A methodology for estimating the shape of biconcave red blood cells using multicolor scattering images

Biomedical Signal Processing and Control 8 (2013) 263–272

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A methodology for estimating the shape of biconcave red blood cells using multicolor scattering images G. Apostolopoulos a,∗ , S.V. Tsinopoulos b , E. Dermatas a a b

Department of Electrical Engineering and Computer Technology, University of Patras, Campus, 6 Eratosthenous Str, 26500, Patras, Greece Department of Mechanical Engineering, Technological Educational Institute of Patras, 26334 Patras, Greece

a r t i c l e

i n f o

Article history: Received 17 February 2012 Received in revised form 3 November 2012 Accepted 6 November 2012 Available online 5 December 2012 Keywords: Human red blood cell Neural network Light scattering Angular radial transform Gabor filters bank Radial basis function Boundary element method Independent component analysis Principal component analysis

a b s t r a c t In this paper, a novel methodology for estimating the shape of human biconcave red blood cells (RBCs), using color scattering images, is presented. The information retrieval process includes, image normalization, features extraction using two-dimensional discrete transforms, such as angular radial transform (ART), Zernike moments and Gabor filters bank and features dimension reduction using both independent component analysis (ICA) and principal component analysis (PCA). A radial basis neural network (RBFNN) estimates the RBC geometrical properties. The proposed method is evaluated in both regression and identification tasks by processing images of a simulated device used to acquire scattering phenomena of moving RBCs. The simulated device consists of a tricolor light source (light emitting diode – LED) and moving RBCs in a thin glass. The evaluation database includes 23,625 scattering images, obtained by means of the boundary element method. The regression and identification accuracy of the actual RBC shape is estimated using three feature sets in the presence of additive white Gaussian noise from 60 to 10 dB SNR and systematic distortion, giving a mean error rate less than 1% of the actual RBC shape, and more than 99% mean identification rate. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction Red blood cells (RBCs) are the most common type of blood cell, filled with hemoglobin, a bio-molecule that can bind to oxygen. In humans, red blood cells take the form of flexible biconcave disks, lack a cell nucleus, sub-cellular organelles and the ability to synthesize protein, and live for about 120 days. Several blood diseases change the typical size and distribution of red blood cells, including: Anemia, malaria parasites, microangiopathic diseases etc., these pathologies generate fibrin strands that sever RBCs as they try to move past a thrombus. In medical diagnostic systems, understanding how a light beam interacts with blood suspensions or a whole-blood medium is of paramount importance in quantifying the RBCs inspection process in many commercial devices. The correlation between the obtained patterns and the physical characteristics of blood, such as the relative concentration of hemoglobin and the degree of oxygen saturation, is determined with the aid of simple multiple-scattering theories when dilute suspensions of blood are used [1–3]. Light

∗ Corresponding author. Tel.: +30 2610 991722; fax: +30 2610 991855. E-mail addresses: [email protected], [email protected] (G. Apostolopoulos), [email protected] (S.V. Tsinopoulos), [email protected] (E. Dermatas). 1746-8094/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.bspc.2012.11.002

scattering has been used for efficient and accurate measurement of the geometrical properties of micro-particles [4–7]. The human RBCs’ size and shape is estimated using simulated scattering images first at 632.8 nm and thereafter the method was expanded at twelve discrete equally spaced wavelengths, from 432.8 to 1032.8 nm [8–10]. Real scattering images are obtained using similar device given in [11–18]. In this paper, the design of a novel low-cost device for acquisition of scattering images of biconcave-shaped RBCs is proposed and shown in Fig. 1, consisting of multi-LED light sources, two iris diaphragms, a Fourier convex lens, the flow chamber, a color filter wheel and a digital camera. The digital images are derived when a LED beam illuminates the RBCs-flow at different positions of the color filter wheel. The simulated device is used to estimate the diameter, maximum and the minimum thickness of the human RBCs and to identify the RBCs geometrical properties using image processing, data reduction and non-linear regression techniques. According to the linear theory of light, the acquisition of multiple images for the same RBC solution using the low-cost but broad spectrum LEDs and color filters produces rich but also redundant information, related to wavelength-dependent absorption and scattering phenomena. Therefore, in the neural-network based estimator and identification system of the RBC geometric properties, noise and data reduction methods are implemented using robust feature extraction and feature compression algorithms,

