Tham khảo tài liệu 'advanced biomedical engineering part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Image Processing Methods for Automatic Cell Counting In Vivo or In Situ Using 3D Confocal Microscopy 191 Apoptotic cells The typical histogram h q where q is the grey level intensity of median-filtered Caspase images is composed of two modes the first one corresponding to the background and the second one to the sample. There isn t a third mode that would belong to the apoptotic cells due to the very small number of pixels belonging to them. In some Caspase images the histogram becomes unimodal when the background is so low as to disappear and images only include the sample. The following thresholding method was developed. The shape of the second mode corresponding to the sample can be roughly approximated to a Gaussian function G q and the pixels belonging to the Caspase cells are considered outliers. The highest local maximum of the histogram serves to identify the sample mode. To identify the outliers assuming the sample s pixel grey level intensities are normally distributed the Gaussian function Gb q that best fits the shape of the sample s mode is found. This is achieved by minimizing the square error between the histogram h q in the interval corresponding to the mode and G q that is Gb q arg I min error q I 3 qmin qc qmax J where error q qq G q - h q 2 4 q and - q-P q 2 G q e 5 Li q and ơ q are the mean and standard deviation of the mode respectively calculated in the interval q qmax given by qmax qmax qj i Pi qh q q - P 2 qmax qmax q h q q h q q q q qc is a cut-off value given by the global minimum between the first and the second modes if the histogram is bimodal or the first local minimum of the histogram if it is unimodal and qmax is the maximum grey level of the histogram. The threshold is obtained from the standard score z-score which rejects the outliers of the Gaussian function. The z-score is given by z q - pb 7 ơb where iib and ơb are the mean and standard deviation of the best Gaussian function respectively and q is pixel intensity. It is .
