A Variational Framework for Structure from Motion inOmnidirectional Image Sequences

We address the problem of depth and ego-motion estimation from omnidirectional images. We propose a correspondence-free structure-from-motion problem for sequences of images mapped on the 2-sphere. A novel graph-based variational framework is first proposed for depth estimation between pairs of images. The estimation is cast as a TV-L1 optimization problem that is solved by a fast graph-based algorithm. The ego-motion is then estimated directly from the depth information without explicit computation of the optical flow. Both problems are finally addressed together in an iterative algorithm that alternates between depth and ego-motion estimation for fast computation of 3D information from motion in image sequences. Experimental results demonstrate the effective performance of the proposed algorithm for 3D reconstruction from synthetic and natural omnidirectional image

Spherical Diffusion for Surface Smoothing and Denoising

Data defined on spherical domains occurs in various applications, such as surface modeling, omnidirectional imaging, and the analysis of keypoints in volumetric data. The theory of spherical signals lacks important concepts like the Gaussian function, which is permanently used in planar image processing. We propose a definition of a spherical Gaussian function as the Green\u27s function of the spherical diffusion process. This allows to introduce a linear scale space on the sphere. We apply this new filter to the smoothing of 3D object surfaces

Geodesic Active Fields - A Geometric Framework for Image Registration

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including non-flat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Secondly, this method is, to the best of our knowledge, the first re-parametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization