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Reconstruction and Visualization of Planetary Nebulae Authors: M. Magnor, G. Kindlmann, C. Hansen, N. Duric. Visualization II Instructor: Jessica Crouch. Problem. Would like to use 2D photographs to construct a 3D model of planetary nebulae (PNe)

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## Visualization II Instructor: Jessica Crouch

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**Reconstruction and Visualization of Planetary**NebulaeAuthors: M. Magnor, G. Kindlmann, C. Hansen, N. Duric Visualization II Instructor: Jessica Crouch**Problem**• Would like to use 2D photographs to construct a 3D model of planetary nebulae (PNe) • 3D model would allow fly-through and other dynamic visualizations • How do you build a 3D model from 2D data? • In general, insufficiently constrained problem**http://www.chiro.org/LINKS/WALLPAPER/AQUILA_PLANETARY_NEBULAE.JPG**http://www.chiro.org/LINKS/WALLPAPER/AQUILA_PLANETARY_NEBULAE.JPG**http://nssdc.gsfc.nasa.gov/photo_gallery/photogallery-astro-nebula.html**http://nssdc.gsfc.nasa.gov/photo_gallery/photogallery-astro-nebula.html**Motivation**• Education and entertainment of the public • Visualization can be the fastest way to the “oooo”, “ahhh” • Science is interesting, important, beautiful • Good PR helps with funding… • Facilitate scientific exploration by astrophysicists • See the gas distributions predicted by different models • Compare model images to real images**Motivation**• Prior work on 3D PNe visualization has focused on visualizing scientific models produced by astronomers • Need a method to get 3D visualizations from observational data (telescope photographs)**Methods: Overview**• This is an inverse volume rendering problem • Instead of developing a method to create an image of a volume, we need a method to create a volume from an image • An optimization approach is described • Guess the volume contents • Render the hypothetical volume • Compare the rendering to the photograph • Make a better guess for the volume that (hopefully) reduces the difference between the rendering and the photograph • Repeat Until the photograph and rendered image match or other termination criteria are met**PNe Model**• How do you make a reasonable guess about the contents of the volume? • Pick random values? • Use everything you know about the structure of the volume to reduce the complexity of the problem • Constrained Inverse Volume Rendering (CIVR) • The more correct constraints you apply, the faster your optimization will converge**PNe Model**• What is known about the structure of PNe? • Axisymmetric • Rotationally symmetric about an axis • Every slice through the volume that passes through the axis shows the same data = Only need to guess the contents of a slice Reconstruct the volume by rotating the slice around the axis**Model Justification**• Empirical evidence: • Different shapes visible in photographs, all reasonably explained by different projections of axisymmetric volumes**Model Justification**• Why are PNe axisymmetric? • Interacting solar wind theory: • Old gas collected around equator • High volume of new gas is deflected away from equator out toward poles**Photo-Ionization**• Wind blows off PNe surface (predominantly hydrogen) • Atoms are ionized by UV photons • As ions and electrons recombine to form stable atoms they transition from a high energy state to successively lower energy states • Each transition involves emission of a photon of a specific wavelength of light • Result: we see different colors**Rendering Model**• PNe photo-ionization creates light that travels out into space unhindered • Model volume as completely emmissive • Each voxel generate a certain amount of light in each wavelength • Light is not attenuated as it travels through the volume • Rendered color is integral of all emmissions along a ray**Rendering Algorithm**• How many times must be the model be rendered before convergence? • Estimate: 106 • How long will it take to do that many volume renderings? • Rendering efficiency is critical**Rendering Algorithm**• Use GPU processing: • Load 2D density map as texture image • Create a series of texture mapped viewport-filling parallel quadrilaterals • Automatically generate Cartesian texture coordinates for the quads • Use a fragment shader program to convert Cartesian (u,v,t) coordinates to cylindrical (theta, h, r) coordinates • Accumulate (add) the color contributions of each quad to get the final image - Axis directions on texture map correspond to height & radius of axisymmetric volume**Rendering Algorithm**• Hardware supported texture mapping approach is much faster than ray casting • Could be parallelized. How? • 10 fps for 128 x 128 x128 with an nVidia GeForce FX 3000 graphics card**Error Function**• Optimization