Pose Invariant Shape Prior Segmentation Using Continuous Cuts and Gradient Descent on Lie Groups

This paper proposes a novel formulation of the Chan-Vese model for pose invariant shape prior segmentation as a continuous cut problem. The model is based on the classic L 2 shape dissimilarity measure and with pose invariance under the full (Lie-) group of similarity transforms in the plane. To overcome the common numerical problems associated with step size control for translation, rotation and scaling in the discretization of the pose model, a new gradient descent procedure for the pose estimation is introduced. This procedure is based on the construction of a Riemannian structure on the group of transformations and a derivation of the corresponding pose energy gradient. Numerically, this amounts to an adaptive step size selection in the discretization of the gradient descent equations. Together with efficient numerics for TV-minimization we get a fast and reliable implementation of the model. Moreover, the theory introduced is generic and reliable enough for application to more general segmentation- and shape-models

Discontinuity preserving convex image registration model for MRI of the lung

Imaging the structure and function of the human lungs is of importance for early detection of lung diseases. With the new development of steady state free precession (SSFP) imaging concepts in combination with dedicated image registration methods for fast functional and morphological MRI, it is expected that we are able to study the lung functions. We propose a novel method for image registration of the lung MRI sequences by using a convex optical flow model. The model is based on combined local and global optical flow method and regularized by an anisotropic total variation (TV) norm. The anisotropy derived from the structure tensor in order to take into account local variations at each point and to preserve the discontinuities of the motion fields. Qualitative and quantitative evaluations are done to show the robustness of the method

Variational Segmentation of Image Sequences Using Region-Based Active Contours and Deformable Shape Priors

In this paper we address the problem of segmentation in image sequences using region-based active contours and level set methods. We propose a novel method for variational segmentation of image sequences containing nonrigid, moving objects. The method is based on the classical Chan-Vese model augmented with a novel frame-to-frame interaction term, which allow us to update the segmentation result from one image frame to the next using the previous segmentation result as a shape prior. The interaction term is constructed to be pose-invariant and to allow moderate deformations in shape. It is expected to handle the appearance of occlusions which otherwise can make segmentation fail. The performance of the model is illustrated with experiments on synthetic and real image sequences

View Point Tracking of Rigid Objects based on Shape Sub-Manifolds

We study the task to infer and to track the viewpoint onto a 3D rigid object by observing its image contours in a sequence of images. To this end, we consider the manifold of invariant planar contours and learn the low-dimensional submanifold corresponding to the object contours by observing the object off-line from a number of different viewpoints. This submanifold of object contours can be parametrized by the view sphere and, in turn, be used for keeping track of the object orientation relative to the observer, through interpolating samples on the submanifold in a geometrically proper way. Our approach replaces explicit 3D object models by the corresponding invariant shape submanifolds that are learnt from a sufficiently large number of image contours, and is applicable to arbitrary objects