Smoothness of the Green functions for the complement of rarefied Cantortype sets is described in terms of the function φ(δ) = (1/ log 1 δ ) that gives the logarithmic measure of sets. Markov’s constants of the corresponding sets are evaluated.

An iterative method for computing shape from shading using occluding boundary information is proposed. Some applications of this method are shown. We employ the stereographic plane to express the orientations of surface patches, rather than the more commonly .used gradient space. Use of the stereographic plane makes it possible to incorporate occluding boundary information, but forces us to emp...

An iterative method of using occluding boundary information is proposed to compute surface slope from shading. We use a stereographic space rather than the more commonly used gradient space in order to express occluding boundary information. Further, we use "average" smoothness constraints rather than the more obvious "closed loop" smoothness constraints. We develop alternate constraints from t...

We introduce the concept of complementarity between data and smoothness term in modern variational optic flow methods. First we design a sophisticated data term that incorporates HSV colour representation with higher order constancy assumptions, completely separate robust penalisation, and constraint normalisation. Our anisotropic smoothness term reduces smoothing in the data constraint directi...

Non-rigid image registration is an ill-posed yet challenging problem due to its supernormal high degree of freedoms and inherent requirement of smoothness. Graph-cuts method is a powerful combinatorial optimization tool which has been successfully applied into image segmentation and stereo matching. Under some specific constraints, graph-cuts method yields either a global minimum or a local min...

Over the last five years, new “voxel-based” approaches have allowed important progress in multimodal image registration, notably due to the increasing use of information-theoretic similarity measures. Their wide success has led to the progressive abandon of measures using standard image statistics (mean and variance). Until now, such measures have essentially been based on heuristics. In this p...

A probabilistic framework using two random fields, DeTEC (Detection of Touching Elongated Cells) is proposed to detect cells in scanning electron microscopy images with inhomogeneous illumination. The first random field provides a binary segmentation of the image to superpixels that are candidates belonging to cells, and to superpixels that are part of the background, by imposing a prior on the...

Spectral data estimation from image data is an ill-posed problem since (i) due to the integral nature of solid-state light sensors the same output can be obtained from an infinity of input signals and (ii) color signals are spectrally smooth in nature and therefore limit the number of linear independent equation that can be formulated for the identification problem. To enable the solution of th...