The problem of computing depth from stereo images is approached as a mathematically ill-posed problem by using regularization theory. A variational principle for the reconstruction of surfaces in the presence of depth discontinuities is presented. Discontinuities are preserved using a controlled-continuity stabilizing functional which provides a local control over the smoothness properties of the solution. A discontinuity stabilizing functional imposes a curvilinear smoothness constraint on discontinuities to enable their reconstruction. The location of depth discontinuities is further restricted by using information from intensity edges. An iterative optimization method for the computation of depth is obtained, and a computer experiment with synthetic data is shown.
Si descrive un metodo per la risoluzione approssimata delle equazioni per acque basse ed il software sviluppato per la implementazione dello schema numerico.
shallow water
numerical scheme
numerical solution of PDE
hydrodynamics
The computation of stereo disparity is a mathematical ill-posed problem. However, using regularization theory it may be transformed into a well-posed problem. Standard regularization can be to solve ill-posed problems by using stabilizing functionals that impose global smoothness constraints on acceptable solutions. However, the presence of depth discontinuities causes serious difficulties in standard regularizations, since smoothness assumptions do not hold across discontinuities. This paper presents a regularization approach to stereopsis based on controlled-continuity stabilizing functionals. These functionals provide a spatial control over smoothness, allowing the introduction of discontinuities into the solution.An iterative method for the computation of stereo disparity is derived, and the result of a computer simulation with a synthetic stereo pair of image is shown.
The matrix recursive expression for the computation of the Discrete Fourier Transform of a complex sequence is constructed. The properties of the matrices involved in the recursive expression are exposed. The report contains also a software for the computation of the FFT.
