An operator-theoretical approach to error estimation

Error estimates (as opposed to bounds) may involve unspecified constants, in which case they have no direct value for numerical purposes. A practical method for obtaining realistic upper bounds of such generic constants is devised. Directly applicable as it stands to a wide class of pointwise approximation problems, this method can further be adapted technically to that alternative class of important problems which is concerned with mean-square approximation. It is based on an explicitly motivated analysis of the general problem of bounding errors, which essentially evolves in the setting of operator theory while referring to such classical tools as the Peano kernel theorem and its generalization known as the Bramble-Hilbert lemma.Anglai

Feature matching and deformation for texture synthesis

One significant problem in patch-based texture synthesis is the presence of broken features at the boundary of adjacent patches. The reason is that optimization schemes for patch merging may fail when neighborhood search cannot find satisfactory candidates in the sample texture because of an inaccurate similarity measure. In this paper, we consider both curvilinear features and their deformation. We develop a novel algorithm to perform feature matching and alignment by measuring structural similarity. Our technique extracts a feature map from the sample texture, and produces both a new feature map and texture map. Texture synthesis guided by feature maps can significantly reduce the number of feature discontinuities and related artifacts, and gives rise to satisfactory results.link_to_subscribed_fulltex