Abstract-We propose a novel method for iterative learning of point correspondences between image sequences. Points moving on surfaces in 3D space are projected into two images. Given a point in either view, the considered problem is to determine the corresponding location in the other view. The geometry and distortions of the projections are unknown as is the shape of the surface. Given several pairs of point-sets but no access to the 3D scene, correspondence mappings can be found by excessive global optimization or by the fundamental matrix if a perspective projective model is assumed. However, an iterative solution on sequences of point-set pairs with general imaging geometry is preferable. We derive such a method that optimizes the mapping based on Neyman's chi-square divergence between the densities representing the uncertainties of the estimated and the actual locations. The densities are represented as channel vectors computed with a basis function approach. The mapping between these vectors is updated with each new pair of images such that fast convergence and high accuracy are achieved. The resulting algorithm runs in real-time and is superior to state-of-the-art methods in terms of convergence and accuracy in a number of experiments.
. Modelling cell lineage using a meta-Boolean tree model with a relation to Gene Regulatory Networks. Journal of Theoretical Biology, Elsevier, 2010, 268 (1) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Modelling cell lineage using a meta-Boolean tree model with a relation to Gene Regulatory Networks AbstractA cell lineage is the ancestral relationship between a group of cells that originate from a single founder cell. For example, in the embryo of the nematode Caenorhabditis elegans an invariant cell lineage has been traced, and with this information at hand it is possible to theoretically model the emergence of different cell types in the lineage, starting from the single fertilized egg. In this report we outline a modelling technique for cell lineage trees, which can be used for the C. elegans embryonic cell lineage but also extended to other lineages. The model takes into account both cell-intrinsic (transcription factor-based) and -extrinsic (extracellular) factors as well as synergies within and between these two types of factors. The model can faithfully recapitulate the entire C. elegans cell lineage, but is also general, i.e. it can be applied to describe any cell lineage. We show that synergy between factors, as well as the use of extrinsic factors, drastically reduce the number of regulatory factors needed for recapitulating the lineage. The model gives indications regarding co-variation of factors, number of involved genes and where in the cell lineage tree that asymmetry might be controlled by external influence. Furthermore, the model is able to emulate other (Boolean, discrete and differential-equation-based) models. As an example, we show that the model can be translated to the language of a previous linear sigmoid-limited concentration-based model (Geard and Wiles, 2005). This means that this latter model also can exhibit synergy effects, and also that the cumbersome iterative technique for parameter estimation previously used is no longer needed. In conclusion, the proposed model is general and simple to use, can be mapped onto other models to extend and simplify their use, and can also be used to indicate where synergy and external influence would reduce the complexity of the regulatory process.
We present an automatization of Barnsley's manual algorithm for the solution of the inverse problem of iterated function systems (IFSs). The problem is to retrieve the number of mappings and the parameters of an IFS from a digital binary image approximating the attractor induced by the IFS. M.F. Barnsley et al. described a way to solve manually the inverse problem by identifying the fragments of which the collage is composed, and then computing the parameters of the mappings (Barnsley et al., Proc. Nat. Acad. Sci. USA, vol.83, p.1975-7, 1986; Barnsley, "Fractals Everywhere", Academic, 1988; Barnsley and Hurd, L., "Fractal Image Compression", A.K. Peters, 1992). The automatic algorithm searches through a finite set of points in the parameter space determining a set of affine mappings. The algorithm uses the collage theorem and the Hausdorff metric. The inverse problem of IFSs is related to the image coding of binary images. If the number of mappings and the parameters of an IFS, with not too many mappings, could be obtained from a binary image, then this would give an efficient representation of the image. It is shown that the inverse problem solved by the automatic algorithm has a solution and some experiments show that the automatic algorithm is able to retrieve an IFS, including the number of mappings, from a digital binary image approximating the attractor induced by the IFS.
Recursive image subsampling which yields support areas approaching fractals is described and analyzed using iterated function systems. The subsampling scheme is suitable in, e.g., hierarchical image processing and image coding schemes. For hexagonally sampled images a hierarchical subsampling structure is given which yields hexagon-like regions with fractal borders.
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