Foreground automata

AbstractThis paper defines a class of on-line foreground automata, which make distinctions between the “foreground” or relevant inputs and outputs and the “blank” ones that serve as a background. It is shown that there is a well-defined operation that maps the substring of relevant inputs into an eventually appearing substring of relevant outputs, without regard for the blanks scattered among the inputs. This operation plays the role of the computation of an off-line automaton and a computational time can be measured by comparing the automaton to a “benchmark automaton” that produces each relevant output as soon as theoretically possible. Properties of these computational times are explored, both for finite automata and “Turing automata,” which are modeled by multi-tape Turing machines. An analogue of Church's Thesis can be stated for the computations associated with the operations of Turing automata, but it is argued that there is no clear cut formalization for the concept of an “effective foreground automata.

Cellular automata segmentation of brain tumors on post contrast MR images

In this paper, we re-examine the cellular automata(CA) al- gorithm to show that the result of its state evolution converges to that of the shortest path algorithm. We proposed a complete tumor segmenta- tion method on post contrast T1 MR images, which standardizes the VOI and seed selection, uses CA transition rules adapted to the problem and evolves a level set surface on CA states to impose spatial smoothness. Val- idation studies on 13 clinical and 5 synthetic brain tumors demonstrated the proposed algorithm outperforms graph cut and grow cut algorithms in all cases with a lower sensitivity to initialization and tumor type

Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation

In this paper we provide rigorous proof for the convergence of an iterative voting-based image segmentation algorithm called Active Masks. Active Masks (AM) was proposed to solve the challenging task of delineating punctate patterns of cells from fluorescence microscope images. Each iteration of AM consists of a linear convolution composed with a nonlinear thresholding; what makes this process special in our case is the presence of additive terms whose role is to "skew" the voting when prior information is available. In real-world implementation, the AM algorithm always converges to a fixed point. We study the behavior of AM rigorously and present a proof of this convergence. The key idea is to formulate AM as a generalized (parallel) majority cellular automaton, adapting proof techniques from discrete dynamical systems