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Edge-Directed Image Interpolation
Edge-Directed Image Interpolation
Nickolaus Mueller, Yue Lu, and Minh N. DoNickolaus Mueller, Yue Lu, and Minh N. Do
“In theory, there is no difference between theory and practice; In practice, there is.”-Chuck Reid
I. Description of ProblemA. ExamplesB. One-Dimensional SignalsC. Two-Dimensional Images
II. State of the ArtA. Description of MethodsB. Results
III. Wavelet AlgorithmsA. Regularity Preserving Image InterpolationB. Proposed Method using Contourlets
Outline of the TalkOutline of the Talk
Basic Image InterpolationBasic Image Interpolation
n Given a low-resolution image, increase resolution by a factor of 2 or larger
Description of ProblemDescription 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
Examples of Edge Artifacts
Original
Bilinear Bilinear Bicubic
Original Original
One-Dimensional Problem
One-Dimensional Problem
Images: A More Difficult Task
Images: A More Difficult Task
n 2-D Edges - Magnitude and directional component
n Edges have “Geometric Regularity”
n Challenge: Estimate orientation so that edges are both sharp and free from artifacts.
State of the Art MethodsState of the Art Methodsn Sub-pixel Edge Localization
n Kris Jensen and Dimitris Anastassiou, 1995
n New Edge Directed Interpolationn Xin Li and Michael T. Orchard, 2001
n Canny Edge Based Interpolationn Hongjian Shi and Rabab Ward, 2002
n Data-Dependent Triangulationn Dan Su and Phillip Willis, 2004
n Edge-Guided Interpolationn Lei Zhang and Xiaolin Wu, 2006
Sub-pixel Edge Localization
Sub-pixel Edge Localization
n Explicitly calculate edges in 3 x 3 window of image
n Ideal step edge assumption
n Calculating the parameters:
n Develop continuous space theory - projections onto an orthonormal basis
n Use discrete approximations to inner products.
A
B
New Edge-Directed Interpolation
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 LatticeRed Pixel: Pixel to be Interpolated in
Step 1Green Pixels: Pixels Interpolated in
Step 2
Canny Edge Based Expansion
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
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
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 MethodsComparison of Methods
Original Bilinear Sub-pixel Edge Loc.
NEDI Canny Edge Based DDT
Comparison of MethodsComparison of Methods
Original Bilinear Sub-pixel Edge Loc.
NEDI Canny Edge Based DDT
Comparison of MethodsComparison of Methods
Original Bilinear Sub-pixel Edge Loc.
NEDI Canny Edge Based DDT
Factor of Four InterpolationFactor of Four Interpolation
Original Bilinear
NEDI Canny Edge Based DDT
Algorithm ComparisonAlgorithm Comparison
Lena Gaussian Disc
Bilinear 32.42 39.58
SEL 33.09 46.04
NEDI 37.37 42.76
Canny 37.29 40.37
DDT 37.42 41.68
Edge Guided 37.37 41.68
PSNR 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
Speed in Seconds
Regularity Preserving Image Interpolation
Regularity Preserving Image Interpolation
n 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
Regularity Preserving Image Interpolation
Take Home MessageTake 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: Edge-Directed Interpolation using Multiscale Geometric Representations
n Questions?
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