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DETECTION OF THE MALARIAL PARASITE INFECTED BLOOD IMAGES BY 3D-ANALYSIS OF THE CELL CURVED SURFACE

Abstractâ€ In blood samples, if the red corpuscles of vertebrates are infected by malarial parasites, they will have a specific shape which can identify their presence. Recent research has suggested that the shape of the affected red blood cells can be detected using the 2D moments of the image of the infected cell. Since real blood cells are 3D in nature, the image has to be treated as 3D. We have extended this 2D approach to 3D image processing for detecting and classifying malarial parasites in images of Giemsa stained blood slides, by evaluating the surface of the parasitaemia in the infected blood, which will yield better accuracy to the diagnosis. The primary aim is to detect the blood cells infected by malarial parasites based on the 3D-statistical approach of evaluating the curved surface area of cell structure by computing the 3D moments of the image.

Presented By:

P. M. Rubesh Anand1, G. Bajpai2, Vidhyacharan Bhaskar1, Sam M. Job2

1 SRM University/Department of Electronics and Communication Engineering, Kattankulathur, India

2 Kigali Institute of Science and Technology/Department of Computer Engineering and Information Technology, Rwanda

I. INTRODUCTION

Malaria [12] is caused by the protozoan parasites transmitted by the Anopheles mosquito from one person to another. The infection is caused by minute parasitic protozoa of the genus Plasmodium, which infect human liver cells first, then the red cells, and then the insect hosts alternatively. Malaria originated in Africa probably from the marshy areas of the continent. The detection techniques today include manual laboratory diagnosis by visual analysis of the infected blood images [10, 11].

Generally, in blood analysis three different kinds of cells red, white and blood platelets are noticed. Their dimensions and color distinguish them from one another. The red corpuscles of vertebrates are infected by malarial parasites when they enter the blood stream. The Plasmodium that causes malaria exists in a variety of different forms [9], which have been successfully adapted to different cellular environments, in both the vertebrate host and the mosquito vector. The parasite develops in a highly regulated manner through distinct cycles in the vertebrate host. During the life cycle of Plasmodium, it has stages of development and growth where it exhibits several shapes as in Fig. 1. Since they exist in the real world as 3D objects, the blood has to be analyzed in 3D, in order to diagnose protozoan presence for recognition. 3D imaging of the cell surface from the top view resolves the Plasmodium in a range of 6-8 Ã‚Âµm with nearly spherical, cylindrical and elliptical shapes over the cell surface.

Fig. 1: Plasmodium vivax trophozoite [14]

The aim of this paper is to present a model to detect the parasites using a 3D-digital image representation [1,2,3] in order to evaluate the curved surface of the parasite[8]. Digital analysis reduces the processing time taken over manual process. We propose a method to automatically diagnose the parasiteâ„¢s presence by comparing the statistical moments of 3D-image of the uninfected and infected samples after the appropriate transformations to statistically analyze the same with the concept of moments [5,6,7].

II. MOMENT THEOREM

The moments of a function commonly used in probability theory are also applicable to shape analysis. Region moments representation interpret a normalized gray-level image function as a probability density of a 2-D random variable which can also be described using 3D-statistical characteristic moments [4]. Assuming that non-zero pixel values represent a regionâ„¢s moment, a moment of the order is dependent on scaling, translation and even on gray-level transformations.

The set of moments of a bounded function of three variables is defined by the expression,

Â¦..2.1

where j,k,l takes on all non-negative integer values.

The moments of an image are widely used in probability theory. As j,k,l take on all non-negative values, this function generates an infinite set of moments. This set is sufficient to specify the function completely. In other words the set is unique for and only has that particular set of moments. In digitized images we evaluate their sum:

.2.2

where x, y, z and j, k and l are the region point co-ordinates that is pixel co-ordinates of the 3D digitized image. For shape descriptive purposes, we assume that takes on the value 1 inside the object and 0 elsewhere.

The silhouette function reflects only the shape of the object and ignores internal gray-level details. Every unique shape corresponds to a unique silhouette and, to a unique set of moments. The parameter + l is the order of the moment and there is only one zero-order moment.

.Â¦..... 2.3

The central moments are the co-ordinates of the center of gravity of an object.

..Â¦Â¦Â¦Â¦Â¦. 2.4

where, are the central moments that are computed using the center of gravity as the origin.

..2.5

The central moments are position invariant in digitized images.

.2.6

Where xc, yc, zc are the co-ordinates of the regionâ„¢s center of gravity which are obtained using

Â¦.Â¦..... 2.7

In this case represents the region volume. Scale invariant features are found in scaled central moments (scale change x=ax, y=ay ,z=az).

