Color information plays a significant role in the segmentation of WBCs from peripheral blood smear images. Different staining protocols produce characteristic color distributions in blood components, allowing color-based segmentation algorithms to distinguish nucleus, cytoplasm, RBCs, and background regions more effectively than grayscale approaches [14].

The RGB color space is the most commonly used representation in digital imaging. However, its channels are highly correlated and often fail to provide sufficient discrimination between blood components under varying illumination and staining conditions. Consequently, alternative color spaces have been investigated for hematological image analysis [15].

Among them, the Lab color space has attracted considerable attention because of its perceptual uniformity and ability to separate luminance information from chromatic information. The transformation decomposes an image into three channels:

I. L*: Lightness component.

II. a*: Green-to-red chromatic component.

III. b*: Blue-to-yellow chromatic component.

In stained blood smear images, leukocyte nuclei generally appear as dark purple regions. Since purple coloration is strongly represented within the a* channel, this channel often provides enhanced contrast between nucleus pixels and surrounding structures [16].

Another color representation frequently used in image analysis is the CMYK color space. Unlike RGB, CMYK describes image colors using cyan (C), magenta (M), yellow (Y), and black (K) components. The conversion from RGB to CMYK is expressed as:

K = 1 - max(R,G,B), C = (1 - R - K)/(1 - K), M = (1 - G - K)/(1 - K), Y = (1 - B - K)/(1 - K),

where R, G, and B are normalized RGB values in the range [0,1].

The CMYK representation provides additional information regarding background and non-cellular regions, making it useful for separating blood cells from the slide background under varying acquisition conditions [17].

Classical fuzzy set theory introduced by Zadeh [18] represents uncertainty through a membership function only. However, in many practical image segmentation problems, uncertainty cannot be adequately described using a single membership value.

To address this limitation, Atanassov introduced the concept of IFS, which characterize each element using both membership and non-membership degrees [18].

Let X={x1,x2,…,xn} be a finite universe of discourse.

An IFS A is defined as:

A={⟨x,μA(x),νA(x)⟩:x∈X}, (2)

where μA(x):X→[0,1] denotes the membership degree and νA(x):X→[0,1] represents the non-membership degree. These values satisfy

0 ≤ μA(x)+νA(x)≤1. (3)

The uncertainty associated with element x is represented by the hesitation degree:

πA(x)=1−μA(x)−νA(x). (4)

The hesitation component provides additional information regarding ambiguity and uncertainty, making intuitionistic fuzzy theory particularly suitable for medical image segmentation tasks where boundaries are often ill-defined [19].

The similarity or dissimilarity between two IFS can be quantified using an IFD measure.

Suppose A and B are two IFS defined over the same universe X.

For each element x, the corresponding membership and non-membership values are represented as (μA(x),νA (x)) and (μB(x),νB(x)) respectively.

The IFD proposed by Jati et al. [20] measures the discrepancy between two intuitionistic fuzzy representations and can be employed as an objective criterion in image thresholding problems.

The divergence becomes minimum when the segmented image closely resembles the ideal segmentation and increases as the discrepancy between the two representations grows.

This property makes IFD particularly suitable for determining optimal threshold values in image segmentation applications.

Thresholding aims to partition image pixels into meaningful regions according to their intensity distributions. In IFD-based thresholding, an image is first represented as an IFS. Assume that the image is partitioned into K regions. The mean intensity of the kth region is defined mk. For a pixel with intensity value xi the membership function is computed as [20]:

(xi − mk)2

μ(xi) = exp⁡(− 2 ), (5)

2σk where σk denotes the standard deviation of the corresponding region. The non-membership value is then determined by Yager's complement:

1 − μ(xi)

v(xi) = , (6)

1 + ⁡λμ(xi) where λ>0 is a controlling parameter.

After obtaining the intuitionistic fuzzy representation, divergence values are computed for all candidate threshold combinations.

Let D(t1,t2) denote the IFD corresponding to thresholds t1 and t2 The optimal thresholds are selected according to:

(t1 ∗, t∗ 2) = argmin⁡D(t1, t2). (7)

The selected thresholds are subsequently used to generate the segmented image.

