Image Processing Model

A Report On The Existing

Various Selective

Segmentation Model

By:

Muhammad Khobaib, Musa Khan, Muhammad

Hashim

Abdullah,Izaz Ali

Supervised By:

Dr. Haider Ali

Contents

• Introduction

i. Digital Image

ii. Image Segmentation

• Selective Segmentation Models

i. The Badshah-Chen (BC) Model

ii. The Rada Model

iii. The Mabood Model

iv. The Liu Model

• Review Of Shehryar Model

• Test Results

• Conclusion

• Bibliography

Introduction

Digital Image:-

Digital image are comprised of pixels.

Each pixel have numerical representation for its color level or intensity.

Digital image is a multi variable function say Moi,j

Where i and j denotes the coordinates and Mo represent the gray level of image. Forms of Images

Gray scale image

It consists of gray shades.

It ranges from black to white (from 0 to 255).

Where 0 is for black and 255 is for white.

Color Image

Color image is made of 3 colors i.e Green, Blue and Red.

Each of these colors needs to be 1 byte or 8 bits.

Color image is explained as the 2D arrangement of vectors. Binary Image

It is two dimensional arrangement of real values.

It is also called bitmapped images.

This image is either 0 for black or 1 for white.

Image Segmentaion

The process of partitioning a digital image into meaningful segments.

It plays an important role to identify the noisy, clear and intensity in images.

It is typically used to locate objects and boundaries in images.

The main uses are in crops department, medical field, remote sensing area and forests of satellite images.

There are different methods used to segment images. Edge Based Segmentation

It represent a class of models having information about the image.

For this type of segmentation, we use edge detector function.

But edge based segmentation models are fail to segment noisy images efficiently.

Region Based Segmentation

It uses statistical informations of the given image.

It display better results in noisy images than edge detector functions.

But its performance is not satisfactory in images which has intensity inhomogeneity.

Threshold Mechanism

This mechanism for image segmentation is based on intensity level or pixels.

It separates objects by converting color images into binary images.

In this mechanism the image is segmented in two parts.

Each pixel having the values 1 or 0 respectively. Selective Segmentation Models

The Badshah-Chen (BC) Model:-

CV model is a particular case of the MS model of the piecewise constant of the MS model. The CV model is not designed only for the gradient of the images. This model recognizes both type of contours as with and without gradient. It also works for noisy image. Badshah and Chen [50] utilized the advantages of the CV model for selective image segmentation model and added the term” µ1 inside(Ω)

T0 − t1 2dx + µ2 outside(Ω) T0 − t2 2dx’’ to the model S(Ω) = Ω d.g( T0 )dx

where µ1, µ2 are constants. t1, t2 are the average values of the given image T0. The energy functional of the proposed model Is:

S(t1, t2, Ω) = ν Ω d.g( T0 )dx + µ1 inside(Ω) T0 − t1 2 dx

+ µ2 outside(Ω) T0 − t2 2 dx

The Rada Model:-

Rada et al proposed the following variational selective segmentation model.The energy functional is given by;

min ϕ(x,y),t2 Fϵ ( ϕ(x, y), t2 ) = ν Ω g ( T0(x, y) ) δϵ(ϕ(x, y)) (ϕ(x, y)) dxdy

+ µ1 Ω T0(x, y) − t1 2 Hϵ(ϕ(x, y))dxdy

+ µ2 Ω T0(x, y) − t2 2 (1 − Hϵ(ϕ(x, y)))dxdy

+ α ( ( Ω Hϵ(ϕ(x, y))dxdy − A1 )2

+ ( Ω (1 − (Heaviside)ϵ(ϕ(x, y))dxdy) − A2 )2 ) dxdy, where µ1, µ2 and α are non negative real numbers, A1 is an area inside the object and A2 is an area outside the object.

The Mabood Model:-

The idea behind Mabood et al. model is to use more convenient form of a given image data to accurately guide the level set function for efficient segmentation of image having textural and noise.

