Bosco-and-Mancuso Filter for Image Denoising

The second one is spatial masking. Natural images contain large changes in luminance, and these changes suppress the ability of the eyes to detect distortions spatially adjacent to them, this is so-called spatial masking. As a result of masking, noises in images are less detectable along strong edges and in highly textured areas, than in smooth areas of the image as illustrated in Fig. 4.

Fig. 4. Spatial Masking effect.

2.4 Bosco-and-Mancuso Filter for Image Denoising

Bosco and Mancuso [1]-[3] invented an adaptive image filter which is used to reduce the amount of noise in images captured by sensors in Bayer pattern format. The concept of this filter acts mainly on smoothing the high spatial frequency components which are hardly

In Bosco and Mancuso’s paper [1] and patent [2],[3], they made use of the Weber’s Law to determine the JND, ΔI, which could be differentiated between intensity I and I+ΔI. Bosco and Mancuso’s HVS model assume that the uniform areas are the ones with details amplitude under JND. Having these considerations in mind they designed an algorithm that can distinguish if the current processed area is uniform area or not. Once the current processed area is not uniform, the algorithm will go to detect how textural the area is and adapts its filtering strength for the noisy pixel.

The system block diagram they designed is illustrated in Fig. 5. As mentioned above, the local feature detector is to compute texture degree of the area. The estimation is based on the information of distances, noise level, JND and exposure condition from distance and noise level estimator, HVS evaluator and exposure controller respectively. Once texture degree of this current processed area is decided, it would be able to determine the strength of the filtering strength.

Fig. 5. System block diagram of Bosco-and-Mancuso filter.

The algorithm they proposed is to use two different filter masks, depending on which color is current processed pixel. One mask is for green pixels exclusively, the other one is for red/blue pixels, but not operated simultaneously. Fig. 6 is to illustrate those two kinds of operating windows established from Bayer pattern through 2 masks.

Operating Window Establisher

Distance and Noise

Level Estimator

HVS Evaluator

Local Feature Detector

Filtering Strength Calculator Exposure

Controller

Filter

G R G1 R G Fig. 6. Two kinds of operating windows established from Bayer pattern.

Definitely, green operating window is established when current pixel is green. Red and blue operating window will also be established once current pixel is red or blue respectively.

The green operating window is different from red and blue, since the green channel has double information comparing with either red or blue channel in Bayer pattern format.

In each case of operating window for red, green and blue, let’s define the current pixel C0

and eight neighboring pixels C1 to C8 respectively. C will also represent for C_i 1 to C8 to describe easier in many cases. So now we have symbol C0 to C8 or C0 and C to stand for _i elements of operating window such as C represent for G when current color channel is green,

C0 is the current pixel with noise needed to be filtered. As described in Bosco and Mancuso’s paper and patent, C0 will be filtered and replaced with a weighted average of C1 to C8. However, how much is the weight of C1 to C8? That will depend on how similar of them to C0. In the design, the higher similarity degree of neighboring pixels, the bigger weight of them to C0. The similarity degree is calculated based on the brightness of current processed pixel and takes into account of the predicted noise level NL of current area as following:

( )

[

]

( )

0

0 t =K Dmax + −K NL t−

NL_{c n n c}

where, Dmax is the maximum distance derived from calculating each distance D of _i neighboring pixel C to C_i 0 and Kn is a parameter to determine the strength of filtering. In the definition, Kn=1 stands for almost flat area since this area could be filtered strongly, and Kn=0 stands for highest texture area as this area could not be filtered too much.

Recall the assumption of uniform area by using Weber’s Law and refers to the Kn

definition as above, we can assume the curve of Kn versus Dmax can be drawn as Fig. 7. That’s to say, filter current pixel strongly if Dmax not greater than HVS threshold ThHVS and filter current pixel lighter depending on how noisy the current area is. If Dmax is greater than ThHVS

+ NL, then the area has to look as a highly texture area without strongly filter needed.

However, they used Figs. 8 and 9 instead.

Fig. 7. A candidate of Kn curve.

Kn

Dmax

ThHVS ThHVS + NL 1

Fig. 8. Kn curve for G channel in Bosco and Mancuso’s patents.

Fig. 9. Kn curve for R/B channel in Bosco and Mancuso’s patents.

Kn is the overall filtering strength of current processed area. Although the filtering strength is given, we still need to determine the filtering strength of each neighboring pixel C to target pixel Ci 0. Therefore, in order to evaluate similarity of each neighboring pixel C _i to the target pixel C0, two boundary thresholds refer to Th1 and Th2 are used to stand for most similar and least similar according to following equations:

(

)

* _{max min}

1 K D K D

Th = _n + − _n

( )

* 2 1

* _max ^{max min}

2 ⎟

⎠

⎜ ⎞

⎝

⎛ +

− +

= D D

K D

K

Th _{n n}

where, Dmin is the minimum distance between C0 to C . The value of similarity _i K_i can be determined by

Dmax

Kn

ThHVS + NL 1

Kn

NL ThHVS + NL Dmax

1

)

and Fig. 10 is the illustration for it. At the end, the result of pixel out is expressed as

( )