Optical Flow From 1D Correlation: Application to a Simple Time-To-Crash Detector

In the first part of this paper we show that a new technique exploiting 1D correlation of 2D or even 1D patches between successive frames may be sufficient to compute a satisfactory estimation of the optical flow field. The algorithm is well-suited to VLSI implementations. The sparse measurements provided by the technique can be used to compute qualitative properties of the flow for a number of different visual tsks. In particular, the second part of the paper shows how to combine our 1D correlation technique with a scheme for detecting expansion or rotation ([5]) in a simple algorithm which also suggests interesting biological implications. The algorithm provides a rough estimate of time-to-crash. It was tested on real image sequences. We show its performance and compare the results to previous approaches.

A Conservative Front Tracking Algorithm

The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical fluxes. Some numerical tests in 1D and preliminary results in 2D are presented.