Automatic detection of objects with circular pattern in digital images is an important topic in many fields of research especially in cell imaging. There are many cells in microscopic images that are circular such as Red Blood Cells (RBCs), White Blood Cells, hematopoietic cells and different types of parasite eggs. Automatic detecting, recognizing and quantifying of these cells provide rich information to pathologists to improve the study/diagnosis of different diseases. Many previously proposed methods utilize the edge information of a given image to detect circles that are not usually applicable for complex images. Fast Circlet Transform (FCT) is a new atomic representation based on using circular basis functions in different scales and frequencies which provides a novel and practical tool for circle detection and analysis of images with circular objects/patterns such as microscopic images. In this paper, three strategies based on FCT are proposed with the applications of FCT in cell and tissue microscopy as follows: In first application, a strategy is proposed for detecting and counting RBCs in microscopic images of blood smear in which an initial estimation of the number of RBCs is made and conflict circles are then removed to detect final and true RBCs. In second application, an algorithm is proposed to count and localize glomeruli in microscopic images of kidney sections by analyzing FCT coefficients in order to directly find circular objects. In third application, a method based on FCT is proposed to detect parasites in microscopic images with high unwanted impurities by modifying FCT coefficients and reconstructing the images. Our experimental results show the effectiveness and better performance of the proposed circlet-based methodologies in microscopic image analysis.

自动检测数字图像中带有圆形图案的对象是许多研究领域的重要课题，尤其是在细胞成像领域。显微图像中有许多圆形的细胞，例如红细胞（RBC），白细胞，造血细胞和不同类型的寄生虫卵。这些细胞的自动检测，识别和定量为病理学家提供了丰富的信息，以改善对不同疾病的研究/诊断。许多先前提出的方法利用给定图像的边缘信息来检测通常不适用于复杂图像的圆。快速圆环变换（FCT）是一种新的原子表示形式，它基于使用不同比例和频率的圆形基础函数，它为圆形检测和分析带有圆形物体/图案的图像（如显微图像）提供了一种新颖实用的工具。在本文中，提出了三种基于FCT的策略，并将FCT在细胞和组织显微镜中的应用如下：在第一个应用中，提出了一种用于检测和计数血液涂片显微图像中的RBC的策略，其中初始估计为制作了RBC数量，然后删除了冲突圈，以检测最终的和真实的RBC。在第二个应用中，提出了一种通过分析FCT系数对肾脏切片的显微图像中的肾小球进行计数和定位的算法，以便直接找到圆形物体。在第三项应用中，提出了一种基于FCT的方法，即通过修改FCT系数并重建图像，以检测具有高有害杂质的显微图像中的寄生虫。我们的实验结果表明，在显微图像分析中所提出的基于圆环的方法的有效性和更好的性能。