Texture analysis using graphs generated by deterministic partially self-avoiding walks

Texture is one of the most important visual attributes for image analysis. It has been widely used in image analysis and pattern recognition. A partially self-avoiding deterministic walk has recently been proposed as an approach for texture analysis with promising results. This approach uses walkers (called tourists) to exploit the gray scale image contexts in several levels. Here, we present an approach to generate graphs out of the trajectories produced by the tourist walks. The generated graphs embody important characteristics related to tourist transitivity in the image. Computed from these graphs, the statistical position (degree mean) and dispersion (entropy of two vertices with the same degree) measures are used as texture descriptors. A comparison with traditional texture analysis methods is performed to illustrate the high performance of this novel approach. (C) 2011 Elsevier Ltd. All rights reserved.

Dynamic texture segmentation based on deterministic partially self-avoiding walks

Recently there has been a considerable interest in dynamic textures due to the explosive growth of multimedia databases. In addition, dynamic texture appears in a wide range of videos, which makes it very important in applications concerning to model physical phenomena. Thus, dynamic textures have emerged as a new field of investigation that extends the static or spatial textures to the spatio-temporal domain. In this paper, we propose a novel approach for dynamic texture segmentation based on automata theory and k-means algorithm. In this approach, a feature vector is extracted for each pixel by applying deterministic partially self-avoiding walks on three orthogonal planes of the video. Then, these feature vectors are clustered by the well-known k-means algorithm. Although the k-means algorithm has shown interesting results, it only ensures its convergence to a local minimum, which affects the final result of segmentation. In order to overcome this drawback, we compare six methods of initialization of the k-means. The experimental results have demonstrated the effectiveness of our proposed approach compared to the state-of-the-art segmentation methods.

Dynamic texture analysis and segmentation using deterministic partially self-avoiding walks

Dynamic texture is a recent field of investigation that has received growing attention from computer vision community in the last years. These patterns are moving texture in which the concept of selfsimilarity for static textures is extended to the spatiotemporal domain. In this paper, we propose a novel approach for dynamic texture representation, that can be used for both texture analysis and segmentation. In this method, deterministic partially self-avoiding walks are performed in three orthogonal planes of the video in order to combine appearance and motion features. We validate our method on three applications of dynamic texture that present interesting challenges: recognition, clustering and segmentation. Experimental results on these applications indicate that the proposed method improves the dynamic texture representation compared to the state of the art.

Crossover between the extended and localized regimes in stochastic partially self-avoiding walks in one-dimensional disordered systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Complex network classification using partially self-avoiding deterministic walks

Complex networks have attracted increasing interest from various fields of science. It has been demonstrated that each complex network model presents specific topological structures which characterize its connectivity and dynamics. Complex network classification relies on the use of representative measurements that describe topological structures. Although there are a large number of measurements, most of them are correlated. To overcome this limitation, this paper presents a new measurement for complex network classification based on partially self-avoiding walks. We validate the measurement on a data set composed by 40000 complex networks of four well-known models. Our results indicate that the proposed measurement improves correct classification of networks compared to the traditional ones. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4737515]

Texture descriptor based on partially self-avoiding deterministic walker on networks

Texture image analysis is an important field of investigation that has attracted the attention from computer vision community in the last decades. In this paper, a novel approach for texture image analysis is proposed by using a combination of graph theory and partially self-avoiding deterministic walks. From the image, we build a regular graph where each vertex represents a pixel and it is connected to neighboring pixels (pixels whose spatial distance is less than a given radius). Transformations on the regular graph are applied to emphasize different image features. To characterize the transformed graphs, partially self-avoiding deterministic walks are performed to compose the feature vector. Experimental results on three databases indicate that the proposed method significantly improves correct classification rate compared to the state-of-the-art, e.g. from 89.37% (original tourist walk) to 94.32% on the Brodatz database, from 84.86% (Gabor filter) to 85.07% on the Vistex database and from 92.60% (original tourist walk) to 98.00% on the plant leaves database. In view of these results, it is expected that this method could provide good results in other applications such as texture synthesis and texture segmentation. (C) 2012 Elsevier Ltd. All rights reserved.

Ergodic crossover in partially self-avoiding stochastic walks

Consider a one-dimensional environment with N randomly distributed sites. An agent explores this random medium moving deterministically with a spatial memory μ. A crossover from local to global exploration occurs in one dimension at a well-defined memory value μ1=log2N. In its stochastic version, the dynamics is ruled by the memory and by temperature T, which affects the hopping displacement. This dynamics also shows a crossover in one dimension, obtained computationally, between exploration schemes, characterized yet by the trajectory size (Np) (aging effect). In this paper we provide an analytical approach considering the modified stochastic version where the parameter T plays the role of a maximum hopping distance. This modification allows us to obtain a general analytical expression for the crossover, as a function of the parameters μ, T, and Np. Differently from what has been proposed by previous studies, we find that the crossover occurs in any dimension d. These results have been validated by numerical experiments and may be of great value for fixing optimal parameters in search algorithms. © 2013 American Physical Society.

Combining fractal and deterministic walkers for texture analysis and classification

In this paper,we present a novel texture analysis method based on deterministic partially self-avoiding walks and fractal dimension theory. After finding the attractors of the image (set of pixels) using deterministic partially self-avoiding walks, they are dilated in direction to the whole image by adding pixels according to their relevance. The relevance of each pixel is calculated as the shortest path between the pixel and the pixels that belongs to the attractors. The proposed texture analysis method is demonstrated to outperform popular and state-of-the-art methods (e.g. Fourier descriptors, occurrence matrix, Gabor filter and local binary patterns) as well as deterministic tourist walk method and recent fractal methods using well-known texture image datasets.

