An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration

We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial differential equation (PDE) constrained optimization problem. The PDE constraint consists, in its simplest form, of a hyperbolic transport equation for the evolution of the image intensity. The control variable is the velocity field. Tikhonov regularization on the control ensures well-posedness. We consider standard smoothness regularization based on $H^1$- or $H^2$-seminorms. We augment this regularization scheme with a constraint on the divergence of the velocity field rendering the deformation incompressible and thus ensuring that the determinant of the deformation gradient is equal to one, up to the numerical error. We use a Fourier pseudospectral discretization in space and a Chebyshev pseudospectral discretization in time. We use a preconditioned, globalized, matrix-free, inexact Newton-Krylov method for numerical optimization. A parameter continuation is designed to estimate an optimal regularization parameter. Regularity is ensured by controlling the geometric properties of the deformation field. Overall, we arrive at a black-box solver. We study spectral properties of the Hessian, grid convergence, numerical accuracy, computational efficiency, and deformation regularity of our scheme. We compare the designed Newton-Krylov methods with a globalized preconditioned gradient descent. We study the influence of a varying number of unknowns in time. The reported results demonstrate excellent numerical accuracy, guaranteed local deformation regularity, and computational efficiency with an optional control on local mass conservation. The Newton-Krylov methods clearly outperform the Picard method if high accuracy of the inversion is required.Comment: 32 pages; 10 figures; 9 table

Automatic Face Recognition System Based on Local Fourier-Bessel Features

We present an automatic face verification system inspired by known properties of biological systems. In the proposed algorithm the whole image is converted from the spatial to polar frequency domain by a Fourier-Bessel Transform (FBT). Using the whole image is compared to the case where only face image regions (local analysis) are considered. The resulting representations are embedded in a dissimilarity space, where each image is represented by its distance to all the other images, and a Pseudo-Fisher discriminator is built. Verification test results on the FERET database showed that the local-based algorithm outperforms the global-FBT version. The local-FBT algorithm performed as state-of-the-art methods under different testing conditions, indicating that the proposed system is highly robust for expression, age, and illumination variations. We also evaluated the performance of the proposed system under strong occlusion conditions and found that it is highly robust for up to 50% of face occlusion. Finally, we automated completely the verification system by implementing face and eye detection algorithms. Under this condition, the local approach was only slightly superior to the global approach.Comment: 2005, Brazilian Symposium on Computer Graphics and Image Processing, 18 (SIBGRAPI