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Fig. 1. The schematic diagram of the proposed device used to acquire scattering images in a RBC-flow.

preserving the scattering information. The ICA and PCA algorithms achieve significant dimensionality reduction, decreasing also the required data-size of the neural-network training algorithm. The structure of this paper is as follows: Section 2 presents the acquisition process of the RBC scattering images and the linear theory of light. Section 3 presents both feature extraction and compression process and the proposed neural regression and identification methods. The evaluation process including the numerical experiments, the regression and identification results are presented and discussed in Section 4. A short conclusion is given in the last section.

2. The acquisition device of RBCs scattering images A schematic diagram of the LED-based acquisition device of RBCs scattering images is shown in Fig. 1, consisting of multi-LED light sources, two iris diaphragms, a Fourier convex lens, a thin flow chamber, a color filter wheel and a digital camera. In the real device, the test-sample must be washed in an isotonic sodium chloride dilute solution [11], must be fed continuously into the flow chamber at a constant flow rate by a syringe pump and must be dilute minimizing the discrepancies between the acquired real images and the simulated images derived by solving single EM scattering problems. The simulated images are used to train the neural estimators. As the concentration of RBCs increases, the multiple scattering phenomena become more pronounced and for that reason the proposed methodology is limited to low RBC concentrations. In the real device, due to flow effect, the RBCs in the flow chamber become aligned with respect to the macroscopic flow direction. The polarized light beam is propagated in the direction of the large diameter of the RBC and the electrical wave is parallel to its axis of axisymmetry. The forward light-scattering pattern is created by a light emitting diode focused on the camera photoelectric sensor. The beam stopper, used in the previous device [8–12], is not required because LEDs have low and easily controlled power emission. When the oriented moving RBCs are illuminated by a wide spectrum LED source (Fig. 1), scattering phenomena of a single RBC type are recorded and can be approximated using the linear theory of light: Jnk =



G Ledn · G PS · G CF · I ,

(1)

k



where I are the scattering images at  different wavelengths, i.e., each pixel of the image Jnk is a linear weighted sum of the emis sion power of the nth LED GLed , the gain of the optical components n

 and the kth color filter absorption and the photoelectric sensor GPS  GCF . k

3. RBC shape estimation According to [19,20], healthy human RBCs (Fig. 2) have an axisymmetric biconcave-shaped geometry with z indicating the axis of the symmetry. Typical values of the important parameters: diameter (R1 ), the maximum thickness (R2 ) and the ratio (R3 /R2 ) of the RBC (shown in Fig. 2) vary from 4.5 to 10.5 ␮m, 1.5 to 3 ␮m and 0.4 to 0.8, respectively. In the proposed device, scattering phenomena of a single RBC type are recorded in multiple scattering images using a wheel of K color filters and N LEDs. Each image is acquired using a unique pair of LED and color filter. Therefore, for each RBC solution M = N × K scattering images are acquired. In this framework, two inverse problems are solved using non-linear regression and identification methods. The Geometry Estimation of Erythrocyte using Multiple Color Filters (GEEMCoF) derives the three most important geometrical properties R1 , R2 , R3 of the RBC as shown in Fig. 2, and the corresponding identification problem detects the RBC type from a finite set of RBC alternatives. Both solutions share the same processing steps: Image normalization, feature extraction, linear feature transformation and reduction. In the regression problem, the last processing module consists of a three output RBF-NN where the three geometrical properties are estimated. In the identification problem the same type of RBF-NN is used and the number of output neurons is equal to the number of RBC types. The identified RBC type is located in the most activated output neuron.

