Robust Processing of Optical Flow of Fluids

Abstract

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.

Ortho-diffusion decompositions of graph-based representation of images

“…Unlike the classical diffusion processing on Markov random fields [12,13], in the proposed methodology, diffusion is embedded on graphs at various scales in order to smooth complex data structures by removing noise and non-essential detail and thus enhancing the main data characteristics. Graph based representations are appropriate for representing complex data due to their ability to model distributed similarity.…”

“…A series of properties of diffusion maps in the context of various applications have been investigated in [8,9,10,11]. Classical diffusion methodology was applied on Markov random fields representations of vector fields for in-painting colour images [12] as well as for smoothing optical flow [13]. A new framework for building multiresolution structures on graphs which allows the study of functions on manifolds at different scales, as generated by the geometry of the manifold, was proposed by Magioni and Mahadevan in the diffusion wavelets approach [14].…”

“…(e) Image of a happy male face of size 56 × 46. (f) Face of a female showing neutral expression, of size 56 × 46.of representative ortho-diffusion bases in(13). Always, after several iterations, we have observed that most significant image information is contained in the leading ortho-diffusion bases from [Φ j+1 ] Φ 0 .…”

ViCoMo: visual context modeling for scene understanding in video surveillance

“…Smoothing of the optical field to extract motion trends is a common technique from the research on fluid dynamics modeling. 39 Based on spatial locality, the remaining grid cells are formed into motion clusters, also referred to as …”

A polar representation of motion and implications for optical flow

“…The same is true for alternative regularizers based on differential properties of the flow [21]. Of course, special-purpose regularizations can be designed for these cases, and examples for fluids include approaches that minimize second-order divergence and curl [14,25] or employ the Helmholtz decomposition [13]. However, these methods are often much more difficult to optimize and implement, they are harder to use, and they do not transfer easily to new types of flows.…”