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A perspective shape-from-shading metod using fast sweeping numerical scheme

Yang L., Han J.

Optica Applicata

2008

Vol. 38, nr 2

387-398

Shape-from-shading (SFS) is an approach of 3-D shape reconstruction from only one image. A new perspective SFS method is proposed in this paper. Firstly, a reflectance map equation under perspective projection is introduced. Then, the reflectance map equation turns into a static Hamilton-Jacobi equation. So the SFS problem is formulated as a viscosity solution of the static Hamilton-Jacobi equation. The fast sweeping numerical method is used to solve the Hamilton-Jacobi equation and a new SFS method is gained. At last, experiments on both synthetic and real images are given. Experiments on the synthetic image show that the proposed SFS method is fast and accurate. Results of the real image show the efficiency of the proposed method when dealing with complicated real surface, and new criteria to evaluate the performance of the method are proposed.

A Method for Constructing ε-value Functions for The Bolza Problem of Optimal Control

Pustelnik J.

International Journal of Applied Mathematics and Computer Science

2005

Vol. 15, no 2

177-186

The problem considered is that of approximate minimisation of the Bolza problem of optimal control. Starting from Bellman's method of dynamic programming, we define the ε-value function to be an approximation to the value function being a solution to the Hamilton-Jacobi equation. The paper shows an approach that can be used to construct an algorithm for calculating the values of an ε-value function at given points, thus approximating the respective values of the value function.

Optimal synthesis via superdifferentials of value function

Frankowska H.

Control and Cybernetics

2005

Vol. 34, no 3

787-803

We derive a differential inclusion governing the evolution of optimal trajectories to the Mayor problem. The value function is allowed to be discontinuous. This inclusion has convex compact right-hand sides.

An Algorithm for Construction of varepsilon-Value Functions for the Bolza Control Problem

Jacewicz E.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 2

391-428

The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an varepsilon-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an varepsilon-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper shows the numerical closeness of the approximate minimum to the infimum of the Bolza functional.