3.1. Image normalization - features extraction Taking into account that the mean image brightness is not related to the RBC size, a linear normalization of the pixel intensity values, according to actual mean brightest of the acquired image, is applied to eliminate this irrelevant information. At each of the M images, the same information extraction process is applied and a feature vector is estimated. The individual M feature vectors are used to construct the extended feature vector. The extraction of the most effective scattering information, which is directly related to the RBC geometrical properties, is close related to the features selection problem. In the absence of related studies, robust feature sets related to the Angular Radial Transform (ART), the Zernike moments and Gabor filters are used to encode the image data. The proposed feature extraction method is shown in Fig. 3.

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Fig. 2. A representation of a healthy human RBC according to [19,20].

Fig. 3. Features extraction process from multiple scattering images.

3.1.1. Angular radial transform The angular radial transform (ART) is a moment-based image description method and can be used to encode region-based information [21]. This integral transformation provides a compact and efficient expression of brightness distribution within a 2-D object region, describing both connected and disconnected region shapes. The ART is a complex orthogonal transformation defined on a unit disk that consists of the complete orthogonal sinusoidal basis functions in polar coordinates [22,23].



2



fn,m =

1

Vn,m (r, ) · I(r, ) · r · dr · d, 0

(2)

the unit disk. In polar coordinates the Zernike function Znm (r, ) is defined by: Zn±m (r, ) = Rnm (r) · ejm ,

(3)

where Rnm (r) are the Zernike polynomials. The index n is the degree of the polynomial, while m is the polynomial order. The Zernike polynomials are defined as a finite sum of powers of r2 :



(n−|m|)/2

Rnm (r) =

k=0

(−1)k · (n − k)! · r n−2k , k! · ((n + |m| /2) − k)! · ((n − |m| /2) − k)! (4)

0

where I(r,) is the RBC image in polar coordinates, Vn,m (r,) the ART basis function that is separable along the angular and radial directions. The ART descriptor is defined as a set of normalized magnitudes of ART coefficients. In applications where rotational invariance is required, the magnitude of the coefficients is estimated. The ART shape feature vector is composed by the real parts of the ART coefficients. In MPEG-7, twelve angular and three radial functions are used, i.e., 0 ≤ n < 3, 0 ≤ m < 12 [22]. 3.1.2. Zernike moments In typical optical systems, lenses, fibers and other components are often circular. Therefore, several properties of the optical systems, such as deformations and aberrations, can be efficiently described using Zernike functions, because these form a complete, orthogonal basis over the unit circle. The moments proposed by Frederik Zernike in 1934 [24], were used in digital image analysis problems in [25] and evaluated for many types of images [26–28]. According to Khotanzad and Hong [28] a neural network using Zernike moments has strong separability to identify shapes. The Zernike moments defined as a family of orthogonal functions over

where n = 0,1,2, . . ., ∞ and m = −n, −n + 2, −n + 4, . . ., +n, with n − |m| = even and |m| ≤ n. The Zernike moments are orthogonal, ensuring that there is minimum correlation among the moments and therefore minimum redundancy of information, invariant both to rotation and displacement. The Zernike moments of an image I(r,) are the projections of the image onto the orthogonal basis of the Zernike functions and are complex numbers: n+1  ·  ∞

= a±m n

n=0

+n 

I(r, ϑ) · Znm (r, ϑ).

(5)

m = −n, n − |m| = even, |m| ≤ n

The factor (n + 1/␲) is used to normalize the moment’s expression. In this research, Zernike functions of degree n = 6 and order m = −n,−n + 2,−n + 4, . . ., +n have been chosen.

