Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations

This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook) schemes in the framework of finite volume method for the ultra-relativistic flows. Different from the existing kinetic flux-vector splitting (KFVS) or BGK-type schemes for the ultra-relativistic Euler equations, the present genuine BGK schemes are derived from the analytical solution of the Anderson-Witting model, which is given for the first time and includes the "genuine" particle collisions in the gas transport process. The BGK schemes for the ultra-relativistic viscous flows are also developed and two examples of ultra-relativistic viscous flow are designed. Several 1D and 2D numerical experiments are conducted to demonstrate that the proposed BGK schemes not only are accurate and stable in simulating ultra-relativistic inviscid and viscous flows, but also have higher resolution at the contact discontinuity than the KFVS or BGK-type schemes.Comment: 41 pages, 13 figure

Color Image Analysis by Quaternion-Type Moments

International audienceIn this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. appears to be an optimal choice

Fast Computation of Sliding Discrete Tchebichef Moments and Its Application in Duplicated Regions Detection

International audienceComputational load remains a major concern when processing signals by means of sliding transforms. In this paper, we present an efficient algorithm for the fast computation of one-dimensional and two-dimensional sliding discrete Tchebichef moments. To do so, we first establish the relationships that exist between the Tchebichef moments of two neighboring windows taking advantage of Tchebichef polynomials’ properties. We then propose an original way to fast compute the moments of one window by utilizing the moment values of its previous window. We further theoretically establish the complexity of our fast algorithm and illustrate its interest within the framework of digital forensics and more precisely the detection of duplicated regions in an audio signal or an image. Our algorithm is used to extract local features of such a signal tampering. Experimental results show that its complexity is independent of the window size, validating the theory. They also exhibit that our algorithm is suitable to digital forensics and beyond to any applications based on sliding Tchebichef moments