Bilinear Accelerated Filter Approximation

Josiah Manson and Scott Schaefer

Texas A&M University

Motivation

Trilinear Interpolation

Motivation

Optimized Combination of 2 Bilinear Samples

Mipmap Basis

Mipmap Basis

Mipmap Basis

Mipmap Basis

Mipmap Basis

Filter Approximation

Filter to Approximate

Filter Approximation

Bilinear Interpolation

Filter Approximation

Best fit using 4 samples

Cache Coherence

Cardinality-Constrained Texture Filtering

Cache Coherence

Bilinear Accelerated Filter Approximation

Freedom in Bilinear Samples

5 degrees of freedom + mipmap levels

Optimization

Optimization

Filter to approximate

Optimization

Filter to approximateBilinear combination of mipmap filters

Optimization

Filter to approximateBilinear combination of mipmap filtersBilinear parameters

Optimize

Optimization

Filter to approximateBilinear combination of mipmap filtersBilinear parametersRelative weights of bilinear probes

Optimize

Optimization

Filter to approximateBilinear combination of mipmap filtersBilinear parametersRelative weights of bilinear probesPoints in image

Optimize

Optimization

Filter to approximateBilinear combination of mipmap filtersBilinear parametersRelative weights of bilinear probesPoints in imageScale and translation of input filter

Optimize

Discretization of Domain

Discretization of Domain

4x4

Discretization of Domain

4x4x2

Coupled vs. Decoupled

Coupled vs. Decoupled

Coupled vs. Decoupled

Lanczos 2 Error w.r.t. Discretization

Lanczos 2 Error w.r.t. Discretization

Lanczos 2 Error w.r.t. Discretization

4x4x2

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

Symmetry of Domain

32 subdomains

Symmetry of Domain

16 subdomains

Symmetry of Domain

8 subdomains

Symmetry of Domain

6 subdomains

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 byteNumber of parameters and fetchesBits per linear fit of parameterInteger choice of texel/level

Uniform Scaling: Lanczos 2

Trilinear Interpolation

Uniform Scaling: Lanczos 2

Coupled Bilinear

Uniform Scaling: Lanczos 2

Decoupled Bilinear

Uniform Scaling: Lanczos 2

CCTF

3D Rotation: Lanczos 2

Coupled Bilinear

3D Rotation: Lanczos 2

Decoupled Bilinear

3D Rotation: Lanczos 2

CCTF

Speed in FPS

Conclusion

• Improved quality over trilinear interpolation

• Almost same quality as CCTF

• 2x faster than CCTF

• Decoupling samples removes constraints

• Small GPU lookup table

Lanczos 2 Error w.r.t. Discretization

Uniform Scaling: Lanczos 2

Exact Evaluation

2D Translation: Lanczos 2

Exact Evaluation

3D Rotation: Lanczos 2

Trilinear Interpolation

2D Translation: Lanczos 2

Trilinear Interpolation

Optimization

Cubic

Optimization

Cubic

Sextic!

Optimization

Cubic

Sextic!Levenberg-Marquardt

Optimization

Cubic

Sextic!Levenberg-Marquardt

X

Optimization

Cubic

Sextic!Levenberg-Marquardt

X

3D Plane: Lanczos 2

Trilinear Interpolation

3D Plane: Lanczos 2

Coupled Bilinear

3D Plane: Lanczos 2

Decoupled Bilinear

3D Plane: Lanczos 2

CCTF

2D Translation: Lanczos 2

Coupled Bilinear

2D Translation: Lanczos 2

Decoupled Bilinear

2D Translation: Lanczos 2

CCTF

Anisotropic Filtering

Anisotropic Filtering

Anisotropic Filtering

Anisotropic

Trilinear

Anisotropic

Trilinear Anisotropic

Anisotropic

Decoupled Anisotropic

Anisotropic

CCTF