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A Fokker–Planck Model for Optical Flow Estimation and Image Registration

Author

Listed:
  • Tudor Barbu

    (Institute of Computer Science of the Romanian Academy—Iasi Branch, Bd. Carol I, No. 8, 700506 Iaşi, Romania
    Academy of Romanian Scientists, 050044 Bucharest, Romania)

  • Costică Moroşanu

    (Faculty of Mathematics, “Al. I. Cuza” University, Bd. Carol I, No. 11, 700506 Iaşi, Romania)

  • Silviu-Dumitru Pavăl

    (Faculty of Automatic Control and Computer Engineering, Technical University “Gheorghe Asachi” of Iasi, Str. Prof. dr. doc. Dimitrie Mangeron, nr. 27, 700050 Iaşi, Romania)

Abstract

The optical flow problem and image registration problem are treated as optimal control problems associated with Fokker–Planck equations with controller u in the drift term. The payoff is of the form 1 2 | y ( T ) − y 1 | 2 + α ∫ 0 T | u ( t ) | 4 4 d t , where y 1 is the observed final state and y = y u is the solution to the state control system. Here, we prove the existence of a solution and obtain also the Euler–Lagrange optimality conditions which generate a gradient type algorithm for the above optimal control problem. A conceptual algorithm to compute the approximating optimal control and numerical implementation of this algorithm is discussed.

Suggested Citation

  • Tudor Barbu & Costică Moroşanu & Silviu-Dumitru Pavăl, 2025. "A Fokker–Planck Model for Optical Flow Estimation and Image Registration," Mathematics, MDPI, vol. 13(17), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2807-:d:1739595
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