Traditional methods of imaging Muller-matrix polarimetry ensure obtaining large arrays of experimental data in the form of 16 Muller-matrix images. Processing and comparative analysis of the received information is quite time-consuming and requires a long time. A new algorithmic polarization-singular approach to the analysis of coordinate distributions of matrix elements (Mueller-matrix maps) of polycrystalline birefringent structure of biological tissues is considered. A Mueller-matrix model for describing the optical anisotropy of biological layers is proposed. Analytical correlations between polarization-singular states of the object field and characteristic values of Mueller-matrix images of birefringence soft tissue objects were found. The proposed algorithmic polarization-singular theory is experimentally verified. Examples of polarization singularities networks of Mueller-matrix maps of histological preparations of real tissues of female reproductive sphere are given. Diagnostic possibilities of the developed polarization-singular algorithms in diagnostics and differentiation of the stages of extragenital endometriosis are illustrated. Another area of biomedical diagnostics has been successfully tested: polarization-singular criteria for forensic Mueller-matrix determination of the age of myocardial injury of the deceased have been defined.