its a ppt based on ieee journal jan 2016 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 25, NO. 1, JANUARY 2016 A Decomposition Framework for Image Denoising Algorithms Gabriela Ghimpe¸teanu, Thomas Batard, Marcelo Bertalmío, and Stacey Levine

1. A DECOMPOSITION FRAMEWORK
FOR IMAGE DENOISING
ALGORITHMS
IEEE TRANSACTION ON IMAGE
PROCESSING VOL.25, NO.1
YEAR OF PUBLICATION : JAN 2016

2. INTRODUCTION
DENOISING an image is a fundamental task for
correcting defects produced during acquisition
process of a real world scene.
An image decomposition model that provides
a novel framework for image denoising.
This framework provide better results than
denoising the image directly, both in terms of
PSNR and SSIM.

3. Flow diagram
ADD LOW RESOLUTION IMAGE
INITIALISATION
PRE-PROCESSING
NLM FILTERING
POST-PROCESSING
BM3D FILTERING
DENOISED IMAGE
PERFORMANCE MEASURE

4. Let I be a gray-level image, and (x, y) be the
standard coordinate system.
Ix = derivative of I w.r.t. x
Iy = derivative of I w.r.t. y
∇I = gradient of I
METHODOLOGY

5. we consider a scaled version μI of I, for μ ∈]0, 1],
and its graph, which is the surface S in R3
parametrized by
ψ : (x, y) −→ (x, y, μ I(x, y))
 Z1 : tangent to the surface S and indicates the
direction of the steepest slope.
 Z2 : tangent to the surface S and indicates the
direction of the lowest slope.
 N : Normal to the surface.

6. The moving frame (Z1, Z2, N) can be constructed as
follows.
Let z1 = (μIx , μIy )T be the gradient of μI and
z2 = (−μIy , μIx )T indicating the direction of the level-
lines of μI.
Zi = dψ(zi) /||dψ(zi)|| , i = 1, 2

7. -
Fig. From left to right: gray-level image “Lena”, component J 1, component J 3.
The explicit expressions of the vector fields Z1, Z2, N are given by the matrix field
The components J1, J2, J3 are computed from matrix P are given by,

8. • 1) Process I with some denoising technique F and call the
output image Iden.
• 2) Compute the components (J 1, J 2, J 3) of I in the moving
frame , for some scalar μ, with formula . Apply the same
denoising technique F to the components to obtain the
processed components (J 1 den, J 2 den, J 3 den).Then, apply
the inverse frame change matrix field to the processed
components, i.e.
and denote by IdenM F the third component I 3 denM F .
• 3) Compare Iden and IdenM F with the metrics PSNR and SSIM.

9. Observation

10. CONCLUSION
• Different approaches for image decomposition are
described. Through comparative study,
• the decomposition framework using moving frame
approach is the most effective method. In this
• approach, it computes the components of the image to
be processed in a moving frame that encodes
• its local geometry (directions of gradients and level
lines). Then, the strategy denoise the components
• of the image in the moving frame in order to preserve
its local geometry, which would have been
• more affected if processing the image directly.