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ProxImaL: Efficient Image Optimization
using Proximal Algorithms
Steven Diamond1Felix Heide1,2
Wolfgang Heidrich3,2 Gordon Wetzstein1
2University of British Columbia 3KAUST1Stanford University
www.proximal-lang.org
Matthias Nießner1 Jonathan Ragan-Kelley1
Low-Light Burst
Imaging
Pelican Color
Array
Interlaced HDR
and RGB-IR
Light.co Array
Camera Kinect ToF Depth
Imaging
Formal Optimization
Zoran and Weiss 2011 Levin et al. 2004
Krishnan and Szeliski 2011
Krishnan and Fergus 2009
Heide et al. 2015
Deconvolution Denoising Inpainting + Colorization Camera Image Processing
Schmidt et al. 2015 Chen et al. 2015
Demosaic Denoise
Bad Pixel
Correction
Image
Enhancing
Tone
Mapping
Lens
Correction
Black
Level
Metering
Formal Optimization
Image Processing Pipeline
Formal Optimization
Formal Optimization
Brooke et al. 1988 Grant and Boyd. 2014 Lofberg 2004
DSLs for convex optimization:
Formal Optimization
Brooke et al. 1988Grant and Boyd. 2014 Lofberg 2004
DSLs for convex optimization:
Infeasible for Imaging problems:
• Millions of Variables
• Large-Scale Operators
ProxImaL
ProxImaLAndroid HDR+First Frame
ProxImaL Code:
ProxImaLAndroid HDR+
Objective:
An example:
Proximal Code:
OriginalBlurredSubsampled
Translation “by Hand”:
Objective:
or:with either:
ADMM:
Objective:
or:with either:
100 sec 10 sec
Blurred
Blurred + Subsampled
Result
Ambiguous translations drastically
affect solver performance !
Translation “by Hand”:
Sum of “proxable” functions:
General Problem Representation:
• . are “proxable” penalty functions with the proximal operator:
are linear transforms on the unknowns.• .
Proximal algorithms:
• ADMM [Boyd 2011]
• Linearized ADMM [Boyd 2011]
• PC [Chambolle and Pock 2011]
• (HQS [Geman and Yang 1995])
Proximal Compiler:
Objective:
Algorithm Implementation:
Halide
Function Numpy [ms] Halide [ms]
sum_of_squares 246 42
dot product 97 16
subsample 356 73
grad 1188 95
conv 7791 121
warp 458 153
norm1 202 27
group_norm1 1037 68
FFT 23 9
Runtime of TV-Deconvolution:
Runtime of TV-Deconvolution:
Applications:
Demosaicking Interlaced HDR Low-Light Burst
Imaging
Poisson
Deconvolution
Phase
Retrieval
Applications:
Demosaicking Interlaced HDR Low-Light Burst
Imaging
Poisson
Deconvolution
Phase
Retrieval
ProxImaL
ProxImaL Code:
ProxImaLKrishnan and Fergus 2009
Applications:
Demosaicking Interlaced HDR Low-Light Burst
Imaging
Poisson
Deconvolution
Phase
Retrieval
ProxImaL Code:
40 dB34 dB
Applications:
Demosaicking Interlaced HDR Low-Light Burst
Imaging
Poisson
Deconvolution
Phase
Retrieval
ProxImaL Code:
Applications:
Demosaicking Interlaced HDR Low-Light Burst
Imaging
Poisson
Deconvolution
Phase
Retrieval
ProxImaL Code:
Applications:
Demosaicking Interlaced HDR Low-Light Burst
Imaging
Poisson
Deconvolution
Phase
Retrieval
Applications:
Demosaicking Interlaced HDR Low-Light Burst
Imaging
Poisson
Deconvolution
Phase
Retrieval
Please see paper !
ProxImaL
www.proximal-lang.org
Open Source !

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ProxImaL | SIGGRAPH 2016

Notas del editor

  1. In summary, ProxImaL is a DSL for image optimization that allows for rapid prototyping of inverse problems in imaging while providing high-performance execution. Using ProxImaL, we achieved state-of-the-art performance and quality for a variety of applications. Our implementations were only a few lines of code. ProxImaL is open-source and available at proximal-lang.org. Check out proximal-lang.org for installation instructions, examples, and a tutorial. Image optimization offers a unified approach to image processing tasks, which is essential as we move towards increasingly diverse computational photography systems. With ProxImaL we have made image optimization easy and user friendly. Our long term goal is to make optimization-based approaches fast and efficient enough to be running on every imaging system. We will do this by extending ProxImaL to generate compiled code optimized for CPU, GPU, and emerging programmable ISPs. NOTE know timings for results.