Results 1 - 10 of 21

Estimation of geometric entities and operators from uncertain data

by Christian Perwass, Christian Gebken, Gerald Sommer - In 27. Symposium für Mustererkennung, DAGM 2005, Wien, 29.8.- 2.9.005, number 3663 in LNCS , 2005
"... Abstract. In this text we show how points, point pairs, lines, planes, circles, spheres, and rotation, translation and dilation operators and their uncertainty can be evaluated from uncertain data in a unified manner using the Geometric Algebra of conformal space. This extends previous work by Först ..."
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Abstract. In this text we show how points, point pairs, lines, planes, circles, spheres, and rotation, translation and dilation operators and their uncertainty can be evaluated from uncertain data in a unified manner using the Geometric Algebra of conformal space. This extends previous work by Förstner et al. [3] from points, lines and planes to non-linear entities and operators, while keeping the linearity of the estimation method. We give a theoretical description of our approach and show the results of some synthetic experiments. 1
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PARITY SYMMETRY IN MULTI-DIMENSIONAL SIGNALS

by Gerald Sommer, Di Zang
"... Parity symmetry is an important local feature for qualitative signal analysis. It is strongly related to the local phase of the signal. In image processing parity symmetry is a cue for the line-like or edge-like quality of a local image structure. The analytic signal is a well-known representation ..."
Abstract - Cited by 7 (7 self) - Add to MetaCart
Parity symmetry is an important local feature for qualitative signal analysis. It is strongly related to the local phase of the signal. In image processing parity symmetry is a cue for the line-like or edge-like quality of a local image structure. The analytic signal is a well-known representation for 1D signals, which enables the extraction of local spectral representations as amplitude and phase. Its representation domain is that of the complex numbers. We will give an overview how the analytic signal can be generalized to the monogenic signal in the nD case within a Clifford valued domain. The approach is based on the Riesz transform as a generalization of the Hilbert transform with respect to the embedding dimension of the structure. So far we realized the extension to 2D and 3D signals. We learned to take advantage of interesting effects of the proposed generalization as the simultaneous estimation of the local amplitude, phase and orientation, and of image analysis in the monogenic scale-space.

Pose estimation of free-form surface models

by Bodo Rosenhahn, Christian Perwass, Gerald Sommer - In 25. Symposium für Mustererkennung, DAGM 2003 , 2003
"... Abstract. In this article we discuss the 2D-3D pose estimation problem of 3D free-form surface models. In our scenario we observe free-form surface models in an image of a calibrated camera. Pose estimation means to estimate the relative position and orientation of the 3D object to the reference cam ..."
Abstract - Cited by 5 (3 self) - Add to MetaCart
Abstract. In this article we discuss the 2D-3D pose estimation problem of 3D free-form surface models. In our scenario we observe free-form surface models in an image of a calibrated camera. Pose estimation means to estimate the relative position and orientation of the 3D object to the reference camera system. The object itself is modelled as a twoparametric surface model which is represented by Fourier descriptors. It enables a low-pass description of the surface model, which is advantageously applied to the pose problem. To achieve the combination of such a signal-based model within the geometry of the pose scenario, the conformal geometric algebra is used and applied. 1
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The inversion camera model

by Christian Perwass, Gerald Sommer - IN: 28. SYMPOSIUM FÜR MUSTERERKENNUNG, DAGM 2006 , 2006
"... In this paper a novel camera model, the inversion camera model, is introduced, which encompasses the standard pinhole camera model, an extension of the division model for lens distortion, and the model for catadioptric cameras with parabolic mirror. All these different camera types can be modeled by ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
In this paper a novel camera model, the inversion camera model, is introduced, which encompasses the standard pinhole camera model, an extension of the division model for lens distortion, and the model for catadioptric cameras with parabolic mirror. All these different camera types can be modeled by essentially varying two parameters. The feasibility of this camera model is presented in experiments where object pose, camera focal length and lens distortion are estimated simultaneously.
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Geometry and kinematics with uncertain data

by Christian Perwass, Christian Gebken, Gerald Sommer - 9TH EUROPEAN CONFERENCE ON COMPUTER VISION, ECCV 2006, MAY 2006 , 2006
"... Abstract. In Computer Vision applications, one usually has to work with uncertain data. It is therefore important to be able to deal with uncertain geometry and uncertain transformations in a uniform way. The Geometric Algebra of conformal space offers a unifying framework to treat not only geometri ..."
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Abstract. In Computer Vision applications, one usually has to work with uncertain data. It is therefore important to be able to deal with uncertain geometry and uncertain transformations in a uniform way. The Geometric Algebra of conformal space offers a unifying framework to treat not only geometric entities like points, lines, planes, circles and spheres, but also transformations like reflection, inversion, rotation and translation. In this text we show how the uncertainty of all elements of the Geometric Algebra of conformal space can be appropriately described by covariance matrices. In particular, it will be shown that it is advantageous to represent uncertain transformations in Geometric Algebra as compared to matrices. Other important results are a novel pose estimation approach, a uniform framework for geometric entity fitting and triangulation, the testing of uncertain tangentiality relations and the treatment of catadioptric cameras with parabolic mirrors within this framework. This extends previous work by Förstner and Heuel from points, lines and planes to non-linear geometric entities and transformations, while keeping the linearity of the estimation method. We give a theoretical description of our approach and show exemplary applications.
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Generative models for maneuvering target tracking

