# On the Problems of Constructing Minimal Realizations for Two-Dimensional Filters

@article{Fornasini1980OnTP, title={On the Problems of Constructing Minimal Realizations for Two-Dimensional Filters}, author={Ettore Fornasini and Giovanni Marchesini}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, year={1980}, volume={PAMI-2}, pages={172-176} }

The input-output behavior of a two-dimensional linear filter is defined by a formal power series in two variables. If the power series is rational the dynamics of the filter is described by updating equations on finite dimensional local state spaces. The class of realizations considered in this paper is constituted by doubly indexed dynamical systems of reduced structure. The construction of the class of minimal realizations is based on matrix representation techniques of noncommutative power… CONTINUE READING

#### Topics from this paper.

#### Citations

##### Publications citing this paper.

SHOWING 1-8 OF 8 CITATIONS

## Linearizing the word problem in (some) free fields

VIEW 2 EXCERPTS

CITES METHODS

HIGHLY INFLUENCED

## Geometric Fault Detection and Isolation of Infinite Dimensional Systems

VIEW 1 EXCERPT

CITES BACKGROUND

## A Geometric Approach to Fault Detection and Isolation of Two-Dimensional (2D) Systems

VIEW 2 EXCERPTS

CITES BACKGROUND

## Noncommuting multidimensional realization theory: minimality, reachability, and observability

VIEW 3 EXCERPTS

CITES RESULTS & BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-2 OF 2 REFERENCES

## Algebraic Realization Theory of Two-Dimensional Filters

VIEW 3 EXCERPTS