Automatic image vectorization using superpixels and random walkers

The field of smooth vector graphics explores the representation, creation, rasterization, and automatic generation of light-weight image representations, frequently used for scalable image content. Over the past decades, several conceptual approaches on the representation of images with smooth gradients have emerged that each led to separate research threads, including the popular gradient meshes and diffusion curves. As the computational models matured, the mathematical descriptions diverged and article started to focus more narrowly on subproblems, such as on the representation and creation of vector graphics, or the automatic vectorization from raster images. Most of the work concentrated on a specific mathematical model only. With this survey, we describe the established computational models in a consistent notation to spur further knowledge transfer, leveraging the recent advances in each field. We therefore categorize vector graphics article from the last decades based on their underlying mathematical representations as well as on their contribution to the vector graphics content creation pipeline, comprising representation, creation, rasterization, and automatic image vectorization. This survey is meant as an entry point for both artists and researchers. We conclude this survey with an outlook on promising research directions and challenges to overcome in the future.

Percolation process, which is intrinsically a phase transition process near the critical point, is ubiquitous in nature. Many of its applications embrace a wide spectrum of natural phenomena ranging from the forest fires, spread of contagious diseases, social behaviour dynamics to mathematical finance, formation of bedrocks and biological systems. The topology generated by the percolation process near the critical point is a random (stochastic) fractal. It is fundamental to the percolation theory that near the critical point, a unique infinite fractal structure, namely the infinite cluster, would emerge. As de Gennes suggested, the properties of the infinite cluster could be deduced by studying the dynamical behaviour of the random walk process taking place on it. He coined the term the ant in the labyrinth. The random walk process on such an infinite fractal cluster exhibits a subdiffusive dynamics in the sense that the mean squared displacement grows as ~t2/dw, where dw, called the fractal dimension of the random walk path, is greater than 2. Thus, the random walk process on the infinite cluster is classified as a process exhibiting the properties of anomalous diffusions. Yet near the critical point, the infinite cluster is not the sole emergent topology, but it coexists with other clusters whose size is finite. Though finite, on specific length scales these finite clusters exhibit fractal properties as well. In this work, it is assumed that the random walk process could take place on these finite size objects as well. Bearing this assumption in mind requires one address the non-equilibrium initial condition. Due to the lack of knowledge on the propagator of the random walk process in stochastic random environments, a phenomenological correspondence between the renowned Ornstein-Uhlenbeck process and the random walk process on finite size clusters is established. It is elucidated that when an ensemble of these finite size clusters and the infinite cluster is considered, the anisotropy and size of these finite clusters effects the mean squared displacement and its time averaged counterpart to grow in time as ~t(d+df (t-2))/dw, where d is the embedding Euclidean dimension, df is the fractal dimension of the infinite cluster, and , called the Fisher exponent, is a critical exponent governing the power-law distribution of the finite size clusters. Moreover, it is demonstrated that, even though the random walk process on a specific finite size cluster is ergodic, it exhibits a persistent non-ergodic behaviour when an ensemble of finite size and the infinite clusters is considered.

Image vectorization is one of the primary means of creating vector graphics. The quality of a vectorized image depends crucially on extracting accurate features from input raster images. However, correct object edges can be difficult to detect when color gradients are weak. We present an image vectorization technique that operates on a color image augmented with a depth map and uses both color and depth edges to define vectorized paths. We output a vectorized result as a diffusion curve image. The information extracted from the depth map allows us more flexibility in the manipulation of the diffusion curves, in particular permitting high-level object segmentation. Our experimental results demonstrate that this method achieves high reconstruction quality and provides greater control in the organization and editing of vectorized images than existing work based on diffusion curves.

