Enhancement of Underwater Image Quality using ...

Enhancement of Underwater Image Quality using Speckle Reducing Anisotropic Diffusion Algorithm Aju John K.K., Supriya M.H., P.R. Saseendran Pillai Department of Electronics, Cochin University of Science and Technology, Kerala, India,682022 [email protected], [email protected], [email protected]

Enhancement of Underwater Image Quality using Speckle Reducing Anisotropic Diffusion Algorithm Aju John K.K., Supriya M.H., P.R. Saseendran Pillai Department of Electronics, Cochin University of Science and Technology, Kerala, India,682022 [email protected], [email protected], [email protected]

Underwater acoustic imaging systems provide images of underwater objects, when the water turbidity precludes the use of optical means of viewing. The applications of underwater acoustic imaging span a wide variety of disciplines. Challenges associated with obtaining visibility of objects at long or short distances have been difficult to overcome due to the absorptive and scattering nature of seawater. Mitigating these effects have been the focus of the underwater imaging community for decades. Speckle, which is a form of multiplicative and locally correlated noise, stands in the way of interpreting the images accurately and degrades the image quality while retaining the fine details. The edge preservation of the images can be achieved through Partial Differential Equation (PDE) based speckle reduction approach. The PDE based approaches not only preserves the edges but also enhances its quality. The prototype algorithm uses the partial differential equation approach for speckle removal known as Speckle Reducing Anisotropic Diffusion(SRAD).This diffusion technique based on minimum mean square error (MMSE) approach outperforms the conventional adaptive speckle filter as regards to the edge preservation feature is concerned.

1

Introduction

Underwater images captured by the image sensors are adulterated with the different type of noises. Because of Specific transmission properties of light in water, the underwater images suffer from limited range, non uniform lighting, low contrast, color diminishing, image blurring, etc. Underwater environment limits the scale and quality of the image obtained. Basically three type of noise are present in underwater images namely, speckle noise, impulsive noise and gaussian noise, of which the speckle is more complex and affects the image severely.The Speckle noise is granular in nature that inherently exists and degrades the quality of the images, due to which the captured underwater images require a bare minimum denoising process to correct and adjust the image for further processing. A denoising filter is used to remove the noise from an image and the most widely used denoising filters include the Lee , Frost [2], Kuan , and Gamma MAP filters. The speckling[3] filters are of two types, ‘edge preserving and ‘feature preserving’. These filters suffer from the following limitations. (i) These filters are sensitive to the size and shape of the window, (ii) The existing filters do not enhance edges, they inhibit smoothing near edges. (iii) They are not directional. To overcome these limitations, partial differential equation (PDE) approach has been adopted for speckle removal and the technique which uses the PDE approach for speckle

removal is known as the Speckle reducing anisotropic diffusion (SRAD). SRAD not only preserves edges, but also enhances it by inhibiting diffusion across the edges and allowing diffusion on either side of the edges.

2

Noise reduction techniques

Partial Differential Equation (PDE) based approaches have been widely used for image denoising with edge preservation. The PDE based speckle reduction approach allows the generation of an image scale space which is a set of filtered image that vary from fine to coarse level, without bias due to filter window size and shape. This approach is adaptive and does not use hard threshold to alter the performance in homogenous region or inregions near the edges.The Speckle Reducing Anisotropic Diffusion (SRAD) technique has been implemented and applied on various test images,underwater images and real ultrasound images.

2.1 Objective of this proposed work The proposed work deals with the implementation of speckle reduction algorithms so as to improve the quality and productivity by improving the accuracy and reducing the time taken in the manual analysis of the images. The main goal of this proposed work is to reduce the speckles in the ultrasound images while retaining the fine details. Since there is no standard speckle free image available, for the purpose of evaluating the performance of the filtering algorithms the speckles will have to be simulated using the Loupas’ model. Then the SRAD algorithm will be applied

on the corrupted images and their results will be quantified using the figure of merit, S/mse and correlation parameters.

I it,+j1 = I it, j + λ [c N .∇ N I + cS .∇ S I + cE ∇ E I + cW ∇W I ]i , j t

2.2 Anisotropic Diffusion

where 0≤ λ ≤ ¼ for the numerical scheme to be stable, ∇ indicates nearest-neighbor differences.

