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Kiel, Germany

Fleischmann O.,University of Kiel | Wietzke L.,Raytrix GmbH | Sommer G.,University of Kiel
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

We propose a novel curvature estimation algorithm which is capable of estimating the curvature of digital curves and two-dimensional curved image structures. The algorithm is based on the conformal projection of the curve or image signal to the two-sphere. Due to the geometric structure of the embedded signal the curvature may be estimated in terms of first order partial derivatives in ℝ3. This structure allows us to obtain the curvature by just convolving the projected signal with the appropriate kernels. We show that the method performs an implicit plane fitting by convolving the projected signals with the derivative kernels. Since the algorithm is based on convolutions its implementation is straightforward for digital curves as well as images. We compare the proposed method with differential geometric curvature estimators. It turns out that the novel estimator is as accurate as the standard differential geometric methods in synthetic as well as real and noise perturbed environments. © 2010 Springer-Verlag.

Wietzke L.,Raytrix GmbH | Sommer G.,University of Kiel
Journal of Mathematical Imaging and Vision | Year: 2010

This work covers a fundamental problem of local phase based image analysis: the isotropic generalization of the classical 1D analytic signal to two dimensions. The analytic signal enables the analysis of local phase and amplitude information of 1D signals. Local phase, amplitude and additional orientation information can be extracted by the 2D monogenic signal with the restriction to intrinsically 1D signals. In case of 2D image signals the monogenic signal enables the rotationally invariant analysis of lines and edges. In this work we present the 2D analytic signal as a novel generalization of both the analytic signal and the 2D monogenic signal. In case of 2D image signals the 2D analytic signal enables the isotropic analysis of lines, edges, corners and junctions in one unified framework. Furthermore, we show that 2D signals are defined on a 3D projective subspace of the homogeneous conformal space which delivers a descriptive geometric interpretation of signals providing new insights on the relation of geometry and 2D image signals. Finally, we will introduce a novel algebraic signal representation, which can be regarded as an alternative and fully isomorphic representation to classical matrices and tensors. We will show the solution of isotropic intrinsically 2D image analysis without the need of steering techniques. © Springer Science+Business Media, LLC 2010.

Wietzke L.,Raytrix GmbH | Fleischmann O.,University of Kiel | Sedlazeck A.,University of Kiel | Sommer G.,University of Kiel
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

This work presents the isotropic and orthogonal decomposition of 2D signals into local geometrical and structural components. We will present the solution for 2D image signals in four steps: signal modeling in scale space, signal extension by higher order generalized Hilbert transforms, signal representation in classical matrix form, followed by the most important step, in which the matrix-valued signal will be mapped to a so called multivector. We will show that this novel multivector-valued signal representation is an interesting space for complete geometrical and structural signal analysis. In practical computer vision applications lines, edges, corners, and junctions as well as local texture patterns can be analyzed in one unified algebraic framework. Our novel approach will be applied to parameter-free multilayer decomposition. © 2010 Springer-Verlag.

Damghanian M.,Mid Sweden University | Olsson R.,Mid Sweden University | Sjostrom M.,Mid Sweden University | Erdmann A.,Raytrix GmbH | Perwass C.,Raytrix GmbH
2014 IEEE International Conference on Image Processing, ICIP 2014 | Year: 2014

Evaluation of the state of the art plenoptic cameras is necessary for design and application purposes. In this work, spatial resolution is investigated in a multi-focus plenoptic camera using two approaches: empirical and model-based. The Raytrix R29 plenoptic camera is studied which utilizes three types of micro lenses with different focal lengths in a hexagonal array structure to increase the depth of field. The modelbased approach utilizes the previously proposed sampling pattern cube (SPC) model for representation and evaluation of the plenoptic capturing systems. For the experimental resolution measurements, spatial resolution values are extracted from images reconstructed by the provided Raytrix reconstruction method. Both the measurement and the SPC model based approaches demonstrate a gradual variation of the resolution values in a wide depth range for the multi focus R29 camera. Moreover, the good agreement between the results from the model-based approach and those from the empirical approach confirms suitability of the SPC model in evaluating high-level camera parameters such as the spatial resolution in a complex capturing system as R29 multi-focus plenoptic camera. © 2014 IEEE.

Perwass C.,Raytrix GmbH | Wietzke L.,Raytrix GmbH
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2012

Placing a micro lens array in front of an image sensor transforms a normal camera into a single lens 3D camera, which also allows the user to change the focus and the point of view after a picture has been taken. While the concept of such plenoptic cameras is known since 1908, only recently the increased computing power of low-cost hardware and the advances in micro lens array production, have made the application of plenoptic cameras feasible. This text presents a detailed analysis of plenoptic cameras as well as introducing a new type of plenoptic camera with an extended depth of field and a maximal effective resolution of up to a quarter of the sensor resolution. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

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