Self-Avoiding Walks in the Plane

Румен Руменов Данговски, Калина Христова Петрова - Разглеждаме броя на несамопресичащите се разходки с фиксирана дължина върху целочислената решетка. Завършваме анализа върху случая за лента, с дължина едно. Чрез комбинаторни аргументи получаваме точна формула за броя на разходките върху лента, ограничена отляво и отдясно. Формулата я изследваме и асимптотично.

Texture analysis and classification using deterministic tourist walk

In this paper, we present a study on a deterministic partially self-avoiding walk (tourist walk), which provides a novel method for texture feature extraction. The method is able to explore an image on all scales simultaneously. Experiments were conducted using different dynamics concerning the tourist walk. A new strategy, based on histograms. to extract information from its joint probability distribution is presented. The promising results are discussed and compared to the best-known methods for texture description reported in the literature. (C) 2009 Elsevier Ltd. All rights reserved.

Dynamics of the reaction between the free end of a tethered self-avoiding polymer and a flat penetrable surface: A renormalization group study

The average time tau(r) for one end of a long, self-avoiding polymer to interact for the first time with a flat penetrable surface to which it is attached at the other end is shown here to scale essentially as the square of the chain's contour length N. This result is obtained within the framework of the Wilemski-Fixman approximation to diffusion-limited reactions, in which the reaction time is expressed as a time correlation function of a ``sink'' term. In the present work, this sink-sink correlation function is calculated using perturbation expansions in the excluded volume and the polymer-surface interactions, with renormalization group methods being used to resum the expansion into a power law form. The quadratic dependence of tau(r) on N mirrors the behavior of the average time tau(c) of a free random walk to cyclize, but contrasts with the cyclization time of a free self-avoiding walk (SAW), for which tau(r) similar to N-2.2. A simulation study by Cheng and Makarov J. Phys. Chem. B 114, 3321 (2010)] of the chain-end reaction time of an SAW on a flat impenetrable surface leads to the same N-2.2 behavior, which is surprising given the reduced conformational space a tethered polymer has to explore in order to react. (C) 2014 AIP Publishing LLC.

How the interplay between individual spatial memory and landscape persistence can generate population distribution patterns

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamik von Polymerschmelzen und Quellverhalten ungeordneter Netzwerke

Deutsch:Mit Hilfe eines parallelen Molekulardynamik-Programmswurden einfach Modelle von Homopolymerschmelzen simuliert.Langkettige Schmelzen zeigten eine sehr gute Übereinstimmungmit den Vorhersagendes Reptationsmodells. Die intermediären Reptationsbereichemit den vorhergesagtenExponenten konnten wesentlich klarer als bisher verifiziertwerden. Es stellteVerschiedene, gebräuchliche Analyse-Methoden führten jedochzuunterschiedlichen Aussagen für die Verhakungslänge. Fürkurze Kettenbzw. kurze Unterketten wurden in dichten Schmelzendie Abweichungen vom Rouse-Modell aufgezeigt. DieseAbweichungenkönnen als Korrelationslocheffekt interpretiert werden undsteht in teilweiser Übereinstimmung zu den Vorhersagenrenormierter Rouse-Modelle. Aus den Schmelzen wurden Netzwerke in einem speziellenZufallsvernetzungsprozeßhergestellt, der die Bildung von Defektstrukturenunterbindet. Diesewurden bzgl. ihres Quell- und Deformationsverhaltenuntersucht. Der maximaleQuellgrad eines Netzwerkes war bereits bei verhaltnismäßigkurzen Kettenlängenverhakungslimitiert. Die Struktur der Ketten in einem biszum osmotischenGleichgewicht gequollenen Netzwerk unterhalb derMaschengröße ist die überstreckter,selbstvermeidender Ketten mit einer Fraktaldimension von D =1.4,jenseits der Maschengröße (bzw. Verhakungslänge) nehmen siedie Struktur einesIrrfluges an (D = 2). Gequollene Netzwerke zeigten, wie auch in Experimenten, einestarkeZunahme von Dichtefluktuationen, welche unter Verstreckunganisotropwurde und in der Streufunktion zu sogenanntenButterfly-Mustern führt.Diese Fluktuationen sind statischer Natur als Folge desEinfrierenseines ungeordneten Zustandes während der Vernetzung.

A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).

A Deterministic Optimization Approach to Protein Sequence Design Using Continuous Models

Determining the sequence of amino acid residues in a heteropolymer chain of a protein with a given conformation is a discrete combinatorial problem that is not generally amenable for gradient-based continuous optimization algorithms. In this paper we present a new approach to this problem using continuous models. In this modeling, continuous "state functions" are proposed to designate the type of each residue in the chain. Such a continuous model helps define a continuous sequence space in which a chosen criterion is optimized to find the most appropriate sequence. Searching a continuous sequence space using a deterministic optimization algorithm makes it possible to find the optimal sequences with much less computation than many other approaches. The computational efficiency of this method is further improved by combining it with a graph spectral method, which explicitly takes into account the topology of the desired conformation and also helps make the combined method more robust. The continuous modeling used here appears to have additional advantages in mimicking the folding pathways and in creating the energy landscapes that help find sequences with high stability and kinetic accessibility. To illustrate the new approach, a widely used simplifying assumption is made by considering only two types of residues: hydrophobic (H) and polar (P). Self-avoiding compact lattice models are used to validate the method with known results in the literature and data that can be practically obtained by exhaustive enumeration on a desktop computer. We also present examples of sequence design for the HP models of some real proteins, which are solved in less than five minutes on a single-processor desktop computer Some open issues and future extensions are noted.