Image-based Remapping of Material Appearance

Digital 3D content creation requires the ability to exchange assets across multiple software applications. For many 3D asset types, standard formats and interchange conventions are available. For material definitions, however, inter-application exchange is still hampered by different software packages supporting different BRDF models. To make matters worse, even if nominally identical BRDF models are supported, these often differ in their implementation, due to optimisations and safeguards in individual renderers. To facilitate appearance-preserving translation between different BRDF models whose precise implementation is not known (arguably the standard case with commercial systems), we propose a robust translation scheme which leaves BRDF evaluation to the targeted rendering system, and which expresses BRDF similarity in image space. As we will show, even naïve applications of a nonlinear fit which uses such an image space residual metric work well in some cases; however, it does suffer from instabilities for certain material parameters. We propose strategies to mitigate these instabilities and perform reliable parameter remappings between differing BRDF definitions. We report on experiences with this remapping scheme, both with respect to robustness and visual differences of the fits

Clustering with partial information

The Correlation Clustering problem, also known as the Cluster Editing problem, seeks to edit a given graph by adding and deleting edges to obtain a collection of vertex-disjoint cliques, such that the editing cost is minimized. The Edge Clique Partitioning problem seeks to partition the edges of a given graph into edge-disjoint cliques, such that the number of cliques is minimized. Both problems are known to be NP-hard, and they have been previously studied with respect to approximation and fixed parameter tractability. In this paper we study these two problems in a more general setting that we term fuzzy graphs, where the input graphs may have missing information, meaning that whether or not there is an edge between some pairs of vertices of the input graph can be undecided. For fuzzy graphs the Correlation Clustering and Edge Clique Partitioning problems have previously been studied only with respect to approximation. Here we give parameterized algorithms based on kernelization for both problems. We prove that the Correlation Clustering problem is fixed-parameter tractable on fuzzy graphs when parameterized by (k,r), where k is the editing cost and r is the minimum number of vertices required to cover the undecided edges. In particular we show that it has a polynomial-time reduction to a problem kernel on O(k² + r) vertices. We provide an analogous result for the Edge Clique Partitioning problem on fuzzy graphs. Using (k,r) as parameters, where k bounds the size of the partition, and r is the minimum number of vertices required to cover the undecided edges, we describe a polynomial-time kernelization to a problem kernel on O(k⁴‧3r) vertices. This implies fixed-parameter tractability for this parameterization. Furthermore we also show that parameterizing only by the number of cliques k, is not enough to obtain fixed-parameter tractability. The problem remains, in fact, NP-hard for each fixed k > 2

Constructing optimal ultrametrics

10.1007/BF02626093Journal of Classification102241-26