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3.1.3. Gabor filters bank The spatial band-pass Gabor filters have excellent resolution in both spatial and frequency domains. The Daugman [29] generalized the Gabor filters in two dimensions, which can be represented as a complex sinusoidal signal modulated by a Gaussian kernel function [30]: G(x, y, , f ) = e−(1/2)·((x /x )

2

+(y /y )2 )

· cos(2 ·  · f · x ),

(6)

where x = x · cos() + y · sin(), y = y · cos() − x · sin(),  x and  y are the standard deviations of the Gaussian envelope along the x and y dimensions, f is the central frequency of the sinusoidal plane wave, and  is the orientation. The convolution of the scattering image with each of the Gabor filters gives: gf, (x, y) = Is (x, y) × Gf, (x, y)

1. The extended feature vector Xtrain is formed. 2. The ICA is used to estimate both weight matrix WICA and the independent sources S (Eq. (8)). 3. The first q independent components (ICs) with the largest eigenvalues are estimated. The number of components q is equal to the lowest integer that satisfies the following criterion:

min q

j > 0.95 ·

j=1

4.

(7)

where g is the output of the filter, IS the scattering image and G the filter Gabor. Due to the fact that filter’s output is a complex function, the filtered image is given by the corresponding magnitude.

q 

5. 6. 7.

Q 

j ,

j=1

with, q < Q, j ≥ j+1 , Q is the number of features and j is the jth eigenvalue of the covariance matrix of vector Xtrain . The reduced training vector XICs is derived multiplying the pseudo-inverse of matrix WICA , which is composed by the eigen† vectors estimated in step 3, and Xtrain , i.e. XICs = WICA · Xtrain . The covariance matrix C of the XICs vectors is estimated. Both eigenvectors and eigenvalues of the covariance matrix C are estimated. The p eigenvectors with the largest eigenvalues which are also greater than the mean eigenvalue are estimated:

3.2. Features reduction 1   i , · p p

As shown in (Eq. (1)), where the relation between the scattering images at wavelength  and the image acquired by the proposed device is given, the scattering image of the RBCs solution at any wavelength  is linearly mixed in the acquired images. Therefore, the adopted feature extraction method must be effectively extract, eliminate redundancy and compress the scattering information related to the RBC size and shape from the acquired images. The elimination of the information redundancy is achieved using the well-known ICA [31,32], applied on linearly mixtures sources in the feature space. Taking into account that multiple features describe the same geometrical properties, a solution to the blind source separation problem can be used to define a set of statistically independent features, assuming a linear mixture model: X = W · S,

(8)

where W is the weight matrix, X is the actual extended feature vector, and S is the statistically independent features related to scattering information. In the framework of ICA, both S and W are estimated using the algorithm proposed by Hyvarinen [33], maximizing an approximation of the differential entropy which represents the distance of any distribution from the normal distribution with same mean value and variance. In the ordinal ICA the number of estimated parameters is equal to the number of features. The ICA parameters can be further reduced using PCA [34]. This process does not significantly affect the system response time because the new reduced feature vector is the linear weighted sum of the independent sources and the ICA parameters. Both ICA and PCA linear transformation process can be simplify to: †

Y = WPCA · WICA · X = WIPCA · X,

(9)

†

where WICA is the pseudo-inverse ICA matrix, WPCA is the matrix composed by the most important eigenvectors, and WIPCA = WPCA · † WICA is the features transformation matrix. 3.3. Estimation of the features transformation matrix Given a set of extended feature vectors, the training matrix Xtrain is composed. As shown in (Eq. (9)) the dimensionality of the feature vector is linearly reduced using the transformation matrix WIPCA . The estimation of WIPCA is derived using the following algorithm:

k >

i=1

where  are the eigenvalues of the covariance matrix C. 8. The WPCA is constructed by the k eigenvectors of the greater eigenvalue and the final transformation matrix WIPCA is given † by WIPCA = WPCA · WICA . 3.4. Estimation of RBC shape using the RBF neural network Artificial neural networks have been used widely in many non-linear regression and classification problems [35–39] using computing elements, simulating the information processing of biological neurons. The popular RBF-NN has very efficient training algorithms and only the number of hidden neurons must be defined by the network designer. In the proposed method, the reduced feature vector is normalized and non-linear processed by the RBF-NN to derive the actual RBC size as in [40], i.e. each coefficient of the reduced feature vector is divided by the corresponding standard deviation, estimated in the complete set of training data. The radius of the adopted radial-basis functions, de-noted as spread, can be a network or neuron dependent parameter or can be estimated as part of the training process [41]. 4. Numerical experimental results 4.1. Image database A database of (3 Leds) × (5 filters) × (1575 RBCs) = 23,625 images of 50 × 50 pixels size each is developed. The image database has been designed to cover the RBCs typical size in equal steps of 0.250 ␮m for R1 and R2 and 0.05 for the ratio (R3 /R2 ). The light source is a GaAlP-type light emitting diode (LED) at 570, 587 and 628 nm manufactured by OSRAM, and 5 real color filters [42,43] provided from ROSCO. In the appendix, the corresponding spectral responses of color filters can be found. In regression numerical experiments, the geometrical properties of RBCs are estimated from the set of scattering images simulating the proposed device. In identification numerical experiments, each set of scattering images is classified into a valid set of 787 unique RBC geometry configurations. The simulated images are estimated using the linear theory of light (Eq. (1)), the spectral responses of three LEDs, the five

G. Apostolopoulos et al. / Biomedical Signal Processing and Control 8 (2013) 263–272

100

Mie Soluon [44] BEM results [12]

10

Parallel scaering plane

10 10 10

1

10

0.1

10

S11(θ )

Normalized Differenal Scaering Cross Secon

1000

0.01

10

1E-3 10

267

6

DDA [45] BEM 6 elements per wavelength BEM 20 elements per wavelength

5

4

β=0

o

3

2

1

0

1E-4 10

1E-5

10

1E-6 0

20

40

60

80

100

120

140

160

180

10

-1

-2

-3

Scaering angle [deg]

0

20

40

optical color filters and the solution of the scattering problem of a monochromatic EM plane wave, taking into account both axisymmetric geometry of the scatterer and the non-axisymmetric boundary conditions. Multiple wavelength scattering images are derived using the boundary element method (BEM) developed in [12]. The calculation time for one simulation of RBC scattering with BEM is 404.16 s, using a PC with dual core CPU at 2.40 GHz rate clock and 8.00 GB of RAM. In appendix, simulated scattering images of biconcave shaped erythrocytes are shown. 4.2. Verification of the BEM code The accuracy of the utilized BEM code is demonstrated by solving two scattering problems. The first one has a known exact analytical solution and deals with the scattering of an EM plane wave by a dielectric spherical particle of radius a. The relative refractive index of the particle is 1.05 and the dimensionless frequency of the problem is kext a = 80, with kext being the free-space wave number. The Differential Scattering Cross Section (DSCS), as defined in [12], is calculated on the plane formed by the wavepropagation and the wave polarization vectors (parallel scattering plane). The calculated DSCS, normalized by a2 , is plotted in the Fig. 4 as a function of the scattering angle, noting that the forward direction corresponds to 0◦ . The analytical solution provided by the exact Mie solution [44] is also plotted and is in excellent agreement with the obtained BEM results. The second problem deals with the EM scattering of a RBC and has been solved in [45] by means of the discrete dipole approximation (DDA). In [45], the geometry of a RBC has been modeled as a biconcave discoid according to the equation:



z() = R ·

1−

  2  R

·

C0 + C1 ·

  2 R

+ C2 ·

  4  R

,

(10)