functions try to pick a set of input parameters that minimize the value returned by the error function • If the rendered image closely matches the photograph, the error function should return a small value • If the rendered image poorly matches the photograph, the error function should return a large value**Error Function: SSD**• Sum of Squared Differences (SSD) • Very commonly used to gauge image similarity • Subtract image A from image B to get the difference image • Square the difference image’s pixel values, and sum over the whole image • SSD = 0 iff the images are identical • Additional error penalty for negative emmision values**Optimization Algorithm**• Initial guess: • Density map = 0 everywhere • PN center is guessed based on brightest spot in the photograph • Axis orientation is guessed based on first eigenvector of photograph • Intuition: First eigenvector will be parallel to the primary swath of brightness • Guess for axis inclination toward earth is 0.**Optimization Algorithm**• Given: • A guess for the density map • A guess for the axis direction (2 angles) • A rendering algorithm • An error metric (objective function) • How do you intelligently improve your guess? • Specifically, how do you make a guess that reduces the SSD?**Powell’s Optimization Method**• A conjugate gradient optimization algorithm • Famous, widely used • In Numerical Recipes in C • Requires evaluation of the gradient of the error function • Since we don’t have an analytical representation of the error function, the derivatives must be evaluated numerically • For each model input parameter, evaluate for (parameter +Δ) and (parameter - Δ) . • Use central difference formula to estimate the error derivative**Powell’s Optimization Method**• Try to take steps “downhill” on the error function • You find local minima, if it works**Optimization Efficiency**• How does the resolution of the image impact the number of frames that must be volume rendered? • How many parameters must be differentiated at each optimization iteration? • Further improvement in efficiency: • Take a multi-scale approach • Compute the best coarse image • After coarse image converges, up-sample and optimize for a higher resolution • Paper indicates 4 level density map pyramid: 16 x 4 image 32 x 8 image 64 x 16 image 128 x 32 image Higher resolution model would require less noisy photographic data to produce a meaningful result. Earth’s atmospheric turbulence contributes to noise. Run time: 1 Day**Optimize Per Color (Per Element)**• Results were generated for separate images of the hydrogen, oxygen, and nitrogen/sulfur gasses • Whole optimization process is repeated for each element type • Final result is the sum of the three optimized volumes**Evaluation: Results for 3 PNe**• Left: Photograph Right: Model viz.**Evaluation: Results for 3 PNe**• 2 new views**Evaluation: Results for 3 PNe**• Left: Photograph Right: Model viz.**Evaluation: Results for 3 PNe**• 2 new views**Evaluation: Results for 3 PNe**• Left: Photograph Right: Model viz.**Evaluation: Results for 3 PNe**• 2 new views**Final Visualization**• Typical rendering methods can be applied to reconstructed volume • Iso-surfaces, etc.**Evaluation: Error Visualization**• Local contrast image**Evaluation**• No data exists for the actual PNe gas distribution • Can only evaluate for real PNe by demonstrating image match • Is this a reliable way to evaluate the method?**Evaluation**• Method can be validated more rigorously when synthetic data is input • Develop a artificial axisymmetric volume • Render to create one image • Apply reconstruction algorithm to rendered image, and see how well the reconstructed volume matches the artifical volume**Evaluation**• Performance is tied to axis inclination angle • Works well from 90º (perpendicular) to 40º inclination • Problem is too ill-defined from 0º-40º • At 0º the axis is parallel to the view direction • Authors report the reconstructed density values for the synthetic data fall within the “optimization routine’s preset termination error threshold.” • Would be nice to know what this is, and get a sense for the magnitude of the error in the reconstruction**Conclusion**• Nice results for a difficult problem • Validation is nicely done, as thorough as possible given the nature of the problem • Pretty slow, but ok for an off-line solution • Better resolution would be nice: • Paper gives 256 x 256 images of something that has a diameter of 1 light year = 5.9 trillion miles • Must be missing important detail • Authors note that ignoring light absorption by dust causes error in some situations**Discussion Questions**What changes would be necessary to account for light absorption by dust? What effect would they have on computational complexity?

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