Home > Optimizing and Learning for Super-resolution
Optimizing and Learning
for
Super-resolution
Lyndsey C. Pickup, Stephen J. Roberts
& Andrew Zisserman
Robotics Research Group, University of Oxford
The Super-resolution
Problem
Given a number of low-resolution images
differing in:
Estimate a high-resolution image:
Low-resolution image 1
Low-resolution image 2
Low-resolution image 3
Low-resolution image 4
Low-resolution image 5
Low-resolution image 6
Low-resolution image 7
Low-resolution image 8
Low-resolution image 9
Low-resolution image 10
Super-Resolution Image
Generative Model
Registrations,
lighting and blur.
High-resolution
image, x.
y1
y2
y3
y4
Low-resolution
images
W4
W3
W2
W1
Generative Model
We don’t have:
We have:
Maximum a Posteriori
(MAP) Solution
Standard method:
y1
y2
y3
y4
W4
W3
W2
W1
x
[Irani & Peleg ‘90, Capel ’01, Baker & Kanade ’02, Borman ‘04]
What’s new
parameters in the prior term at the
same time.
i.e. given the
low-res images, y, we solve for the SR image x and
the mappings, W simultaneously.
y1
y2
y3
y4
W4
W3
W2
W1
x
Overview of rest of talk
Maximum a Posteriori (MAP)
Solution
Image x.
Corrupt with additive
Gaussian noise.
Warp, with parameters
Φ.
Blur by point-spread
function.
Decimate by zoom factor.
y1
y2
y3
y4
W4
W3
W2
W1
x
y
Details of Huber Prior
Huber function is quadratic
in the middle, and linear in the tails.
Probability distribution
is like a heavy-tailed Gaussian.
ρ (z,α)
p (z|α,v)
Red: large α
Blue: small α
This is applied to image gradients in the SR image estimate.
Details of Huber Prior
Ground Truth
α=0.1 v=0.4
Too little smoothing
Too much smoothing
α=0.05 v=0.05
α=0.01 v=0.01
α=0.01 v=0.005
Edges are sharper
Advantages: simple, edge-preserving,
leads to convex form for MAP equations.
Solutions as α and v vary:
Advantages of Simultaneous Approach
Overview of Simultaneous Approach
Initialisation
Average image
ML-sharpened estimate
Optimization Loop
Joint MAP Results
Decreasing prior strength
Registration Fixed
Joint MAP
Learning Prior Parameters
α, ν
Use first set to obtain
an SR image.
Find error on validation set.
Learning Prior Parameters
α, ν
Use first set to obtain
an SR image.
Find error on validation
set.
Learning Prior Parameters
α, ν
Learning Prior Parameters
α, ν
Learning Prior Parameters
α, ν
Results: Eye Chart
MAP version: fixing registrations
then super-resolving
Joint MAP version with adaptation of prior’s parameter values
Results: Groundhog Day
Results: Groundhog Day
Blur radius = 1
Blur radius = 1.4
Blur radius = 1.8
Regular MAP
Simultaneous
Lola Rennt
Real Data: Lola Rentt
Real Data: Lola Rentt
Real Data: Lola Rentt
Real Data: Lola Rentt
Conclusions
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