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.
KEYWORDS: Image segmentation, Holograms, Holography, Digital holography, 3D image processing, 3D image reconstruction, Image processing algorithms and systems, Detection and tracking algorithms, 3D acquisition, Image processing
It is necessary to extract target specimens from bioholographic images for high-level analysis such as object identification, recognition, and tracking with the advent of application of digital holographic microscopy to transparent or semi-transparent biological specimens. We present an interactive graph cuts approach to segment the needed target specimens in the reconstructed bioholographic images. This method combines both regional and boundary information and is robust to extract targets with weak boundaries. Moreover, this technique can achieve globally optimal results while minimizing an energy function. We provide a convenient user interface, which can easily differentiate the foreground/background for various types of holographic images, as well as a dynamically modified coefficient, which specifies the importance of the regional and boundary information. The extracted results from our scheme have been compared with those from an advanced level-set-based segmentation method using an unbiased comparison algorithm. Experimental results show that this interactive graph cut technique can not only extract different kinds of target specimens in bioholographic images, but also yield good results when there are multiple similar objects in the holographic image or when the object boundaries are very weak.
Two parallel laser beams are used to align an off-axis parabolic mirror without alignment telescope and reference flat. In this method the optical axis of an off-axis parabolic mirror is made parallel to the incident laser beams, in the plane of incidence, by measuring directions of the reflected beams and by changing height and orientation of the mirror. Then, the focal point ofthe off-axis parabolic mirror is automatically found where the two reflected beams cross each other. The alignment of the optical axis to the incident beams is done without knowing focal length and off-axis distance of the mirror. Alignment sensitivity is derived both numerically and analytically. When focal length is 457 mm, off-axis distance is 127 mm, and diameter is 178 mm, the off-axis parabolic mirror is aligned to the incident beams with an angular error of less than 3 mrad.