100

120

140

160

180

element of the Mueller matrix [44] as a function of the scattering angle , on the x–z plane is presented, for ˇ = 0◦ and ˇ = 90◦ , respectively. The BEM results are compared to those obtained by the DDA in [45] and are in almost excellent agreement. The BEM results for the two different discretizations are identical. 4.3. Training and evaluation of the RBF-NN The original images are distorted using both additive white Gaussian noise from 60 to 10 dB SNR which approximate several phenomena in real image acquisition systems (such as thermal-noise in CCD) and systematic distortions which caused by non-proper alignment of optical and sensor elements. The training data of the RBF-NN consist of 788 RBC configurations, i.e. (3 LEDs) × (5 color filters) × (788 RBCs) = 11,820 images are used, and for the regression and identification numerical experiments the remaining 3 × 5 × 787 = 11,805 images are selected. Both training and testing sets are uniformly distributed in the RBC sizes. The identification process is completed by the nearest classification rule of the Euclidean distance between the regression values of the RBF-NN and the 787 RBC sizes used to build the image database.

10 10 10 10 10 10 10

with C0 = 0.187, C1 = 1.035, C2 = −0.774, whereas z and  are the cylindrical coordinates and D = 2R is the RBC diameter. In the present work, the RBC diameter is D = 7.5 ␮m and the relative refractive index m equals 1.03. The EM incident plane wave is of wavelength  = 0.4936 ␮m and propagates along the z-axis. Two orientations of the RBC are considered; for the first one the axis of symmetry is along the z-axis (ˇ = 0◦ ) and for the second the axis of symmetry is along the x-axis (ˇ = 90◦ ). In order to check the convergence of the BEM code two discretizations, with 6 and 20 elements per wavelength, respectively, are utilized. In Figs. 5 and 6, the S11

80

Fig. 5. S11 element of the Mueller matrix as a function of the scattering angle , on the x–z plane for ˇ = 0◦ .

S11(θ )

Fig. 4. DSCS, normalized by a , as a function the scattering angle for a spherical particle with a relative refractive index of 1.05 and a dimensionless frequency of kext a = 80; (a) analytical results obtained by the exact Mie solution [44] (solid line) and (b) numerical results obtained by the used BEM code [12] (filled circles).

60

Scaering angle θ [deg]

2

10 10 10

6

DDA [45] BEM 6 elements per wavelength BEM 20 elements per wavelength

5

4

β = 90

o

3

2

1

0

-1

-2

-3

0

20

40

60

80

100

120

140

160

180

Scaering angle θ [deg] Fig. 6. S11 element of the Mueller matrix as a function of the scattering angle , on the x–z plane for ˇ = 90◦ .

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Fig. 7. Features extraction using real parts of the ART coefficients.

In the hidden layer of the RBF-NN, both the number of neurons and the spread value of the Gaussian radial function kept constant with values 100 and 10 respectively. In the following regression numerical experiments the features derived by the ART transform, the Zernike moments and Gabor filters are evaluated and the mean absolute error between the actual geometrical properties of the RBC and the RBF-NN is estimated, denoted as regression error (MRE). 4.4. ART features Each simulated scattering image is converted in polar coordinates, the inner product among images and each mask of the ART basis functions is obtained, and thus each image can be described by a vector of 12 × 3 = 36 features. Due to the fact that the real part of coefficient f0,0 is used to normalize the rest 35 coefficients of the feature vector, eventually each image is described by a vector of 35 features (Fig. 7). 4.5. Zernike features The feature vector is composed by the real parts of the Zernike creating 28 coefficients. To verify the robustness of moments a±m n the Zernike moments to additive noise a scattering image is distorted at 10 and 60 dB SNR. The dominant moments of the image

remain almost the same regardless the level of noise, as shown in Fig. 8. 4.6. Gabor filters features In this evaluation, 15 Gabor filters are designed, consisting of five orientation parameters,  ∈ {0, n/2, n, 3n/2, 2n} and three spatial frequencies f ∈ {0.06,0.1,0.14}, respectively. The feature vector is composed by the filter’s outputs, creating 15 filtered images, where the coefficients will be formed by the first two central moments of the filtered images. Therefore, each scattering image will be described by a vector of 30 coefficients: fGabor = [1,1 , 1,1 , 1,2 , 1,2 , . . . , n,m , n,m ]