by Xin Fan, Guoliang Fan, Senior Member, Joseph P. Havlicek, Senior Member - IEEE Trans. on Aerospace and Electronics Systems , 2010
"... We consider the challenging problem of tracking highly maneuverable targets with unknown dynamics and introduce a new generative maneuvering target model (GMTM) that, for a rigid body target, explicitly estimates not only the kinematics, here considered as effect variables, but also the underlying c ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
We consider the challenging problem of tracking highly maneuverable targets with unknown dynamics and introduce a new generative maneuvering target model (GMTM) that, for a rigid body target, explicitly estimates not only the kinematics, here considered as effect variables, but also the underlying causative dynamic variables including forces and torques acting on the rigid body target in a Newtonian mechanics framework. We formulate relationships between the dynamic and kinematic state variables in a novel graphical model that naturally facilitates the feedback of physical constraints from the target kinematics to the maneuvering dynamics model in a probabilistic form, thereby achieving improved tracking accuracy and efficiency compared to competing techniques. We develop a sequential Monte Carlo (SMC) inference algorithm that is embedded with Markov chain Monte Carlo (MCMC) steps to generate probabilistic samples amenable to the feedback constraints. The proposed algorithm can estimate both maneuvering dynamics and target kinematics simultaneously. The robustness and efficacy of this approach are illustrated by experimental results obtained from noisy video sequences of both simulated and real maneuvering ground vehicles.
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Robot vision in the language of geometric algebra

by Gerald Sommer, Christian Gebken - Vision Systems: Applications
"... In recent years, robot vision became an attractive scientific discipline. From a technological point of view, its aim is to endow robots with visual capabilities comparable to those of human beings. Although there is considerable endeavour, the progress is only slowly proceeding, especially in compa ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
In recent years, robot vision became an attractive scientific discipline. From a technological point of view, its aim is to endow robots with visual capabilities comparable to those of human beings. Although there is considerable endeavour, the progress is only slowly proceeding, especially in comparison to the level of behavior of human
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Pose estimation from uncertain omnidirectional image data using line-plane correspondences

by Christian Gebken, Antti Tolvanen, Gerald Sommer - In 28. Symposium für Mustererkennung, DAGM 2006, Berlin, 12.9.-14.9.2006, number 4174 in LNCS , 2006
"... Abstract. Omnidirectional vision is highly beneficial for robot navigation. We present a novel perspective pose estimation for omnidirectional vision involving a parabolic central catadioptric sensor using line-plane correspondences. We incorporate an appropriate and approved stochastic method to de ..."
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Abstract. Omnidirectional vision is highly beneficial for robot navigation. We present a novel perspective pose estimation for omnidirectional vision involving a parabolic central catadioptric sensor using line-plane correspondences. We incorporate an appropriate and approved stochastic method to deal with uncertainties in the data. 1
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Engineering Graphics in Geometric Algebra

by Alyn Rockwood, Dietmar Hildenbrand
"... We illustrate the suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications. A number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics ..."
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We illustrate the suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications. A number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics such as vector algebra and vector fields, quaternions, kinematics and projective geometry, and it easily deals with geometric objects, operations and transformations. Not only are these properties important for computational engineering, but also for the computational point-of-view they provide. We also include the potential of geometric algebra for optimizations and highly efficient implementations.

Geometric Algebra Computers

by Dietmar Hildenbrand - GRAVISMA 2009 , 2009
"... Geometric algebra covers a lot of other mathematical systems like vector algebra, complex numbers, Plücker coordinates, quaternions etc. and it is geometrically intuitive to work with. Furthermore there is a lot of potential for optimization and parallelization. In this paper, we investigate compute ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Geometric algebra covers a lot of other mathematical systems like vector algebra, complex numbers, Plücker coordinates, quaternions etc. and it is geometrically intuitive to work with. Furthermore there is a lot of potential for optimization and parallelization. In this paper, we investigate computers suitable for geometric algebra algorithms. While these geometric algebra computers are working in parallel, the algorithms can be described on a high level without thinking about how to parallelize them. In this context two recent developments are important. On one hand, there is a recent development of geometric algebra to an easy handling of engineering applications, especially in computer graphics, computer vision and robotics. On the other hand, there is a recent development of computer platforms from single processors to parallel computing platforms which are able to handle the high dimensional multivectors of geometric algebra in a better way. We present our geometric algebra compilation approach for current and future hardware platforms like reconfigurable hardware, multi-core architectures as well as modern GPGPUs.