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

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Presentation transcript:

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

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

Filter to approximate

Optimization Filter to approximate Bilinear combination of mipmap filters

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

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

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

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

Discretization of Domain

4x4

Discretization of Domain 4x4x2

Coupled vs. Decoupled

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* ) 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

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 Trilinear

Anisotropic Trilinear Anisotropic

Anisotropic Decoupled Anisotropic

Anisotropic CCTF