Because the optimization process is based on divergence minimization rather than histogram shape alone, the method generally exhibits greater robustness against intensity variations and noise compared with conventional thresholding approaches [20].

The theoretical concepts described in this section constitute the foundation of the proposed WBC segmentation framework. The integration of color-space analysis and IFD-based thresholding for robust WBC segmentation is presented in the next section.

In this paper, images from three different datasets with varying characteristics were employed to evaluate the different stages of the proposed method. Details of each dataset are described below.

Dataset 1: This dataset consists of 400 images acquired from 100 peripheral blood smears. The blood smears were stained using the Giemsa-Wright method. The images were captured by a digital camera (SONY model No. SSC-DC50AP) mounted on an optical microscope (Microscope-Axioskope 40) equipped with a colorless lens at 100× magnification. All images are color images of size 720 × 576 pixels with 24 bits per pixel, stored in BMP format. The images were collected at the Hematology-Oncology Research Center of Imam Khomeini Hospital (Tehran, Iran) and classified into different types of WBCs by a hematologist. In addition, the nuclear and cytoplasmic regions of the WBCs were manually segmented by an expert. The images in this dataset exhibit significant variation in brightness intensity. This dataset is suitable for nucleus and cytoplasm segmentation of WBCs as well as for the classification of different types of leukocytes [21].

Dataset 2: The microscopic images in this dataset were acquired using a KODAK EasyShare V803 digital camera mounted on a Leica microscope at 100× magnification with an oil-immersion lens. The required blood smears were stained with Giemsa. The images are color images of size 3264 × 2448 pixels with 24 bits per pixel, stored in JPG format.

These images were collected by the specialized Hematology Center at Dr. Juan Bruno Zayas Alfonso Hospital in Santiago, Cuba. Healthy and pathological RBCs were classified by a specialist in this dataset. This database can be used for blood smear image segmentation and RBC classification methods.

Dataset 3: The images in this dataset were captured using a CANON Power Shot G5 digital camera attached to a laboratory microscope with variable magnification (ranging from 300× to 500×). The images are color images with 24 bits per pixel, stored in JPG format. This dataset was prepared at the M. Tettamanti Research Center in Monza, Italy, for the detection of Acute Lymphoblastic Leukemia (ALL) using blood sample image processing techniques. It consists of two subsets: ALL-IDB1 and ALL-IDB2.

The first subset (ALL-IDB1) contains 108 images of size 2592 × 1949 pixels, encompassing a total of 3900 blood elements. Overall, there are 510 lymphoblasts across all images, whose center coordinates were determined by an expert. In each image, the presence or absence of at least one lymphoblast is also indicated. The number of images containing lymphoblasts is equal to the number of images without lymphoblasts. This subset can be used to evaluate the algorithm’s performance in blood smear segmentation and separation of overlapping cells. Moreover, due to the availability of labeled lymphoblasts, it is suitable for assessing the classification power of the system in ALL detection at both image and cell levels.

In blood smear images, WBC nuclei typically appear as dark purple structures due to the staining process. Although grayscale conversion simplifies image representation, it also removes valuable chromatic information that can facilitate nucleus discrimination. Fig. 2 presents representative segmentation results obtained using the original grayscale-based IFD approach. It can be observed that the method performs satisfactorily on certain images but fails when RBCs or other structures exhibit intensity levels comparable to those of the nucleus.

To improve segmentation robustness, the RGB image is transformed into the Lab color space. The Lab representation separates luminance information from chromatic information and has been widely employed in medical image segmentation due to its perceptual uniformity. Among the three channels of the Lab color space, the a-channel provides the strongest contrast between nucleus regions and surrounding structures. Since leukocyte nuclei are predominantly purple, their chromatic characteristics are more effectively represented within this channel.

Fig. 3 demonstrates the segmentation results obtained by applying IFD thresholding to the a-channel. Compared with grayscale processing, the proposed strategy substantially reduces false detections and improves nucleus localization across different datasets.

Fig. 4 provides a visual comparison of the performance of the four nucleus segmentation algorithms on three representative images acquired from Datasets 1, 2, and 3, respectively.

It is observed that the proposed algorithm exhibits greater robustness compared to the three other methods and produces segmentation results closer to the expert’s ground-truth segmentation.