| The dramatic increase in number and volume of digital images produced in medical diagnostics, and the escalating demand for rapid access to these relevant medical data, along with the need for interpretation and retrieval has become of paramount importance to a modern healthcare system. Therefore, there is an ever growing need for processed, interpreted and saved images of various types. Due to the high cost and unreliability of human-dependent image analysis, it is necessary to develop an automated method for feature extraction, using sophisticated mathematical algorithms and reasoning.;This work is focused on digital image signal processing of biological and biomedical data in one- two- and three-dimensional space. Methods and algorithms presented in this work were used to acquire data from genomic sequences, breast cancer, and biofilm images. One-dimensional analysis was applied to DNA sequences which were presented as a non-stationary sequence and modeled by a time-dependent autoregressive moving average (TD-ARMA) model. Two-dimensional analyses used 2D-ARMA model and applied it to detect breast cancer from x-ray mammograms or ultrasound images. Three-dimensional detection and classification techniques were applied to biofilm images acquired using confocal laser scanning microscopy.;Modern medical images are geometrically arranged arrays of data. The broadening scope of imaging as a way to organize our observations of the biophysical world has led to a dramatic increase in our ability to apply new processing techniques and to combine multiple channels of data into sophisticated and complex mathematical models of physiological function and dysfunction. With explosion of the amount of data produced in a field of biomedicine, it is crucial to be able to construct accurate mathematical models of the data at hand. Two main purposes of signal modeling are: data size conservation and parameter extraction. Specifically, in biomedical imaging we have four key problems that were addressed in this work: (i) registration, i.e. automated methods of data acquisition and the ability to align multiple data sets with each other; (ii) visualization and reconstruction, i.e. the environment in which registered data sets can be displayed on a plane or in multidimensional space; (iii) segmentation, i.e. automated and semi-automated methods to create models of relevant anatomy from images; (iv) simulation and prediction, i.e. techniques that can be used to simulate growth end evolution of researched phenomenon. Mathematical models can not only be used to verify experimental findings, but also to make qualitative and quantitative predictions, that might serve as guidelines for the future development of technology and/or treatment. |