Â¦Â¦Â¦Â¦...Â¦Â¦2.8

.Â¦Â¦Â¦Â¦Â¦Â¦Â¦Â¦..2.9

and are normalized un-scaled central moments.

Â¦Â¦Â¦..Â¦Â¦Â¦Â¦Â¦Â¦Â¦..Â¦...... 2.10

III. PROPOSED MODEL

Further, the above results rely on the solid angle and distance of focus for calculation of the curved surface over the image in 3D. This provides quicker analysis and detection of the protozoan surface in the case of the infected malarial blood cell by combination of theta function and . This curved surface area comes out to be

Â¦. 2.11

This angle leads to a curved-surface area of the object that is quickly detected and interpreted for further diagnosis. This model relies on a unique feature of curved surface evaluation in three dimensions.

The cell is digitally focused from a solid angle which provides 3-Dimensional view of the cellular surface. This surface is further mapped into grid lines with spacing in the sub-micrometer range. The mapped grid is analyzed by processing the image for any discolored or black spots on the grid.

Fig.2 Simulated Grid view of the cell surface

IV. ALGORITHM

Infection (area(grid), n)

Switch (n)

{

Case 1: If ((area(grid),(n) <x1Ã‚Âµm)){cell not infected};

Case 2: if ((area(grid) < x2Ã‚Âµm)){cell is recently infected};

Case 3: if ((area(grid) > x2Ã‚Âµm)){cell is maturing to infection};

Case 4: if ((area(grid) approx. equal to cell size < x2Ã‚Âµm)){cell is totally infected};

}

This algorithm can analyze the age and degree of infection. Here x1 is the minimum curved surface area of plasmodium from top view while x2 signifies the maximum exposed surface area of plasmodium x1=min(area(plasmodium)) and x2=max(area(plasmodium)). The area of grid shows maximum curved surface area of cell normally in the range of 6-8 Ã‚Âµm, which is equal to the diameter of the cell.

The proposed method along with the application of digital image processing will further lead to faster analysis to detect the presence of plasmodium in the blood cell. It also opens for a new approach in dealing with cells that are partially or fully infected and their detection.

V. CONCLUSION

In this paper, we have presented a 3D statistical method to analyse malaria infected blood images. The aim of malarial blood image processing is to detect the parasites infecting the red cellâ„¢s curved surface by evaluating the curved surface using the above principle and technique. The proposed method automatically identifies the parasites curved surface. Further, other parameters like color, shape and size information, extracted by a digital image operation along with the 3D-statistical approach discussed above will increase the accuracy of detection.

REFERENCES

[1] Gonzalez R.C. and Woods. R.E. Digital Image Processing,, Prentice-Hall, Inc, 2nd edition, 2002.

[2] Jain, A.K. Fundamentals of Digital Image Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989.

[3] Pratt W.K., Digital Image Processing, John Wiley and Sons, New York, 2nd edition, 1991.

[4] Cash, G.L. and Hatamian, M. Optical character recognition by the method of moments, Computer Vision, Graphics, and Image Processing 39 (3): 291â€œ310, 1987.

[5] Savini. M Moments in image analysis, Alta Frequenza, 57(2):145-152, 1988.

[6] Hu. M.K. Visual pattern recognition by moment invariants, IRE Transactions Information Theory, 8(2):179-187, 1962.

[7] Maitra, S. Moment invariants, Proceedings IEEE, 67(4):697-699, 1979.

[8] Dempster, A. Ruerto, C.Di. Morphological Processing of Malarial Slide Images, Matlab DSP Conference 1999, Nov, 16-17 1999, Espoo, Finland.

[9] Smyth, J.D. Introduction to animal parasitology, Cambridge University Press, Cambridge, 1994.

[10] Ruberto, C.Di., Dempster, A. Shahid Khan, Bill Jarra, "Segmentation of Blood Images Using Morphological Operators", ICPR, p.3401, 15th International Conference on Pattern Recognition (ICPR'00) - Volume 3, 2000.

[11] Ruberto, C.Di., Dempster, A. Shahid Khan, Bill Jarra, "Automatic Thresholding of Infected Blood Images Using Granulometry and Regional Extrema," ICPR, p.3445, 15th International Conference on Pattern Recognition (ICPR'00) - Volume 3, 2000.

[12] Royal Perth Hospital, Western Australia, Malaria, An on-line Resource Website: http://rph.wa.gov.au/malaria.html

[13] Raviraja, S, Gaurav Bajpai, Sudhir Kumar Sharma, Analysis Of Detecting The Malarial Parasite Infected Blood Images Using Statistical Based Approach, International Conference On Biomedical Engineering (Biomed), Malaysia, 2006.

Address of the corresponding author:

Author: DR. GAURAV BAJPAI

Institute: KIST

Street: BP 3900, FoE, CE&IT

City: KIGALI

Country: RWANDA