Florent Brunet

Binomial convolutions and derivatives estimation from noisy discretizations

We present a new method to estimate derivatives of digitized functions. Even with noisy data, this approach is convergent and can be computed by using only the arithmetic operations. Moreover, higher order derivatives can also be estimated. To deal with parametrized curves, we introduce a new notion which solves the problem of correspondence between the parametrization of a continuous curve and the pixels numbering of a discrete object.

Feature-Driven Direct Non-Rigid Image Registration

The direct registration problem for images of a deforming surface has been well studied. Parametric flexible warps based, for instance, on the Free-Form Deformation or a Radial Basis Function such as the Thin-Plate Spline, are often estimated using additive Gauss-Newton-like algorithms. The recently proposed compositional framework has been shown to be more efficient, but cannot be directly applied to such non-groupwise warps.Our main contribution in this paper is the Feature-Driven framework. It makes possible the use of compositional algorithms for most parametric warps such as those above mentioned. Two algorithms are proposed to demonstrate the relevance of our Feature-Driven framework: the Feature-Driven Inverse Compositional and the Feature-Driven Learning-based algorithms. As another contribution, a detailed derivation of the Feature-Driven warp parameterization is given for the Thin-Plate Spline and the Free-Form Deformation. We experimentally show that these two types of warps have a similar representational power. Experimental results show that our Feature-Driven registration algorithms are more efficient in terms of computational cost, without loss of accuracy, compared to existing methods.

Monocular Template-Based 3D Surface Reconstruction: Convex Inextensible and Nonconvex Isometric Methods

Abstract We study the 3D reconstruction of an isometric surface from point correspondences between a template and a single input image. The template shows the surface flat and fronto-parallel. We propose three new methods. The first two use a convex relaxation of isometry to inextensibility. They are formulated as Second Order Cone Programs (SOCP). The first proposed method is point-wise (it reconstructs only the input point correspondences) while the second proposed method uses a smooth and continuous surface model, based on Free-Form Deformations (FFD). The third proposed method uses the ‘true’ nonconvex isometric constraint and the same continuous surface model. It is formulated with Nonlinear Least-Squares and can thus be solved with the efficient Levenberg–Marquardt minimization method. The proposed approaches may be combined in a single pipeline whereby one of the convex approximations is used to initialize the nonconvex method. Our contributions solve two important limitations of current state of the art: our convex methods are the first ones to handle noise in both the template and image points, and our nonconvex method is the first one to use ‘true’ isometric constraints. Our experimental results on simulated and real data show that our convex point-wise method and our nonconvex method outperform respectively current initialization and refinement methods in 3D reconstructed surface accuracy.

Pixel-Based Hyperparameter Selection for Feature-Based Image Registration

This paper deals with parametric image registration from point correspondences in deformable environments. In this problem, it is essential to determine correct values for hyperparameters such as the number of control points of the warp, a smoothing parameter weighting a term in the cost function, or an M-estimator threshold. This is usually carried out either manually by a trial-and-error procedure or automatically by optimizing a criterion such as the Cross-Validation score. In this paper, we propose a new criterion that makes use of all the available image photometric information. We use the point correspondences as a training set to determine the warp parameters and the photometric information as a test set to tune the hyperparameters. Our approach is fully robust in the sense that it copes with both erroneous point correspondences and outliers in the images caused by, for instance, occlusions or specularities.

Simultaneous Image Registration and Monocular Volumetric Reconstruction of a Fluid Flow

We propose to combine image registration and volumetric reconstruction from a monocular video of a draining off Hele-Shaw cell filled with water. A Hele-Shaw cell is a tank whose depth is small (e.g. 1 mm) compared to the other dimensions (e.g. 400 800 mm 2 ). We use a technique known as molecular tagging which consists in marking by photobleaching a pattern in the fluid and then tracking its deformations. The evolution of the pattern is filmed with a camera whose principal axis coincides with the depth of the cell. The velocity of the fluid along this direction is not constant. Consequently, tracking the pattern cannot be achieved with classical methods because what is observed is the integration of the marked molecules over the entire depth of the cell. The proposed approach is built on top of classical direct image registration in which we incorporate a volumetric image formation model. It allows us to accurately measure the motion and the velocity profiles for the entire volume (including the depth of the cell) which is something usually hard to achieve. The results we obtain are consistent with the theoretical hydrodynamic behaviour for this flow which is known as the laminar Poiseuille flow.

Direct Image Registration without Region of Interest

Standard direct image registration consists in estimating the geometric warp between a source and a target images by maximizing the photometric similarity for the pixels of a Region of Interest (ROI). The ROI must be included in the real overlap between the images otherwise standard registration algorithms fail. Determining a proper ROI is a hard ‘chicken-and-egg’ problem since the overlap is only known after a successful registration. Almost all algorithms in the literature consider that the ROI is given. This is generally either inconvenient or unreliable. In this paper we propose a new method that registers two images without using a ROI. The key idea of our method is to consider the off-target pixels as outliers. We define the off-target pixels as those pixels of the source image mapped outside the target image by the current warp. We use the classical robust M-estimation framework to handle both the off-target pixels and the usual outliers caused, for instance, by occlusions. With our formulation, the true image overlap is defined as the set of inliers. Experiments on synthetic and real data with the homography and Free-Form Deformation show that our method outperforms standard approaches in terms of accuracy and robustness while precisely retrieving the overlap in the source and target images.