Transcript Image upsampling via Imposed Edge Statistics

IMAGE UPSAMPLING VIA
IMPOSED EDGE STATISTICS
Raanan Fattal. ACM Siggraph 2007
Presenter: 이성호
Previous work
Classical approach

Nearest-Neighbor, Bilinear, Bicubic, Hann, Hamming,
and Lanczos interpolation kernels.
 assumption
 the
that
image data is either spatially smooth or band-limited
More sophisticated methods

[Su and Willis 2004]
Reduce the number of variables that are averaged
 forms a noticeable block-like effect

Bicubic
Su and Willis 2004
[Li and Orchard 2001]

Arbitrary edge orientation is implicitly matched
 By
estimating local intensity covariance
 from


the low-resolution image
Generating smooth curves and of reducing jaggies
Not sharp edges
[Hertzmann et al. 2001]

Image Analogies
[Freeman et al. 2002]

adding high-frequency patches
 from
a non-parametric set of examples
 relating


low and high resolutions
Sharpens edges and yields images with a detailed
appearance
tends to introduce some irregularities
into the constructed image
[Osher et al. 2003]

invert a blurring process
 measures
the L1 norm of the output image
Assumptions on image upsampling

different upsampling techniques correspond to
different assumptions:
 images
are smooth enough to be adequately
approximated by polynomials
 yields
 images
 yields

analytic polynomial-interpolation formulas
are limited in band
a different family of low-pass filters
these assumptions are highly inaccurate
 suffer
from excessive blurriness and the other visual
artifacts
Edge-Frame Continuity Moduli

predict the spatial intensity differences
 at
the high-resolution based on the low-resolution input
image
Approach



Statistics of intensity differences
intensity conservation constraint
we discuss only gray scale images
 later
extend to handle color images
Derivatives
Image statistics
edge-frame continuity modulus (EFCM)
Upsampling using the EFCM
Gauss-Markov Random Field model
Color images

First we upsample the luminance channel


of the YUV color space
compute the absolute value of its luminance difference
d1
d3
d2
d4
Results
High-res original
Downsampled
Bilinear
Ours
Simple Edge Sensitive
New Edge-Directed
magnified by
a factor of 4
magnified by a factor of 8
magnified by a factor of 16
objective error measurements between an upsampled image and the
original ground-truth image (i.e., before downsampling).
Structural Similarity Image Quality (SSIQ) described in [Wang et al. 2004]
Implementations



implemented in C++
Mobile Pentium-M, running at 2.1MHz
Upsample an image of 1282 pixels
twice its resolution (2562).
 2 seconds
 to

To a resolution of 10242 pixels
 22
seconds.
Conclusions

Drawbacks:
Emphasize lack of texture and absence of fine-details
 The jaggies artifact
 Acutely twisted edges
 involves more computations




than some of the existing techniques
generic behavior of edges does not accurately describe
every particular case.
Further improve

Using higher-order edge properties

Such as curvature
Appendix
Numerical analysis on EFCM upsampling
Lagrange multipliers
Apply to the formula in this paper

Solve this linear system
 with
Conjugate Gradient-based Null Space method