(11)

where n,m and  n,m are the mean value and standard deviation respectively, for n spatial frequencies and m orientations. The MRE versus the level of noise is shown in Figs. 9–11. In general, lower MRE is achieved when the ART shape features are used not only for parameter R1 but also for the other two geometrical parameters of erythrocyte, as shown in Figs. 9–11. The Gabor and Zernike feature extraction methods follow with slightly worse results. Moreover, the ART shape features not only give better estimation of geometrical properties of RBC than the other two

Fig. 8. Noisy at 10 dB (blue color) and noiseless 60 dB (dark red color) Zernike moments of a single scattering image. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

G. Apostolopoulos et al. / Biomedical Signal Processing and Control 8 (2013) 263–272

Table 1 Number of features and recognition accuracy applied in the primitive features vector.

ART Zernike moments Gabor

0.9

0.7 0.6 0.5 0.4 0.3 0.2 10

20

30

40

50

60

SNR (dB) Fig. 9. MRE of maximum diameter R1 versus the noise level using ART, Zernike and Gabor features.

Primitive feature vector

Independent components

Reduced feature vector

Recognition rate at 10 dB SNR

ART Zernike Moments Gabor Filters

525 420 450

170 115 120

7 4 4

60.3% 45.2% 41.8%

extraction methods but also have great robustness in the presence of noise. At each features extraction method, the mean identification rate (MIR) versus the level of noise is estimated giving mean error of the estimated geometrical parameters of erythrocyte less than 1% of the actual RBC size. Table 1 shows the number of features at every step of the features reduction algorithm. In the last column, the recognition accuracy of the nearest classification rule of the RBFNN estimator in the extremely noisy environment of additive white noise at 10 dB SNR is shown.

120

Maximum Thickness

Laser, HeNe at, 632.8 nm, ART GEEMCoF, ART

3.5

3.0

MRE (%)

2.5

2.0

1.5

1.0

0.5 10

20

30

40

50

100

Mean Idenficaon Rate (%)

ART Zernike moments Gabor

Spread of RBF-NN = 10, Number of neurons = 100

4.0

80

60

40

20

0 10

20

Fig. 10. MRE of maximum thickness R2 versus the noise level using ART, Zernike and Gabor features.

Laser, HeNe at 632.8 nm, Zernike moments GEEMCoF, Zernike moments

15

10

5

40

50

60

SNR (dB) Fig. 11. MRE of ratio n versus the noise level using ART, Zernike and Gabor features.

100

Mean Idenficaon Rate (%)

20

Spread of RBF-NN = 10, Number of neurons = 100

ART Zernike moments Gabor

25

MRE (%)

60

120

Rao

30

50

Fig. 12. MIR of RBCs geometrical properties for the ART features in noisy environment using the proposed device, and a similar device using a monochromatic red light source laser He–Ne at 632.8 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

30

20

40

SNR (dB)

SNR (dB)

10

30

60

80

60

40

20

0 10

20

30

40

50

Spread of RBF-NN = 10, Number of neurons = 100

MRE (%)

0.8

Feature extraction

Spread of RBF-NN = 10, Number of neurons = 100

1.0

Spread of RBF-NN = 10, Number of neurons = 100

Maximum Diameter 1.1

269

60

SNR (dB) Fig. 13. MIR of RBCs geometrical properties for the Zernike features in noisy environment using the proposed device, and a similar device using a monochromatic red light source laser He–Ne at 632.8 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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80

60

40

20

10

20

30

40

50

60

SNR (dB) Fig. 14. MIR of RBCs geometrical properties for the Gabor features in noisy environment using the proposed device, and a similar device using a monochromatic red light source laser He–Ne at 632.8 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

In the proposed device, multi-LED and multi-color optical filters are used to improve the identification accuracy of the RBCs geometry, compared to the previously proposed device [8–10,12]. A quantitative comparison of the devices accuracy is given in Figs. 12–15 where the MIR is compared with the rate achieved

