Multi-model fitting based on minimum spanning tree

This paper presents a novel approach to the computation of primitive geometrical structures, where no prior knowledge about the visual scene is available and a high level of noise is expected. We based our work on the grouping principles of proximity and similarity, of points and preliminary models. The former was realized using Minimum Spanning Trees (MST), on which we apply a stable alignment and goodness of fit criteria. As for the latter, we used spectral clustering of preliminary models. The algorithm can be generalized to various model fitting settings, without tuning of run parameters. Experiments demonstrate the significant improvement in the localization accuracy of models in plane, homography and motion segmentation examples. The efficiency of the algorithm is not dependent on fine tuning of run parameters like most others in the field.

Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.