IMAGE UPSAMPLING VIA IMPOSED EDGE STATISTICSRaanan Fattal. ACM Siggraph 2007

Presenter: 이성호

Previous workClassical approach

Nearest-Neighbor, Bilinear, Bicubic, Hann, Hamming, and Lanczos interpola-tion kernels. assumption that

the 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 reduc-

ing 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 corre-spond to different assumptions: images are smooth enough to be ade-

quately approximated by polynomials yields analytic polynomial-interpolation formulas

images are limited in band yields 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 d2

d3 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 theoriginal 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

to twice its resolution (2562). 2 seconds

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 de-

scribe every particular case. Further improve

Using higher-order edge properties Such as curvature

Numerical analysis on EFCM upsam-pling

Appendix

Lagrange multipliers

Apply to the formula in this paper

Solve this linear system with Conjugate Gradient-based Null Space

method