In this paper we revisit the Horn and Schunck optical flow method [1], and focus on its interpretation as Gauss-Newton optimisation. We explicitly demonstrate that the standard incremental version of the Horn and Schunck (HS) method1 is equivalent to Gauss-Newton (GN) optimisation of the non-linearised energy, consisting of the sum of squared differences (SSD) criterion and diffusion regularisa...

In this paper, we present Gaussian Process Gauss–Newton (GPGN), an algorithm for non-parametric, continuous-time, nonlinear, batch state estimation. This work adapts the methods of Gaussian process (GP) regression to address the problem of batch simultaneous localization and mapping (SLAM) by using the Gauss–Newton optimization method. In particular, we formulate the estimation problem with a c...

We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...

We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...

Let p be a prime, Zp the ring of p-adic integers, Qp the field of p-adic numbers, and Qp the algebraic closure of Qp. Let Fp be the algebraic closure of the finite field Fp, and ω : Fp → Qp the Techmüller lifting. Let q = pa, χ a multiplicative character of Fq into Q, and ψ a character of Zp[μq−1] into Q of exact order pn > 1, where μr is the set of r-th roots of unity in Qp. For simplicity, we...

Primal-dualinterior-point methods have proven to be very successful for both linear programming (LP) and, more recently, for semideenite programming (SDP) problems. Many of the techniques that have been so successful for LP have been extended to SDP. In fact, interior point methods are currently the only successful techniques for SDP. We present a new paradigm for deriving these methods: 1) usi...

Least squares methods are effective for solving systems of partial differential equations. In the case of nonlinear systems the equations are usually linearized by a Newton iteration or successive substitution method, and then treated as a linear least squares problem. We show that it is often advantageous to form a sum of squared residuals first, and then compute a zero of the gradient with a ...

In order to solve the restriction of the two common calibration modes applied in digital close-range industrial photogrammetry, a new camera calibration method based on orientation points was proposed. Firstly, image sequences were obtained applying a calibration plate with five orientation points. The ellipse detection criteria were applied to eliminate the redundant information from images af...

The preconditioned iteratively regularized Gauss-Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes M−times iterated Tikhonov regularization with line search. Numerical...