Edge-Directed Image
Interpolation
Nickolaus Mueller, Yue Lu, and Minh N. Do
“In theory, there is no difference between theory and practice; In
practice, there is.”
-Chuck Reid
Outline of the Talk
Description of Problem
A. Examples
B. One-Dimensional Signals
C. Two-Dimensional Images
II. State of the Art
A. Description of Methods
B. Results
III. Wavelet Algorithms
A. Regularity Preserving Image Interpolation
B. Proposed Method using Contourlets
I.
Basic Image Interpolation
n
Given a low-resolution
image, increase
resolution by a factor of
2 or larger
Description of Problem
n
Problem: Basic interpolation
techniques cause “jagged” or
“blurred” edges
n
Goal: Reduce artifacts using
edge information
n
Simple image model:
continuous, smooth objects
piecewise continuous,
smooth edges
Examples of Edge Artifacts
Original
Original
Original
Bilinear
Bilinear
Bicubic
One-Dimensional Problem
Images: A More Difficult Task
n
n
n
2-D Edges - Magnitude and
directional component
Edges have “Geometric
Regularity”
Challenge: Estimate
orientation so that edges are
both sharp and free from
artifacts.
n
Sub-pixel Edge Localization
n
Kris Jensen and Dimitris Anastassiou, 1995
State of the Art Methods
n
New Edge Directed Interpolation
n
n
Canny Edge Based Interpolation
n
n
Xin Li and Michael T. Orchard, 2001
Hongjian Shi and Rabab Ward, 2002
Data-Dependent Triangulation
n
Dan Su and Phillip Willis, 2004
Sub-pixel Edge Localization
n
Explicitly calculate edges in
3 window of image
n
Ideal step edge assumption
n
Calculating the parameters:
3x
n
Develop continuous space
theory - projections onto an
orthonormal basis
n
Use discrete approximations to
inner products.
A
B
New Edge-Directed Interpolation
n
Classical Wiener theory to
develop MMSE weighting
scheme for interpolation
n
Estimate high resolution
covariances from low
resolution image.
n
y is the data vector, C is a
matrix used to estimate the
high resolution covariance
matrix
Dark Pixels: Low Resolution Lattice
Red Pixel: Pixel to be Interpolated in Step 1
Green Pixels: Pixels Interpolated in Step 2
Canny Edge Based
Expansion
n
First, expand image using
bilinear or bicubic
interpolation
n
Run Canny edge detector on
expanded image
n
Determine if magnitude of
gradient is larger vertically or
horizontally at each edge
pixel
n
Modify pixels on either side of
edge in vertical or horizontal
direction
Data-Dependent
Triangulation
n
For each set of four low
resolution pixels,
estimate edge as dividing
pixels into two triangles
n
Create an image mesh
which stores the direction
of each edge
n
Use linear interpolation
within triangles
Image Mesh
Edge Guided Image
Interpolation
n
More general
triangulation technique
n
Use directional variances
to produce weighting
scheme
n
Perform interpolation
using both triangles, fuse
with weighting scheme
Comparison of Methods
Original
Bilinear
Sub-pixel Edge Loc.
NEDI
Canny Edge Based
DDT
Comparison of Methods
Original
Bilinear
Sub-pixel Edge Loc.
NEDI
Canny Edge Based
DDT
Comparison of Methods
Original
Bilinear
Sub-pixel Edge Loc.
NEDI
Canny Edge Based
DDT
Factor of Four Interpolation
Original
NEDI
Bilinear
Canny Edge Based
DDT
Algorithm Comparison
Speed in Seconds
Lena
Gaussian
Disc
Bilinear
0.287
0.314
SEL
2.047
3.026
NEDI
42.5
36.1
Canny
1.386
1.299
DDT
0.945
0.982
Edge
Guided
1.124
1.230
PSNR
Bilinear
SEL
NEDI
Canny
DDT
Edge Guided
Lena
32.42
33.09
37.37
37.29
37.42
37.37
Gaussian
Disc
39.58
46.04
42.76
40.37
41.68
41.68
n
Regularity Preserving Image
Interpolation
High similarity between different
wavelet scales in regions of low
regularity
n
Convergence of series of
features across scales for edge
detection
n
Goal: Synthesize a new sub-band
by extrapolating from rate of
decay of features across known
sub-bands
n
Apply algorithm separably along
rows and columns
Regularity Preserving Image
Interpolation
Take Home Message
n
Higher cost methods can result
in significant improvement
n
Still room for improvement using
low-cost algorithms
n
Current wavelet techniques still
have room for improvement
n
Proposed Method: EdgeDirected Interpolation using
Multiscale Geometric
Representations
n
Questions?