Consider the anisotropic diffusion equation [4],

∇ N I i , j = I i −1, j − I i , j ∇ S I i , j = I i +1, j − I i , j

I t = div[c( x, y, t )∇I ] = c( x, y, t )∆I + ∇ c .∇I

,

(1)

where div is the divergence operator, c is the diffusion

coefficient, ∇ the gradient operator with respect to the space variables. I is the image Δ is the Laplacian operating 2 on I defined as Δ I= ∇ I = ∇.∇I which is the divergence of the gradient of I. The locations of the region boundaries appropriate for that scale at the time t are known, then it is possible to perform smoothing within a region in preference to smoothing across the boundaries. This could be achieved by setting the conduction coefficient to be 1 in the interior of each region and 0 at the boundaries. The blurring would then take place separately in each region with no interaction between regions. The region boundaries would remain sharp.

(3)

∇ E I i , j = I i , j +1 − I i , j ∇ W I i , j = I i , j −1 − I i , j ,

I i , j +1

φ north

I i −1, j

φ we

φeast

I i +1, j

I i , j +1 φ sou

Let E(x, y, t) be an estimate, a vector -valued function defined on the image which ideally should have the following properties: 1. E(x, y, t) = 0 in the interior of each region.

I i , j −1

2. E(x, y, t) = Ke(x, y, t) at each edge point, where e is a unit vector normal to the edge at the point and K is the local contrast of the edge. If an estimate E(x, y, t) is available, then the conduction coefficient c(x, y, t) can be chosen to be a function c = g( ||E|| ) of the magnitude of E. According to above strategy, g(.) has to be a nonnegative monotonically decreasing function with g(0) = 1 as shown in fig. This way the diffusion process will mainly take place in the interior of regions and it will not affect the region boundaries where the magnitude of E is large.

Fig.2 Discretization of the diffusion equation The conduction coefficients are updated at every iteration as a function of the brightness gradient.The value of the gradient can be computed on different neighborhood structures achieving different compromises between accuracy and locality.

2.3 Speckle Reduction Anisotropic Diffusion (SRAD) SRAD technique is based on the minimum mean square error (MMSE) approach to filtering as the Lee (Kuan) and Frost filters. In fact, SRAD can be related directly to the Lee and Frost window-based filters. So, SRAD is the edge sensitive extension of conventional adaptive speckle filters.

Fig 2.1.The qualitative shape of the nonlinearity g(.)

2.3.1 Coefficient of Variation The simplest estimate of the edge positions is the gradient of the brightness function, E ( x, y, t ) = ∇I ( x, y, t ) the conduction coefficient c is chosen locally as a function of the magnitude of the gradient of the brightness function,

c(x, y, t ) = g ( ∇I (x, y, t ) ) not only preserve, but also

A more general updated function of Equ. 1 is given by[3] I it,+j∆t = I it, j +

δt _

ηs

[(

)

div c C it, j ∇I it, j

]

(4)

sharpen the brightness edges if the function g(.) is chosen properly.

where c(.) is a bounded nonnegative decreasing function,

Equ. (1) can be discretized on a square lattice, with brightness values associated to the vertices, and conduction coefficients to the arcs as shown in fig. 2.

neighborhood of pixel s, η s is the number of of pixels in

(2)

δt is the time step size, η s represents the spatial the window.As with conventional anisotropic diffusion c(.)

is the diffusion coefficient and C i,j is the coefficient of variation in speckle filtering.

∇RI

n i, j

 I in+1, j − I in, j I in, j +1 − I in, j  = ,  h h  

(11)

∇LI

n i, j

 I in, j − I in−1, j I in, j − I in, j −1  , =  h h  

(12)

∇ I

n i, j

The coefficient of variation is given by C 2 i, j =

 2  1 ∇ 2 I 2 i, j   I i, j + ηs     1 ∇ 2 I i, j   I i, j + ηs  

(5)

−1

2

In the continuous domain, ∇ 2 I 2 = 2 ∇I

2

2

+ 2I∇ 2 I

(6)

On the discrete 2-D grid, Equ. (6) can be represented by ∇ 2 I 2 i, j = ∇ L I i, j

2

+ ∇ R I i, j

2

+ 2I i, j ∇ 2 I i, j

(7)

∇ R I i , j and ∇ L I i , j , Two difference approximations Where to the gradient. Ci2, j

(

2 1 1 ∇I i , j − ∇2 Ii, j 2 16 = 2 1 2   + ∇ I I i j i j , ,   4  

)

