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Conference publicationsAbstractsXXIII conferenceScaling model of natural shapestichomi@gosniias.ru cmr.nazy@gmail.com soralumina@gmail.com 1 pp. (accepted)We present a geometric model of the natural shapes object. The model describes object interaction with the environment by means of global and local scaling. Model provides comparison of the synthesized and observed images of chemical and biological objects in order to evaluate of the dimension and structure of the inner topological and physical spaces. The model describes the topology of the border by fundamental topological group operating in the discrete index space (topological space). Group sets the coincidence and neighborhood relations for border elements as a global scaling procedure associated with the internal nature of the object. Global scaling establishes the fundamental connectedness of object boundaries. The representation of the fundamental connectedness in the physical space is provided by means of a polygon mesh - the fundamental shape of the object. The topology and the metric of physical space set properties of the medium in which the object is created. The connection between the fundamental and the geometric shapes of the object, as well as its texture, is described by a local scaling procedure associated with the dynamic equilibrium of generalized transfer processes - the drift and diffusion. Local scaling is implemented as a procedure of fractal interpolation. The observed shape and texture of the object are obtained by the projection of the shape from the physical space into the observation space of smaller dimension
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