Predictive-DCT Coding for 3D Mesh Sequences Compression

This paper proposes a new compression algorithm for dynamic 3d meshes. In such a sequence of meshes, neighboring vertices have a strong tendency to behave similarly and the degree of dependencies between their locations in two successive frames is very large which can be efficiently exploited using a combination of Predictive and DCT coders (PDCT). Our strategy gathers mesh vertices of similar motions into clusters, establish a local coordinate frame (LCF) for each cluster and encodes frame by frame and each cluster separately. The vertices of each cluster have small variation over a time relative to the LCF. Therefore, the location of each new vertex is well predicted from its location in the previous frame relative to the LCF of its cluster. The difference between the original and the predicted local coordinates are then transformed into frequency domain using DCT. The resulting DCT coefficients are quantized and compressed with entropy coding. The original sequence of meshes can be reconstructed from only a few non-zero DCT coefficients without significant loss in visual quality. Experimental results show that our strategy outperforms or comes close to other coders.

Cost Sharing under Uncertainty: An Algorithmic Approach to Cooperative Interval-Valued Games

Recently, Branzei, Dimitrov, and Tijs (2003) introduced cooperative interval-valued games. Among other insights, the notion of an interval core has been coined and proposed as a solution concept for interval-valued games. In this paper we will present a general mathematical programming algorithm which can be applied to find an element in the interval core. As an example, we discuss lot sizing with uncertain demand to provide an application for interval-valued games and to demonstrate how interval core elements can be computed. Also, we reveal that pitfalls exist if interval core elements are computed in a straightforward manner by considering the interval borders separately.