In this paper we apply the diffusion framework to dense optical flow estimation. Local image information is represented by matrices of gradients between paired locations. Diffusion distances are modelled as sums of eigenvectors weighted by their eigenvalues extracted following the eigen decomposion of these matrices. Local optical flow is estimated by correlating diffusion distances characterizing features from different frames. A feature confidence factor is defined based on the local correlation efficiency when compared to that of its neighbourhood. High confidence optical flow estimates are propagated to areas of lower confidence.

This paper proposes a new approach, coupling physical models and image estimation techniques, for modelling the movement of fluids. The fluid flow is characterized by turbulent movement and dynamically changing patterns which poses challenges to existing optical flow estimation methods. The proposed methodology, which relies on Navier-Stokes equations, is used for processing fluid optical flow by using a succession of stages such as advection, diffusion and mass conservation. A robust diffusion step jointly considering the local data geometry and its statistics is embedded in the proposed framework. The diffusion kernel is Gaussian with the covariance matrix defined by the local second derivatives. Such an anisotropic kernel is able to implicitly detect changes in the vector field orientation and to diffuse accordingly. A new approach is developed for detecting fluid flow structures such as vortices. The proposed methodology is applied on artificially generated vector fields as well as on various image sequences.

This paper proposes a physics-based methodology for the analysis of optical flows displaying complex patterns. Turbulent motion, such as that exhibited by fluid substances, can be modelled using fluid dynamics principles. Together with supplemental equations, such as the conservation of mass, and well formulated boundary conditions, the Navier-Stokes equations can be used to model complex fluid motion estimated from image sequences. In this paper, we propose to use a robust kernel which adapts to the local data geometry in the diffusion stage of the Navier-Stokes formulation. The proposed kernel is Gaussian and embeds the Hessian of the local data as its covariance matrix. The local Hessian models the variation of the flow in a certain neighbourhood. Moreover, we use a robust statistics mechanism in order to eliminate the outliers from the estimation process. The proposed methodology is applied on artificial vector fields and in image sequences showing atmospheric and solar phenomena. 1

In this paper we propose a set of algorithms that combine the anisotropic smoothing using the heat kernel with the outlier rejection capability of robust statistics. The proposed algorithms are applied on structural vector flows that model the internal shape variation in volumetric images. The 3D shapes are represented by sparse cross-sections along the main axis of the object. The dual directional block matching algorithm is used to initially extract the structural flows. This algorithm uses block matching between pixel blocks from consecutive images representing sparse cross-sections through a volume. Two flows are produced using forward and reverse matching along the main axis of the 3D object. After smoothing, the structural flows are used for slice interpolation. Experimental results provide a comparison among the given algorithms when used for digital 3D reconstruction of an incisor and of two human bones.