Image Synthesis

computer graphics & visualization

Image Synthesis

Interactive Terrain Synthesis

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Fractal Terrain Synthesis• Goals:– Generation of fractal terrain– Non-repetitive, infinite extent– Interactive frame rates– Real-time editable

• Methods– Rescale & Add on GPU

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Fractal terrain synthesis• Stochastic Fractals– „Statistical“ Self-Similarity (Stochastic Fractals)

• If blown up in scale, any part appears statistically similar to the whole

– Simulation of Fractal Brownian motion (FBm)• Movement of small particles of solid matter in liquid• Probability as a tool for modelling

– Modelling of (dynamic) natural phenomena• Terrains, clouds, water etc.

– Modelling and rendering of solid textures• Marble, wood etc.• Procedural shaders

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rescale-and-AddNoise synthesis by point evaluation – Summation of scaled and dilated noise functions

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rescale-and-AddAdd weighted noise octaves to simulate 1/f-noise– 1/f noise: as frequency increases, amplitude decreases

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computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rescale-and-AddAnother method to simulate 1/f-noise– Generate noisy copies on-the-fly from a base random

texture

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computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rescale-and-Add

H(x,y): synthesized height fieldF(x,y): basis function n: number of octaves

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rescale And Add• Basis function(s) F:

– Filtered white noise, Perlin noise, images, …– Affects basic appearance of terrain

• Reformulation yields more intuitive parameters:– r: roughness– l: lacunarity (fractal gap)– o: octaves

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rescale And Add - ParametersRoughness r

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rescale And Add - ParametersLacunarity l

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rescale And Add - ParametersOctaves o

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Multifractals and other tricks…Substitute basis function by convex combination:

with and

More editing possibilities,more realism• Add low frequency base geometry

– Edit basic terrain via base geometry– Edit appearance via basis functions– Close to spatial and frequency domain

editing paradigm

• Use „odd“ lacunarity / roughness like2.173482... breaks up repetitions

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yxyxi i ,1),( ii 0

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rotations & Translations• Warp domain with pseudo-random rotations:– Substitutes height field H(x,y) H( Rot(x,y)+T(x,y) )

• Some basic math involved. Key ideas:– Rotation and Translation depend on octave

Levels are warped against each other– Rotation and Translation depend on roughness

Emphasize or de-emphasize high roughness– Avoid sine / cosine computations

Rotation expressed via unit vector (no explicit angle) Entries are treated as cos(),sin()

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Rotations & Translations

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Domain Warping

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

GPU Implementation• Tileable textures– Basis functions– Weights for multifractal– Low frequency basis height field– Final height field

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Demo

computer graphics & visualization

Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Conclusion• Terrain visualization:

– Major challenge: data volume– GPU-friendly compression beyond S3TC needed– GPU-friendly geometry compression needed– In research…

• Terrain Synthesis:– So far, can achieve ~30fps– Faster soon due to improved vertex texture fetches– Powerful, interactive WYSIWYG editing tools

• Editing of basis functions makes sense, now– Future direction: fractal geotypical texture synthesis– Anti-aliasing for some cases still hard