Digital Image Evolution of Artwork Without Human Evaluation Using the Example of the Evolving Mona Lisa Problem

Whether for optimizing the speed of microprocessors or for sequence analysis in molecular biology — evolutionary algorithms are used in astoundingly many fields. Also, the art was influenced by evolutionary algorithms — with principles of natural evolution works of art that can be created or imitated, whereby initially generated art is put through an iterated process of selection and modification. This paper covers an application in which given images are emulated evolutionary using a finite number of semi-transparent overlapping polygons, which also became known under the name “Evolution of Mona Lisa”. In this context, different approaches to solve the problem are tested and presented here. In particular, we want to investigate whether Hill Climbing Algorithm in combination with Delaunay Triangulation and Canny Edge Detector that extracts the initial population directly from the original image performs better than the conventional Hill Climbing and Genetic Algorithm, where the initial population is generated randomly.

SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD

The Douglas–Rachford method is a splitting method frequently employed for finding zeros of sums of maximally monotone operators. When the operators in question are normal cone operators, the iterated process may be used to solve feasibility problems of the following form: Find $x\in \bigcap _{k=1}^{N}S_{k}$ . The success of the method in the context of closed, convex, nonempty sets $S_{1},\ldots ,S_{N}$ is well known and understood from a theoretical standpoint. However, its performance in the nonconvex context is less well understood, yet it is surprisingly impressive. This was particularly compelling to Jonathan M. Borwein who, intrigued by Elser, Rankenburg and Thibault’s success in applying the method to solving sudoku puzzles, began an investigation of his own. We survey the current body of literature on the subject, and we summarize its history. We especially commemorate Professor Borwein’s celebrated contributions to the area.

ON REGULIRATION MULTIPLE EIGENVALUE BY REDUCTION PSEUDOPERTURBATION METHODS

On the base of the bifurcation theory methods it is considered the problem of the retaining multiple eigenvalues and relevant eigenvectors and roots elements. An approch is suggested which allows reduce algebraic multiple to unit, that is reduce the problem of the retaining multiple eigenvalues to simple. For construction iterated process applied pseudoperturbation methods.

epistemic interpretation of bidirectional optimality based on signaling games

To some, the relation between bidirectional optimality theory and game theory seems obvious: strong bidirectional optimality corresponds to Nash equilibrium in a strategic game (Dekker and van Rooij 2000). But in the domain of pragmatics this formally sound parallel is conceptually inadequate: the sequence of utterance and its interpretation cannot be modelled reasonably as a strategic game, because this would mean that speakers choose formulations independently of a meaning that they want to express, and that hearers choose an interpretation irrespective of an utterance that they have observed. Clearly, the sequence of utterance and interpretation requires a dynamic game model. One such model, and one that is widely studied and of manageable complexity, is a signaling game. This paper is therefore concerned with an epistemic interpretation of bidirectional optimality, both strong and weak, in terms of beliefs and strategies of players in a signaling game. In particular, I suggest that strong optimality may be regarded as a process of internal self-monitoring and that weak optimality corresponds to an iterated process of such self-monitoring. This latter process can be derived by assuming that agents act rationally to (possibly partial) beliefs in a self-monitoring opponent.

OVERSEGMENTATION REDUCTION BY FLOODING REGIONS AND DIGGING WATERSHED LINES

The watershed transformation is a primary tool for segmenting a grey-tone image into subsets that are of interest to a visual observer. The resulting image, however, may often appear oversegmented into a large number of tiny regions (basins), most of which are not significant to the problem of domain. In this paper, a method for removing these nonsignificant basins is presented. The notions of relative significance and intrinsic significance are introduced, which lead to the definition of three types of significance for a basin: strong, weak and partial. The merging of a basin with other basins only occurs when the significance of the basin is not strong, and is restricted to suitably selected adjacent basins. The merging is performed by using an iterated process consisting of two phases. The first involves the removal of certain regional minima, and is accomplished by following either a flooding or a digging scheme. The second identifies the basins corresponding to the regional minima remaining in the image and utilizes the watershed transformation. An appropriate selection of the basins to be merged produces a segmented image perceptually close to the original image. The performance of the proposed method is for the case of astronomic images.

ITERATED RANDOM PULSE PROCESSES AND THEIR SPECTRAL PROPERTIES

A new class of scaling random processes is introduced. The processes are obtained as sums of non-negative pulses and are generated through a recursive scheme that proceeds from coarser to finer scales. The representation at any given scale has the form of a filtered doubly-stochastic Poisson point process whose intensity depends linearly on the process at the immediately coarser scale. The filter functions (the pulses) at different scales are related through contractive affine transformations. If the transformations are isotropic in physical space, then the spectral density of the infinitely iterated process, [Formula: see text], is found to decay as [Formula: see text] along any radial direction, where the exponent c depends on the dimension of physical space and the parameters of the affine transformation. Various extensions of the basic scheme are considered, including pulses of random shape and anisotropic affine relations among the pulses at different scales. Processes of this type have several applications, including the representation of width functions in river basin hydrology.