Ill-posed problems in early vision: from computational theory to analogue networks.

*(English)*Zbl 0587.65085Firstly this paper is a review of regularizing variational principles for some physical problems from the physicians point of view. Special emphasis is laid upon ill-posed problems in early vision, f.i. recovering three dimensional shape from the light distribution in the image.

A large gap exists between computational theories of vision and their possible implementation in neural hardware. Here an analogue model of computation in electrical and chemical networks is suggested and an equivalence with the standard regularization principle is shown. A significant advantage of analogue networks is their extreme parallelism, speed of convergence and robustness against random errors. Electrical and chemical networks can be used similarly and mixed systems are possible. A number of elementary circuit elements can be implemented in equivalent neuronal hardware. The style of analogue computation represents a useful model for neural networks and is a challenge for future very large scale integration circuit designs.

A large gap exists between computational theories of vision and their possible implementation in neural hardware. Here an analogue model of computation in electrical and chemical networks is suggested and an equivalence with the standard regularization principle is shown. A significant advantage of analogue networks is their extreme parallelism, speed of convergence and robustness against random errors. Electrical and chemical networks can be used similarly and mixed systems are possible. A number of elementary circuit elements can be implemented in equivalent neuronal hardware. The style of analogue computation represents a useful model for neural networks and is a challenge for future very large scale integration circuit designs.

Reviewer: N.Köckler

##### MSC:

65Z05 | Applications to the sciences |

68U20 | Simulation (MSC2010) |

90C35 | Programming involving graphs or networks |

49S05 | Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX) |

78A10 | Physical optics |

35R25 | Ill-posed problems for PDEs |