2

(8)

If I ij >o everywhere over a 2-D coordinate grid Ω ,then (8) is well defined over Ω. But by assumption, I ij >o for all(i,j) Є Ω,the special case of C i,j, one that is computed over ,by q ij for convenience and assume that the image intensity function has no zero point over its support.As C ij is usually called local coefficient of variation, and the function q is the instantaneous coefficient of variation which allows for edge detection in bright region as well as in dark regions.

q=

2  2 1  ∇I  1 ∇ I − 2 2  I  4  I 

 1  ∇ 2 I   1 +   4  I 

    

2

2

(9)

I in+1, j + I in−1, j + I in, j +1 + I in, j −1 − 4 I in, j

=

(13)

h2 The diffusion coefficient c(q)   1 cin, j = c q n   I i, j  

∇ R I in, j

2

2

+ ∇ L I in, j

,

1 I in, j

 ∇ 2 I in, j   

(14)

Then the divergence of c(.)∇I can be calculated as

d ni, j =

1 h2

[c

n

i +1, j

(I

n

i +1, j

(

)

(

− I n i , j + c n i , j I n i −1, j − I n i , j

)

(

+ c n i , j +1 I n i , j +1 − I n i , j + c n i , j I n i , j −1 − I n i , j

)]

(15)

The numerical approximation to the differential equation is given by (16)

∆t n d i, j 4

I in, +j 1 = I in, j +

Equ. (16) is called the SRAD update function.

3

Assessment Parameters

Two important factors in speckle noise reduction methods are denoising in homogeneous area and preserving edges. Edge preservation plays an important role in efficient diagnoses and making decisions. Therefore different parameters must be defined to evaluate each of he above mentioned factors. In this paper we use s/mse, ρ, Fom and β parameters. s/mse curresponding to the classical SNR in the case of additive Gaussian noise. The other two parameters (ρ and β)are based on the correlation between coefficients.β is defined as edge preservation criteria and, ρ is measure of noise suppression[1]

2.3.2 Discrete Implementation of SRAD Given an intensity image I 0 (x, y) having finite power and no zero values over the image, the output image I(x, y; t) is evolved according to the following PDE

{∂I ( x, y; t ) / ∂t = div[c(q )∇I ( x, y; t )] I ( x, y , ;0 ) = I 0 ( x, y ), (∂I ( x, y; t ) / ∂ n )∂Ω = 0

(10)

N −1   si 2  S = 10 log10  N −1 i =0 mse  (si − s i )2   i =0

∑

∑

N −1

where ∂Ω denotes the border of Ω, n is the outer normal to the ∂Ω. To calculate the right hand side of the SRAD PDE, use the derivative approximations and Laplacian approximations approaches are given as follows

)

β=

∑ (∆s

i

      

(

(17)

  − ∆s ) ∆s i − ∆s

)

i =0

N −1

∑ (∆s i =0

i

− ∆s )2 ×

(18) N −1

∑ (∆s ii = 0

 i

 − ∆s

)2

N −1

∑ (S

i

i =0

ρ=

)

 − S  S i − Sˆ   

N −1

N −1

i =0

ii =0

2 ∑ (Si − S ) × ∑  Si − S 





(19)

2

(d)

^

where s is the original image, s is denoised image and N is ^

the picture size. s and

s

^

are mean values of s and

respectively, over all image coefficients. ∆s and

s,

^

∆ s are

^

high pass filtered versions of s and s ,the closer the correlation parameters β and ρ are to one, the closer the estimated image is to the original image.

(e)

(f)

Fig.3 Original and noisy images (Var=0.2)of underwater image and ultrasound image. In implementing the anisotropic diffusion algorithms, a fixed number of iterations and time step is used.Fig 3 (a),(b) and (c)shows the orginal 2D shape Image, underwater image and ultrasound image respectively. Fig (d),(e) and (f) shows the images after addition of artificial noise(mean=0, variance=0.2).

In case of speckle separation, the Edge preservation is computed using the Figure of merit(FOM),given by

1 FOM : ˆ max N , N ideal

{

 N

1

}∑ 1 + d α i =1

(20)

2 i

^

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

N and N ideal are the number of estimated and ideal edge pixels, respectively, d i is the distance between

where

the ith detected edge pixel and the nearest ideal edge pixel, and α is a constant typically set to 1/9. FOM ranges between 0 and 1, with unity for ideal edge detection.