Bu çalışmada İstanbul Menkul Kıymetler Borsası (İMKB) fiyatlarının rassal yürüyüş süreciyle ya da ortalamaya dönen bir süreçle karakterize edilip edilmediği doğrusal olmayan çerçevede araştırılmaktadır. Çalışmada bootstrap yöntemlerine dayanan otoregresif birim kök ile kısıtsız iki rejimli eşik değerli otoregresif (TAR) model kullanılmıştır. Haftalık veriler kullanılarak yapılan çalışmada elde edilen bulgular İMKB-100 endeksinin Ocak 1999’dan Ocak 2009’a kadar olan dönemde doğrusal olmayan bir yapıda olduğunu ve birim kök süreci ile karakterize edildiğini göstermektedir. Aynı zamanda doğrusal olmayan bağımlılığın test edilmesi için TAR model tahminlerinden elde edilmiş kalıntılara BDS testi uygulanmış ve bağımsız-türdeş dağılım varsayımına dayanan boş hipotez reddedilmiştir. Çalışmanın temel sonucu, İstanbul Menkul Kıymetler Borsası için rassal yürüyüş hipotezinin geçerli olmadığıdır.

In this work I investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. I perform extensive simulations for the calculation of the mean squared displacement, the network coverage, and the survival probability on a network with a concentration c of static traps. It is shown that the random walkers remain close to their origin, but cover a large part of the network at the same time. This behavior is markedly different than usual random walk processes in the literature. For the trapping problem I numerically compute Phi(n,c) , the survival probability of mobile species at time n , as a function of the concentration of trap nodes, c . Comparison of these results to the Rosenstock approximation indicate that this is an adequate description for networks with 2<gamma<3 and yield an exponential decay. For gamma>3 the behavior is more complicated and one needs to employ a truncated cumulant expansion.

Poisson Vector Graphics (PVG) generalize the popular Diffusion Curves (DC) by appending two new geometric primitives -Poisson Region (PR) and Poisson Curve (PC). It is an effective graphic designing tool which extends Laplace's equation to Poisson's equation. DC is a two-sided curve with colors defined on both sides that diffuse colors over the image to produce consistent color except for sharp features along the boundaries. PC is to produce discontinuous colors across the curve, whereas PR is to style smooth shading effect among the predefined region. But DC suffers from -1 or 0 continuity. In comparison, PR is 1 continuous, that can establish smooth shading details. Furthermore, DC based vectorization works for both natural and art images quite well. But it usually requires dense curves for high-quality reconstruction, that makes post-editing difficult.

Analytical representation of stock and stock-indexes returns: Non-Gaussian random walks with various jump laws

Random walks are one of the most fundamental types of stochastic processes and have been applied in various domains, such as ranking systems and searching. In this paper, we investigate random walk process unfolding on a generalized version of the activity-driven modelling framework by considering mutual agreement. The model is characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the fitness of the vertices on both ends of that edge. We investigate two typical forms of linking functions and derive analytically exact expressions for the asymptotic behavior of random walks and the mean first-passage time for the two cases, respectively. We find that, compared with the activity-driven network model, mutual agreement has nontrivial effects on the properties of random walk processes. For the first case, when the fitness of the ends of a link is independent, we find that the capability of vertices to gather walkers is not only related to the vertices' activity, but also determined by their propensity of receiving connections. For the second case, when the creation of the link is determined by whether the sum of the two end points' fitness is larger than a threshold, we find that for vertices with activity larger than a given threshold, the stronger the activity is, the more walkers they will collect in the stationary state. Finally, we confirm our analytical prediction via large-scale numerical simulations performed by controlling flexible parameters. The results presented here contribute to the understanding of the evolution mechanism of the mutual selection network model and give us an insight into their effects on random walks processes.

A moving object recognition approach is presented in this paper. The motion of an object includes the linear or nonlinear translation and rotation. For a 3-D object, the images taken by a camera are in plannar form. They are varied by different distances between camera and the object, variant angles and timing for taking pictures. However, the change rate among these images taken at different instant are logically related. The brightness level between any two neighbour string cells of machine digital scanning raster varies according to the Markovian random walk process. Thus, the direction and position of a moving object can be found by the variations of the cell random walk. The angles between a machine digital scanning raster and the edges of an object in a plannar image are called pseudo-refractional angles. The variations of angles can be used as features for object recognition. Together with the Kolmogorov complexity program, the probability function of the process can be changed into a finite length of string arrays to simplify the recognition procedure. The distance between camera and the object can be measured by a radar or supersonic signal for military or industrial applications. Index Items: Markovian chain, Random walk process, Kolmogorov complexity, Chapman-Kolmogorov process, String array approach, Poisson process, Optical flow technique, 3-D object analysis, Nonlinear motion, Translation and rotation.

