Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher dimension d > 2, because the other methods require the conversion of a scattered dataset to an ordered dataset (i.e. a semiregular mesh is obtained by using some tessellation techniques), which is computationally expensive. The RBF approximation is non-separable, as it is based on the distance between two points. This method leads to a solution of Linear System of Equations (LSE) Ac = h.In this paper several RBF approximation methods are briefly introduced and a comparison of those is made with respect to the stability and accuracy of computation. The proposed RBF approximation offers lower memory requirements and better quality of approximation.
In this paper, we present an extension of dynamic mesh compression techniques based on PCA. Such representation allows very compact representation of moving 3D surfaces; however, it requires some side information to be transmitted along with the main data. The biggest part of this information is the PCA basis, and since the data can be encoded very efficiently, the size of the basis cannot be neglected when considering the overall performance of a compression algorithm.We present a new work in this area, as none of the papers about PCA based compression really addresses this issue. We will show that for an efficient and accurate encoding there are better choices than even sophisticated algorithms such as LPC.We will present results showing that our approach can reduce the size of the basis by 90% with respect to direct encoding, which can lead to approximately 25% increase of performance of the compression algorithm without any significant loss of accuracy. Such improvement moves the performance of the PCA encoder beyond the performance of current state of the art dynamic mesh compression algorithms, such as the recently adopted MPEG standard, FAMC.
There are multiple areas of computer graphics where triangular meshes are being altered in order to reduce their size or complexity, while attempting to preserve the original shape of the mesh as closely as possible. Recently, this area of research has been extended to cover even a dynamic case, i.e., surface animations which are compressed and simplified. However, to date very little effort has been made to develop methods for evaluating the results, namely the amount of distortion introduced by the processing. Even the most sophisticated compression methods use distortion evaluation by some kind of mean squared error while the actual relevance of such measure has not been verified so far. In this paper, we point out some serious drawbacks of the existing error measures. We present results of the subjective testing that we have performed, and we derive a new measure called Spatiotemporal edge difference (STED) which is shown to provide much better correlation with subjective opinions on mesh distortion.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.