The following is the energy functional of Mabood;

S2D = µ Ω d(x, y)δ(ϕ ) ϕ g( T0(x, y) )dx + λD((T0) (x, y)) The initial term in the above energy functional is a blend metric and edge detector function. The second term in above functional is data term which tackle noisy and textural object of interest. The metric function in initial term serve as a prior information by limiting the contour around the desired object for selective segmentation and tries to avoid influence of intensity inhomogeneity. The edge detector function attracts the contour towards the true boundaries of the desired object of interest. The term D((T0) (x, y)) serves good in detecting the objects in constant homogeneity.

The Liu Model:-

In 2017 Liu et al. utilized a two–stage segmentation technique which is based on marker points. In the initial stage, the given image is estimated with smooth function by minimizing the convex variant of model. When the smooth solution is get then segmentation is carried out by simply thresholding in later stage.

The following is the energy functional of the Liu Model; S(t0) = Ω t0 dxdy + µ1 2 Ω t0 2dxdy + µ22 Ωω2 t0 − T0 2dxdy where weight function ω is to adjust the smoothing terms and fidelity terms and is defined as:

ω2(y) = 1 − d(y)g(y),

with ω(y) (0, 1].

Review Of Shehryar Model:-

Image selective segmentation in presence of severe noise and intensity inhomogeneity is a hard case which requires more study in the field of image processing. In order to segment images with severe noise and intensity inhomogeneity but to sustain the local and fine information of image, we avail from a well known Aubert-Aujol image denoising term utilized in a local sense, as it will be explained in the following. In this portion, we present our new model and analyze it mathematically.

• Taking into account the properties of the fitting term in Rada et al. work and the properties of the local regularizing term introduced from Nui et al. we propose the following selective segmentation minimization problem:

where Ny is the neighborhood of pixels around the pixel,A1 is the area inside the polygon and A2 is the area outside the polygon. Test Results:1:-

We have conducted some test upon the existing model and the result is given by; Fig: 1:- First row: result of Mabood et al model; Second row: result of Rada et al model Third row: result of Liu et al model; Fourth row: result of shehryar model. Test Results:2:-

We have conducted some test upon the existing model and the result is given by; Fig: 2:- First row: result of Mabood et al model; Second row: result of Rada et al model Third row: result of Liu et al model; Fourth row: result of shehryar model. Test Results:3:-

We have conducted some test upon the existing model and the result is given by; Fig: 3:- First row: result of Mabood et al model; Second row: result of Rada et al model Third row: result of Liu et al model; Fourth row: result of shehryar model. Test Results:4:-

We have conducted some test upon the existing model and the result is given by; Fig: 4:- First row: result of Mabood et al model; Second row: result of Rada et al model Third row: result of Liu et al model; Fourth row: result of shehryar model. Conclusion:-

In this research, we reviewed some existing variational segmentation models i.e The Bacha-Chen Model, The Rada Model, The Mabood Model, The Liu Model and The shehryar Model.

We conclude that the Shehryar model is of high accuracy and provides improved computational results than that of three competing and state of the art models. Bibliography:-

[1] Badshah, N.; Fast iterative methods for variational models in image segmentation; Ph.D. Thesis, Liverpool University, Liverpool, England; 2009.

[2] Chan, T. F.; Shen, J.; Image processing and analysis; SIAM J Appl Math: Philadelphia, USA; 2005.

[3] Nayar, R.; Sharma, B.; Use and analysis of color model in image processing; Int. J. of Advance in Scientific Research; 2015; 1(08); 328–330.

[4] Aubert, G.; Kornprobst, P.; Mathematical problems in image processing: partial differential equations and the calculus of variations; Springer ; 2006.

[5] Elad, M.; Michal, A. Image denoising via sparse and redundant representations over learned dictionaries, IEEE Trans. Img. Proces., 2006, 15, 3736–3745.

[6] Akram, F.; Kim, J. H.; Lim, H. U.; Choi, K. N.; Segmentation of intensity inhomogeneous brain MR images using active contours; Comput. Math. Methods. Med; 2014; 1–14.

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