptric systems, lines in a scene are projected to conic curves in the image. This work studies the geometry of the central catadioptric projection of lines and its use in calibration. It is shown that the conic curves where the lines are mapped possess several projective invariant properties. From these properties, it follows that any central catadioptric system can be fully calibrated from an image of three or more lines. The image of the absolute conic, the relative pose between the camera and the mirror, and the shape of the reflective surface can be recovered using a geometric construction based on the conic loci where the lines are projected. This result is valid for any central catadioptric system and generalizes previous results for paracatadioptric sensors. Moreover, it is proven that systems with a hyperbolic/elliptical mirror can be calibrated from the image of two lines. If both the shape and the pose of the mirror are known, then two line images are enough to determine the image of the absolute conic encoding the camera’s intrinsic parameters. The sensitivity to errors is evaluated and the approach is used to calibrate a real camera. Index Terms—Catadioptric, omnidirectional vision, projective geometry, lines, calibration. 1
Omni-directional vision for robot navigation
- In Proc. IEEE Workshop on Omnidirectional Vision, South
, 2000
"... We describe a method for visual based robot navigation with a single omni-directional (catadioptric) camera. We show how omni-directional images can be used to generate the representations needed for two main navigation modalities: Topological Navigation and Visual Path Following. Topological Naviga ..."
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Cited by 71 (9 self)
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We describe a method for visual based robot navigation with a single omni-directional (catadioptric) camera. We show how omni-directional images can be used to generate the representations needed for two main navigation modalities: Topological Navigation and Visual Path Following. Topological Navigation relies on the robot’s qualitative global position, estimated from a set of omni-directional images obtained during a training stage (compressed using PCA). To deal with illumination changes, an eigenspace approximation to the Hausdorff measure is exploited. We present a method to transform omni-directional images to Bird’s Eye Views that correspond to scaled orthographic views of the ground plane. These images are used to locally control the orientation of the robot, through visual servoing. Visual Path Following is used to accurately control the robot along a prescribed trajectory, by using bird’s eye views to track landmarks on the ground plane. Due to the simplified geometry of these images, the robot’s pose can be estimated easily and used for accurate trajectory following. Omni-directional images facilitate landmark based navigation, since landmarks remain visible in all images, as opposed to a small field-of-view standard camera. Also, omni-directional images provide the means of having adequate representations to support both accurate or qualitative navigation. Results are described in the paper. 1.
Modeling Focus of Attention for Meeting Indexing Based on Multiple Cues
- IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2002
"... A user's focus of attention plays an important role in human--computer interaction applications, such as a ubiquitous computing environment and intelligent space, where the user's goal and intent have to be continuously monitored. In this paper, we are interested in modeling people's ..."
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Cited by 69 (8 self)
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A user's focus of attention plays an important role in human--computer interaction applications, such as a ubiquitous computing environment and intelligent space, where the user's goal and intent have to be continuously monitored. In this paper, we are interested in modeling people's focus of attention in a meeting situation. We propose to model participants' focus of attention from multiple cues. We have developed a system to estimate participants' focus of attention from gaze directions and sound sources. We employ an omnidirectional camera to simultaneously track participants' faces around a meeting table and use neural networks to estimate their head poses. In addition, we use microphones to detect who is speaking. The system predicts participants' focus of attention from acoustic and visual information separately. The system then combines the output of the audioand video-based focus of attention predictors. We have evaluated the system using the data from three recorded meetings. The acoustic information has provided 8% relative error reduction on average compared to only using one modality. The focus of attention model can be used as an index for a multimedia meeting record. It can also be used for analyzing a meeting.
Caustics of Catadioptric Cameras
- In Proc. International Conference on Computer Vision
, 2001
"... Conventional vision systems and algorithms assume the camera to have a single viewpoint. However, sensors need not always maintain a single viewpoint. For instance, an incorrectly aligned system could cause non-single viewpoints. Also, systems could be designed to specifically deviate from a single ..."
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Cited by 62 (10 self)
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Conventional vision systems and algorithms assume the camera to have a single viewpoint. However, sensors need not always maintain a single viewpoint. For instance, an incorrectly aligned system could cause non-single viewpoints. Also, systems could be designed to specifically deviate from a single viewpoint to trade-off image characteristics such as resolution and field of view. In these cases, the locus of viewpoints forms what is called a caustic. In this paper, we present an in-depth analysis of caustics of catadioptric cameras with conic reflectors. Properties of caustics with respect to field of view and resolution are presented. Finally, we present ways to calibrate conic catadioptric systems and estimate their caustics from known camera motion.
A flexible technique for accurate omnidirectional camera calibration and structure from motion
- In Proc. of IEEE Intl. Conf. of Vision Systems
, 2006
"... In this paper, we present a flexible new technique for single viewpoint omnidirectional camera calibration. The proposed method only requires the camera to observe a planar pattern shown at a few different orientations. Either the camera or the planar pattern can be freely moved. No a priori knowled ..."
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Cited by 60 (12 self)
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In this paper, we present a flexible new technique for single viewpoint omnidirectional camera calibration. The proposed method only requires the camera to observe a planar pattern shown at a few different orientations. Either the camera or the planar pattern can be freely moved. No a priori knowledge of the motion is required, nor a specific model of the omnidirectional sensor. The only assumption is that the image projection function can be described by a Taylor series expansion whose coefficients are estimated by solving a two-step least-squares linear minimization problem. To test the proposed technique, we calibrated a panoramic camera having a field of view greater than 200° in the vertical direction, and we obtained very good results. To investigate the accuracy of the calibration, we also used the estimated omni-camera model in a structure from motion experiment. We obtained a 3D metric reconstruction of a scene from two highly distorted omnidirectional images by using image correspondences only. Compared with classical techniques, which rely on a specific parametric model of the omnidirectional camera, the proposed procedure is independent of the sensor, easy to use, and flexible. 1.
