ion of Abf Parameters

8/2/2019 ion of Abf Parameters

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Adaptive Bilateral Filter for Sharpness

Enhancement and Noise Removal


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SUMMARYWe have Learnt about

1 Bilateral Filters, Its Working, Advantages and

Disadvantages.

2 Adaptive Bilateral Filter, some modifications done for

ABF to perform Smoothing and Sharpening operations.

3 Forms of degradations

4 Sharpening Algorithms


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Introduction

OPTIMIZATION OF ABF PARAMETERS

FEATURE DESIGN

LOG OPERATOR

POINT SPREAD FUNCTION


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OPTIMISATION OF ABF PARAMETERS

The parameter optimization is formulated as a

minimum mean squared error (MMSE) estimation

problem.

We classify the pixels into T classes, and estimate

the optimal and r for each class that minimizes

the overall MSE between the original and restoredimages


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Consider P be the total number of training image sets of

dimensions Mk*Nk. The kth set (k = 1,2.P) consists of an

original image fk[m,n], a degraded image gk[m,n], the class

index image Lk[m,n], and the restored image [m,n].

Let

be the set of indices for the pixels in these images.

Also let

be the set of indices for the pixels belonging to theclass iin image k.


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The optimal parameters { , r} must satisfy

the eqn

fk[m,n] is the original image, is a degraded image

= {i : i = 1, 2, ..., T },and r = {r,i : i =1, 2, ..., T }.

Since the classes are independent and

non overlapping, we can separately

estimate the optimal { , r} for each

class.


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fk[m,n], a degraded image Lk[m,n], and the restored image [m,n].

To find the pair of parameters to minimize the MSE

for each class, we perform an search in the parameterspace.

The parameter space is uniformly quantized.


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The range and the step size of the parameters

are chosen such that they can yield adequate

sharpening and smoothing for all types of imagestructures with a balance between accuracy.


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FEATURE DESIGN

Despite the high correlation between and thedesired sharpening/smoothing effect, is not an

appropriate feature for pixel classification

because it is very sensitive to noise.The main features required are

1) be able to reflect the strength of edges,

2) can distinguish the regions we want toprocess differently, mainly, the regions for

smoothing and sharpening.


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The feature we have chosen to use for pixel

classification is the strength of the edges

measured by a Laplacian of Gaussian (LoG)

operator

m0,n0 is the center pixel of the window


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Log operator

LoG operator is a highpass filter.

It computes the second derivative of the input

image.

The magnitude of its response is high near the

edges, Low in smooth regions, on the center of

an edge, the magnitude of its response is 0


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Two major reasons to choose the LoG

output as our pixel classification feature

The magnitude of the LoG strength reflects the

local edge structure.

It can distinguish smooth regions from edge

regions, where the optimal filter parameters are

most likely to be very different.

But The magnitude of the LoG response cannot

distinguish the center of the edges and the noisysmooth regions very well because both have

small LoG response


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ABF for various input image structures


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Considering 3 sample Pixels

The pixels A and B are located in a noisy smooth

region and on an edge center.Even though the optimal filter parameters are the

same for both pixels, the impulse responses of the

ABF are different for pixels A and B.Pixel C shows how and r impact the ABF.

Without the Offset and the locally adaptive r, the ABF

at pixel C would be the same as that in pixel B,in that

case no sharpening effect would be achieved at pixel CSo ABF with the same and r can satisfy the filtering

needs of both types of regions.


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TRAINING IMAGES

Test image

ABF restored image


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Point Spread FunctionFor the image we apply Blur PSF[The PSF is the

output of the imaging system for an input pointsource] to the original image, and added tone-

dependent noise to the blurred image.

So it pushes pixel values in edge regions from

the edge slope center value either towards the

high or low side of the edge based on whether

the pixel is originally above or below the

midpoint of the edge slope.The choice of whether ABF sharpens or smoothes is

controlled by r


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CONCLUSION

The performance of the ABF is evaluated with

three images. The first test image is degraded

exactly according to the degradation model.

The second test image is to demonstratesharpening effect.

The third test image is outside the context of

our degradation model.


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DENOISED/FILTERED IMAGE

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ion of Abf Parameters