Master's Thesis - Studierstube Augmented Reality Project - Graz ...

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2.1 Technical Visualization Figure 2.12: A visualization taxonomy and therefore some possibilities for datasets as described in chapter 3. The combination of morphological and physiological MRI data requires both; a tissue and a flow visualization technique. Ray casted and isovalue triangulated images of the heart on the left from [Kerwin2007]; Images of spot noise and 3D-texture advected Tornado dataset from [Weiskopf2007]; stream balls-image from [Brill1994]; critical points from [Frits1993]; field topologies on the left from [Tricoche2004]. The rest of the shown images are based on results from this work and prior achieved ones from [Reiter2006]. 22
2.1 Technical Visualization Visualizing glyphs, arrows and color maps are based on rendering of simple geometrical structures at each point of the grid. Therefore these techniques do not need further explanations. The next step will be to make a definition of particle movements in steady or unsteady flows. Related trajectories can be calculated by different approaches. This thesis concentrates on discrete particle injection methods and finite differences approximations. Texture based advection techniques which are based on Lagrangian approaches were not implemented. ∂x ∂t = v(x(t), τ), x(t 0) = x 0 , x : R → R n (2.1) denotes the continuous movement of a massless particle under the influence of a even varying vector field, [Kipfer2004; Krueger2005; Weiskopf2007]. v describes a sampled vector field whose sampled values depend on the current position of an particle x(t). In the case of a time varying vector field, which equals unsteady flow, τ serves as parameterization of the time. Together with the initial condition x(t 0 ) this differential equation is complete. Keeping in mind that the measurement method from chapter 3 produces a vector field defined on a regular spaced lattice and that general programming approaches cannot solve differential equations in complete form, numerical integration methods have to be used. The simplest form to solve the initial value problem 2.1 numerically is the standard explicit Euler-approach [Euler1768]. Choosing a discretization step size ∆t = h > 0 for t k+1 = t k + h, (2.2) leads to an approximation for the exact solution of x k+1 = x k + hv(x k , t k , τ). (2.3) The accuracy depends on the selected step size ∆t which is indirect proportional to the computational costs for the same length of a certain trajectory. To reduce the integration error or the computation effort of the former described numerical solution, several correction mechanisms can be added. One example is the well known Runge-Kutta method [Runge1895; Kutta1901] of a certain order [Albrecht1996; 23
Page 1 and 2: Master’s Thesis Quantitative Meas
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Page 7 and 8: CONTENTS 4.2.2 Noise Suppression .
Page 9 and 10: Chapter 1 Introduction Assessment o
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Chapter 5 Implementation This chapt
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5.2 iMEDgine extensions Figure 5.1:
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5.2 iMEDgine extensions which eases
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5.2 iMEDgine extensions solution fu
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5.2 iMEDgine extensions 23 cam_posi
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5.2 iMEDgine extensions Figure 5.4:
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5.2 iMEDgine extensions • SoSFStr
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5.2 iMEDgine extensions 6 Z=" -238.
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5.3 Visualization nodes and subgrap
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Chapter 6 Experiments Several atten
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6.3 Results 6.3 Results To complete
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6.4 Scalability activity. The highe
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6.4 Scalability (a) Stream lines fo
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6.4 Scalability (a) Stream tubes ap
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6.4 Scalability Figure 6.10: Compar
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Chapter 7 Future Work This chapter
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7.3 Derived Magnitudes possibilitie
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7.5 Clinical Evaluations (a) Stereo
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Beside the improvement of known spa
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Appendix A Intermediate File Format
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A.2 Data Files Offset Name Type Des
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This chapter supplements chapter 5
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143 Figure B.3: An thinned out UML
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Figure B.5: This UML class diagram
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Glossary Notation bipolar gradient
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Glossary Notation Description MIP M
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Glossary Notation Description shade
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LIST OF FIGURES 3.5 The slice-profi
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List of Tables 2.1 CPU - GPU analog
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REFERENCES [Brill1994] M. Brill, W.
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REFERENCES [iMedgine2006] T. Gross,
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REFERENCES [Kniss2002a] Joe Kniss,
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REFERENCES [Markl2003] Michael Mark
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REFERENCES [Roth1982] Scott D. Roth
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REFERENCES [Vivek1999] andAlexPang
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INDEX flow data, 135 format definit
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