100 90 80 70 60 50 40 10

20

30

40

50

Spread of RBF-NN = 10, Number of neurons = 100

Mean Idenficaon Rate (%)

100

GEEMCoF, ART GEEMCoF, ART, Systemac distorons

110

Mean Idenficaon Rate (%)

Laser, HeNe at 632.8 nm, Gabor filter bank GEEMCoF, Gabor filter bank

Spread of RBF-NN = 10, Number of neurons = 100

120

60

SNR (dB) Fig. 15. MIR of RBCs geometrical properties using the proposed device, with the effect of systematic distortion caused by a non-proper alignment of optical and detecting elements in noisy environment.

when scattering phenomena of a single RBC type are recorded using monochromatic red light source laser He–Ne at 632.8 nm. The MIR of the RBCs geometrical properties using the proposed device is significantly improved compared to MIR achieved when

Fig. 16. A noiseless RBC scattering image in which has been added systematic distortion caused by a non-proper alignment of optical and detecting elements.

Fig. 17. A noisy RBC scattering image in which has been added systematic distortion caused by a non-proper alignment of optical and detecting elements.

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Fig. 18. (a) A real healthy RBC scattering image which derived by the device developed in [11]. The black spot on the image been caused by the beam stopper in order to prevent the light from blinding the CCD camera (b) Simulated RBC scattering image derived by the proposed device.

Fig. 19. (a) Blue color, deep-dyed polyester film, 1.5 mm thickness, (b) Green color, deep-dyed polyester film, 2.0 mm thickness (c) Yellow color, deep-dyed polyester film, 2.0 mm thickness (d) Orange color, co-extruded polycarbonate film, 3.0 mm thickness (e) Red color, co-extruded polycarbonate film, 3.0 mm thickness. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

the scattering images are recorded using a single monochromatic red light source laser He–Ne at 632.8 nm. At 10 dB SNR, the success recognition rate using ART shape features increases at least three times, exceeding the 60%. Similar behavior is met for the Gabor and Zernike features but with lightly lower MIRs at the same level of noise. Demonstrating the robustness of the method, the MIR in the presence of systematic distortion caused by a non-proper alignment of optical and detecting elements is estimated. More specific, a constant Gaussian-shaped distortion is added near the image center. Both types of noise, i.e. white Gaussian and constant distortion is used to reduce the image quality. The MIR rate of the estimated properties of RBCs even in case where noisy features are used to train the RBF-NN is excellent as shown in Fig. 15. At 10 dB SNR the recognition rate is slightly worse due to the effect of white noise and the systematic distortion. From the 20 dB SNR and above the recognition rate is less than 1% than the rates derived from images without the systematic distortion. The proposed method regardless of feature extraction process shows better correct recognition rates with remarkable robustness in the noise presence. At 30 dB SNR, the MIR exceeds to 99%, while from 35 dB SNR and above almost the error-free rate is achieved.

On a PC with quad core CPU at 2.53 GHz rate clock and 4.00 GB of RAM, the time of the inversion is 1.9907 s, a frame rate for real-time systems. 5. Conclusions In this paper, the design of a novel device for acquisition of scattering images of biconcave-shaped RBCs is proposed, and a fully automated method for the estimation of RBC shape using image processing and supervised neural network techniques are implemented and numerical evaluated. The single scattering phenomena of a RBC are recorded in images whereas each image is acquired using a unique pair of LED and color filter. As shown in Section 4, excellent detection and identification rates for three important geometrical properties of human biconcave-shaped RBC are obtained by the proposed method, even in cases where the simulated images are distorted by white Gaussian noise at very noisy environment of 10 dB SNR. The use of multi-LED and multi-color optical filters dramatically improves the identification accuracy, compared to device [8–10,12] that had been previously proposed in the literature in which the scattering phenomena of a single RBC type are recorded

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