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Understanding Aliasing in Computer Graphics: Sampling, Antialiasing, and Texture Mapping

This lecture explores the concept of aliasing in computer graphics, emphasizing the importance of dense sampling to accurately capture the essence of continuous images. It discusses the Nyquist Theorem, the conditions needed to prevent aliasing, and various antialiasing techniques such as prefiltering and postfiltering. The significance of filter shapes and sampling strategies are also examined. Additionally, the lecture delves into texture mapping, covering topics like UV mapping and different types of textures used in 3D graphics. The goal is to synthesize these concepts for effective computer graphic representations.

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Understanding Aliasing in Computer Graphics: Sampling, Antialiasing, and Texture Mapping

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Presentation Transcript

  1. CSC418 Computer Graphics • Aliasing • Texture mapping

  2. Aliasing The physical world is continuous… Computer representations of the physical world are often a discrete sampling of the continuous… “A pixel is a discrete sample of a continuous image” The question is : How densely do we need to sample something continuous to capture its essence accurately?

  3. Aliasing

  4. Aliasing Nyquist Theorem: Acontinuous signal can be completely recovered from its samples iff the sampling rate is greater than twice the maximum frequency present in the signal.

  5. Aliasing(examples)

  6. Aliasing(examples)

  7. Aliasing(examples)

  8. Aliasing In order to have any hope of accurately reconstructing a function from a periodically sampled version of it, two conditions must be satisfied: • The function must be bandlimited. • The sampling frequency must be at least twice the maximum frequency of the function. Satisfying these conditions will eliminate aliasing.

  9. Antialiasing • Prefiltering. • Postfiltering (supersampling).

  10. Antialiasing(prefiltering) What is prefiltering?

  11. Antialiasing(prefiltering) Prefiltering example

  12. Antialiasing(postfiltering) What is postfiltering? Given a sample frequency prefiltering computes a lower frequency signal from the continuous representation. Postfiltering first supersamples the signal in its unfiltered form and then filters out the high frequency from the supersamples.

  13. Antialiasing(postfiltering)

  14. Antialiasing(postfiltering)

  15. Antialiasing(postfiltering) How should one combine samples? Simply add? Weight average is better! Filter shape = weight values.

  16. Antialiasing(postfiltering) Filter shapes Gaussian Wide Gaussian

  17. Antialiasing(postfiltering) Is there an ideal filter shape? Box Sinc

  18. Antialiasing(postfiltering) How should one supersample?

  19. Texture mapping Photographic Textures

  20. Texture mapping Photographic Textures

  21. Texture mapping How does one establish correspondence? (UV mapping)

  22. Texture mapping Projective Textures

  23. Texture mapping 3D Textures

  24. Texture mapping Bump mapping

  25. Texture mapping Reflection mapping

  26. Next Lecture Putting it all back together….

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