Some theoretical challenges in digital geometry: A perspective

In recent years image analysis has become a research field of exceptional significance, due to its relevance to real life problems in important societal and governmental sectors, such as medicine, defense, and security. The explicit purpose of the present Perspective is to suggest a number of strategic objectives for theoretical research, with an emphasis on the combinatorial approach in image analysis. Most of the proposed objectives relate to the need to make the theoretical foundations of combinatorial image analysis better integrated within a number of well-established subjects of theoretical computer science and discrete applied mathematics, such as the theory of algorithms and problem complexity, combinatorial optimization and polyhedral combinatorics, integer and linear programming, and computational geometry.