1. Convolution (FFT) Bloom
David Hill
Principal Mathematician
Epic Games
5/25/2017

2. Bloom: Why Invest?
A convincing bloom adds subtle but impactful physically motivated effect. Currently feasible on today’s high end hardware..
Adapt film / offline approach for use in real time
Additional realism with highly detailed effects
Provide ability to customize the camera / eye response
Target Cinematics and High End hardware

3. Bloom As Weak Scattering
Weak Scattering: Some Causes
Haze
Car Windshield (mine is always a little dirty)
Eyelash Diffraction
Inner-Camera Effects
Fraunhofer Diffraction
Physically-Based Glare Effects for Digital Images (1995, Spencer et al)
Glare Generation Based on Wave Optics (2004, Kakimoto et al, Computer Graphics Forum)

4. Bloom As Weak Scattering
A single pin point remains mostly focused
Model Assumptions:
Every point of light is scattered the same
For most sources the scattered amount is imperceptible
The scattering from bright sources creates “bloom”
In Camera scattering of a point

5. Bloom: Standard Game-Style
Weak Scattering
Sum of Gaussian Filter
Image down-sampled multiple times and Gaussian Blur applied
Resulting images are summed and added to original
Every pixel scatters light in a symmetric way to its neighbors
Very Fast!
But...
Standard Bloom in UE4: Recommended for game use

6. Bloom As Weak Scattering
The camera response to a single bright source:
Close Up of center
Center pixel about 10,000 times brighter than any other point in this .exr
Camera scattering of point
Appears to be a very small star
Full image, adjusted contrast
Detail extents far across image!

7. Bloom Scatter As Gather: Convolution
View this as a weighted sum, here in one dimension :
Original Value
Filtered Value
Filter
Each Pixel Scatters to all the others according to the filter.
For Example, simple smoothing

8. Bloom Scatter As Gather: Convolution
Every point is weighted sum of all other points
N points gather from all N points. O(N^2)
We need a faster way! -> FFT

9. Bloom Scatter As Gather: Convolution
Convolution With Fast Fourier Transform:
Image_Frequencies = FFT(Image)
Filter_Frequencies = FFT(Filter)
Convolved_Frequencies = Image_Frequencies x Filter_Freqencies
Convolved_Image = InverseFFT(Convolved_Frequencies)

10. Bloom: Why FFT Convolution?
Better Scaling
FFT from signal to frequencies - O(N Log N)
Convolution in frequency space - O(N)
FFT from frequencies to signal - O(N Log N)
Overall Scaling O(N Log N)
For our purposes, the Fast Fourier Transform (FFT) is an acceleration technique for convolution.

11. Bloom: What is Fourier Transform?
Any finite length signal can be expresses as a sum of sines and cosines
Signal Amplitude of each frequency Sine & Cos
Inverse computes amplitudes of each frequency
Low-Pass filter: only used first few V_k

12. Bloom: Fast Fourier Transform?
Sines and Cosines have symmetries that can be exploited speeding the transform
Split the sum into even and odd terms, and symmetry saves work!
Now recurse, each small transform (Even, Odd) and be treated as new transforms
And subdivided. Due to this splitting FFT does best with power_2 signals.

13. Bloom : Parallel FFT for GPU
GPU: Highly parallel, but with thread-communication limitations.
Similar restriction are found in supercomputing architectures.
Stockham Formulation: Parallel formulation
Used for Vector Computers (1987 D Baily, Journal of Supercomputer Applications)
Applied to GPUs (2008 Govindaraju, Proceedings of ACM/IEEE on Supercomputing)
Our implementation largely follow this
Each Scanline
Transformed independently
Assigned to a thread group with group shared memory

14. Bloom: Compute Shaders
FFT implemented as compute shaders
Pass
Forward Horizontal Transform
Uses 2-for-1 trick to transform (r,g) and (b,a)
Forward Vertical Transform
Convolution, i.e. Multiply, with cached pre-transformed Kernel
Inverse Vertical Transform
Inverse Horizontal Transform
Inverts 2-for-1 trick
From GPUVisualizer