In this paper, we present a new method for refining image annotation by integrating probabilistic latent semantic analysis (PLSA) with random walk (RW) model. First, we construct a PLSA model with asymmetric modalities to estimate the posterior probabilities of each annotating keywords for an image, and then a label similarity graph is constructed by a weighted linear combination of label similarity and visual similarity. Followed by a random walk process over the label graph is employed to further mine the correlation of the keywords so as to capture the refining annotation, which plays a crucial role in semantic based image retrieval. The novelty of our method mainly lies in two aspects: exploiting PLSA to accomplish the initial semantic annotation task and implementing random walk process over the constructed label similarity graph to refine the candidate annotations generated by the PLSA. Compared with several state-of-the-art approaches on Corel5k and Mirflickr25k datasets, the experimental results show that our approach performs more efficiently and accurately.KeywordsRefining Image AnnotationPLSAEMRandom WalkImage Retrieval

HIN_DRL: A random walk based dynamic network representation learning method for heterogeneous information networks

We consider a random walk process on graphs introduced by Orenshtein and Shinkar (2014). At any time, the random walk moves from its current position along a previously unvisited edge chosen uniformly at random, if such an edge exists. Otherwise, it walks along a previously visited edge chosen uniformly at random. For the random $r$-regular graph, with $r$ a constant odd integer, we show that this random walk process has asymptotic vertex and edge cover times $\frac{1}{r-2}n\log n$ and $\frac{r}{2(r-2)}n\log n$, respectively, generalizing a result of Cooper, Frieze and the author (2018) from $r = 3$ to any odd $r\geqslant 3$. The leading term of the asymptotic vertex cover time is now known for all fixed $r\geqslant 3$, with Berenbrink, Cooper and Friedetzky (2015) having shown that $G_r$ has vertex cover time asymptotic to $\frac{rn}{2}$ when $r\geqslant 4$ is even.

As an important tool of social network analysis, network representation learning also called network embedding maps the network to a latent space and learns low-dimensional and dense real vectors of nodes, while preserving the structure and internal attributes of network. The learned representations or embedding vectors can be used for node clustering, link prediction, network visualization and other tasks for network analysis. Most of the existing network representation learning algorithms mainly focus on the preservation of micro or macro network structure, ignoring the mesoscopic community structure information. Although a few network embedding methods are proposed to preserve the community structure, they all ignore the prior information about communities. Inspired by the semi-supervised community detection in complex networks, in this article, a novel Semi-Supervised DeepWalk method(SSDW) is proposed for network representation learning, which successfully preserves the community structure of network in the embedding space. Specifically, a semi-supervised random walk sampling method which effectively integrates the pairwise constraints is proposed. By doing so, the SSDW model can guide the transition probability in the random walk process and obtain the node context sequence in line with the prior knowledge. The experimental results on eight real networks show that comparing with the popular network embedding methods, the node representation vectors integrating pairwise constraints into the random walk process can obtain higher accuracy on node clustering task, and the results of link prediction, network visualization tasks indicate that the semi-supervised model SSDW is more discriminative than unsupervised ones.

The random walk process underlies the description of a large number of real-world phenomena. Here we provide the study of random walk processes in time-varying networks in the regime of time-scale mixing, i.e., when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time-varying networks created from the activity potential of the nodes and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well-known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval, and diffusion processes in time-varying networks.

Investigating if the market is efficient is an old issue as market efficiency is imperative for channeling investments to best-valued projects and its importance endures. There is contradictory evidence in the literature provided by empirical researches. The primary purpose of this research has been to find out whether share prices are a random walk process by applying multiple unit root tests, Runs Test and newly developed State Space Model. The empirical findings of the study provide sufficient evidence that the stock prices of KSE 100 Index, S &amp; P BSE 500 Index, and CSE All Share Index is not a random walk process and are thus weak form inefficient hypothesis. In this study, the concept of the random walk is examined considering only the stock markets while bypassing the other asset markets. This research supply exciting facts about independent samples from Pakistan, India, and Bangladesh and complement the existing literature on emerging markets.DOI: 10.15408/etk.v17i2.7102