Three-dimensional counting of morphologically normal human red blood cells via digital holographic microscopy

Abstract

Abstract. Counting morphologically normal cells in human red blood cells (RBCs) is extremely beneficial in the health care field. We propose a three-dimensional (3-D) classification method of automatically determining the morphologically normal RBCs in the phase image of multiple human RBCs that are obtained by off-axis digital holographic microscopy (DHM). The RBC holograms are first recorded by DHM, and then the phase images of multiple RBCs are reconstructed by a computational numerical algorithm. To design the classifier, the three typical RBC shapes, which are stomatocyte, discocyte, and echinocyte, are used for training and testing. Nonmain or abnormal RBC shapes different from the three normal shapes are defined as the fourth category. Ten features, including projected surface area, average phase value, mean corpuscular hemoglobin, perimeter, mean corpuscular hemoglobin surface density, circularity, mean phase of center part, sphericity coefficient, elongation, and pallor, are extracted from each RBC after segmenting the reconstructed phase images by using a watershed transform algorithm. Moreover, four additional properties, such as projected surface area, perimeter, average phase value, and elongation, are measured from the inner part of each cell, which can give significant information beyond the previous 10 features for the separation of the RBC groups; these are verified in the experiment by the statistical method of Hotelling’s $T$-square test. We also apply the principal component analysis algorithm to reduce the dimension number of variables and establish the Gaussian mixture densities using the projected data with the first eight principal components. Consequently, the Gaussian mixtures are used to design the discriminant functions based on Bayesian decision theory. To improve the performance of the Bayes classifier and the accuracy of estimation of its error rate, the leaving-one-out technique is applied. Experimental results show that the proposed method can yield good results for calculating the percentage of each typical normal RBC shape in a reconstructed phase image of multiple RBCs that will be favorable to the analysis of RBC-related diseases. In addition, we show that the discrimination performance for the counting of normal shapes of RBCs can be improved by using 3-D features of an RBC.