1. Bilinear Accelerated Filter Approximation Josiah Manson and Scott Schaefer Texas A&M University

2. Motivation Trilinear Interpolation

3. Motivation Optimized Combination of 2 Bilinear Samples

4. Mipmap Basis

9. Filter Approximation Filter to Approximate

10. Filter Approximation Bilinear Interpolation

11. Filter Approximation Best fit using 4 samples

12. Cache Coherence Cardinality-Constrained Texture Filtering

13. Cache Coherence Bilinear Accelerated Filter Approximation

14. Freedom in Bilinear Samples 5 degrees of freedom + mipmap levels

15. Optimization

16. Filter to approximate

17. Optimization Filter to approximate Bilinear combination of mipmap filters

18. Optimization Filter to approximate Bilinear combination of mipmap filters Bilinear parameters Optimize

19. Optimization Filter to approximate Bilinear combination of mipmap filters Bilinear parameters Relative weights of bilinear probes Optimize

20. Optimization Filter to approximate Bilinear combination of mipmap filters Bilinear parameters Relative weights of bilinear probes Points in image Optimize

21. Optimization Filter to approximate Bilinear combination of mipmap filters Bilinear parameters Relative weights of bilinear probes Points in image Scale and translation of input filter Optimize

22. Discretization of Domain

23. 4x4

24. Discretization of Domain 4x4x2

25. Coupled vs. Decoupled

28. Lanczos 2 Error w.r.t. Discretization

30. 4x4x2

31. Error w.r.t. Filter Type at 4x4x2

32. Symmetry of Domain 32 subdomains

33. Symmetry of Domain 16 subdomains

34. Symmetry of Domain 8 subdomains

35. Symmetry of Domain 6 subdomains

36. Table Sizes 6/8 * 8*(4*16 + 4+4+2) 6/8 * (5*4*16 + 2*2) 6/8 * (5*4*16 + 2*(4+4+2)) CCTF: Coupled: Decoupled: = 444 bytes = 243 bytes = 255 bytes 6 subdomains, 8 bits per byte Number of parameters and fetches Bits per linear fit of parameter Integer choice of texel/level

37. Uniform Scaling: Lanczos 2 Trilinear Interpolation

38. Uniform Scaling: Lanczos 2 Coupled Bilinear

39. Uniform Scaling: Lanczos 2 Decoupled Bilinear

40. Uniform Scaling: Lanczos 2 CCTF

41. 3D Rotation: Lanczos 2 Coupled Bilinear

42. 3D Rotation: Lanczos 2 Decoupled Bilinear

43. 3D Rotation: Lanczos 2 CCTF

44. Speed in FPS

45. Conclusion Improved quality over trilinear interpolation Almost same quality as CCTF 2x faster than CCTF Decoupling samples removes constraints Small GPU lookup table

47. Lanczos 2 Error w.r.t. Discretization

48. Uniform Scaling: Lanczos 2 Exact Evaluation

49. 2D Translation: Lanczos 2 Exact Evaluation

50. 3D Rotation: Lanczos 2 Trilinear Interpolation

51. 2D Translation: Lanczos 2 Trilinear Interpolation

52. Optimization Cubic

53. Optimization Cubic Sextic!

54. Optimization Cubic Sextic! Levenberg-Marquardt

55. Optimization Cubic Sextic! Levenberg-Marquardt X

56. Optimization Cubic Sextic! Levenberg-Marquardt X

57. 3D Plane: Lanczos 2 Trilinear Interpolation

58. 3D Plane: Lanczos 2 Coupled Bilinear

59. 3D Plane: Lanczos 2 Decoupled Bilinear

60. 3D Plane: Lanczos 2 CCTF

61. 2D Translation: Lanczos 2 Coupled Bilinear

62. 2D Translation: Lanczos 2 Decoupled Bilinear

63. 2D Translation: Lanczos 2 CCTF

64. Anisotropic Filtering

67. Anisotropic Trilinear

68. Anisotropic Trilinear Anisotropic

69. Anisotropic Decoupled Anisotropic

70. Anisotropic CCTF