4

Results and Discussions

For the performance evaluation of the SRAD algorithm implemented, studies have been carried on an image of a 2 D shape as well as underwater image. Also studies were carried out on ultra sound images. The performance has been evaluated on speckle simulated for different variances by Loupas model. To test the accuracy of the non linear Filtering algorithms, three steps are followed. i) First an uncorrupted image is taken as input. ii) Second different noises are added to the image artificially. iii) Third, the filtering algorithms are applied for reconstruction of images.

Fig.4 Denoised images for different iterations On the above noised images, the SRAD algorithm has been implemented and the de speckled filtered image for different iterations of 10, 25, 35 and 50 are shown as Fig 4(a) – (l). (a)

(b)

(c)

(a)

(b)

(c )

From the above figures, it is clear that SRAD is able to reduce the speckle noise and also the fine details are retained. It can be observed that, in shape image the boundaries are delineated and well defined. From the above figures, it can be also be seen that as the number of iterations increases the smoothening effect increases and after that the image may slightly become blurred due to the smearing of edges. These figures show that anisotropic diffusion algorithms are good at preserving the edges while reducing the speckle noise. Fig.7-9 shows the variation of FOM,RHO and S/mse with respect to the number of iterations with variance =0.2 for Shape, underwater and Ultrasound images, respectively.

(d)

(e)

(f)

Fig.5 Original and noisy images (Var=0.4)of underwater image and ultrasound image. Fig.5 (a)-(c)shows the orginal images . Fig (d),(e) and (f) shows the images after addition of artificial noise(mean=0, variance=0.4).

Fig.7 FOM vs. iterations graph of SRAD output of different images

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

Fig.6 Denoised images for different iterations The de speckled filtered image for different iterations of 10, 25, 35 and 50 are shown as Fig 6(a) – (l).

Fig.8 Rho factor vs. iterations graph of SRAD output of different images

Fig.9 S/mse vs. iterations graph of SRAD output of different images.

Parameters Image

Shape image

Underwater

Noise varienc e

No.of iterations

Fom

0.2

10

0.2905

0.9548

1.4335

25

0.2870

0.9611

1.5650

35

0.2873

0.9683

1.6980

50

0.2527

0.9734

1.8295

10

0.8455

0.8891

0.8923

25

0.8311

0.8909

0.8684

0.2

image

Ultrasound liver image

0.2

ρ

s/mse

35

0.8370

0.8918

1.0076

50

0.8406

0.8919

1.0927

10

0.7326

0.9411

2.2581

25

0.7308

0.9571

2.4668

35

0.7744

0.9676

2.8272

50

0.6313

0.9664

2.9716

Table 1 SRAD performance index comparison for all test images ( Var = 0.2)

5

Conclusions

The use of filters in Digital Image Processing improves the image to a great extent. Mainly in the case of presence of Speckle noise, filtering is very much required in order to improve the efficiency of post processing techniques like segmentation. This Paper mainly concentrates on the SRAD method for Speckle Reduction.The SRAD method is implemented and calculated the FOM, RHO and S/mse parameters with respect to the number of iterations with variance v=0.2 and 0.4 for shape underwater image and ultrasound images, respectively.

References [1]

F. Sattar, L. Floreby, G. Salomonsson, B. Lovstrom, Image enhancement based on a nonlinear multiscale method, IEEE Trans. Image Process. 6 (6) (1997) 888–895.

[2] V. S. Frost, J. A. Stiles, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, pp. 157–165, 1982. [3] Yongjian Yu and Scott T. Acton “ Speckle reducing anisotropic diffusion” IEEE Transactions on image processing vol.11,no.11,November 2002. [4]

Pietro Perona and Jitendra Malik “Scale space and edge detection using Anisotropic diffusion” IEEE Transactions on pattern analysis and machine intelligence vol.12.no 7 july 1990

Acknowledgements

[5]

C.Tauber, Haji Batania and Alain Ayache “ A robust speckle reducing anisotropic diffusion” International conference on image processing (ICIP)2004.

The authors gratefully acknowledge the Department of Electronics, Cochin University of Science and Technology, for extending all the facilities for carrying out this work.

[6]

Scott T. Acton, “De-convolution speckle reducing anisotropic diffusion”, IEEE International Conference on Image Processing, 2005, Vol.1, pages: I- 5-8