Texture Space Research Articles

Innovative sensory methods to access acceptability of mixed polymer semisoft ovules for microbicide applications.

Vaginal microbicides are a promising means to prevent the transmission of HIV, empowering women by putting protection under their control. We have been using gel technology to develop microbicides in the intermediate texture space to overcome shortcomings of current solid and liquid forms. We recently formulated semisoft ovules from mixed polymer combinations of carrageenan and Carbopol 940P to overcome some of the flaws with our previous generation of formulations based solely on carrageenan. To determine the user acceptability of the reformulated gels, women first evaluated intact semisoft ovules before evaluating ovules that had been subjected to mechanical crushing to simulate samples that represent post-use discharge. Women then evaluated combinations of intact and discharge samples to understand how ovule textures correlated with texture of the resulting discharge samples. Carbopol concentration directly and inversely correlated with willingness to try for discharge samples and intact samples, respectively. When evaluating intact samples, women focused on the ease of inserting the product and preferred firmer samples; conversely, when evaluating discharge samples, softer samples that resulted in a smooth paste were preferred. Significant differences between samples were lost when evaluating pairs as women made varying trade-offs between their preference for ease of inserting intact ovules and acceptability of discharge appearance. Evaluating samples that represent different stages of the use cycle reveals a more holistic measure of product acceptability. Studying sensory acceptability in parallel with biophysical performance enables an iterative design process that considers what women prefer in terms of insertion as well as possibility of leakage.

Convergence in graded ditopological texture spaces

Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander Sostak (see bibliography). In this paper, the authors generalize the structure of difilters in ditopological texture spaces defined in (see bibliography) to the graded ditopological texture spaces and compare the properties of difilters and graded difilters.

A textural view of semi-separation axioms in soft fuzzy topological spaces

In the present paper, we have continued to study the properties of semi-separation axioms in ditopological texture spaces. We prove that the semi-Ti-spaces (i = 0, 1, 2, 3, 3 1 2 , 4) are productive in ditopological spaces. Finally, semi-separation axioms are given for soft fuzzy topological spaces by using the categorical isomorphism between soft fuzzy topologies and ditopologies.

Soft ditopological spaces

We introduce the concept of a soft ditopological space as the "soft Generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Ert?rk, ?. Dost, Ditopological texture spaces and fuzzy topology, I. Basic Concepts, Fuzzy Sets and Systems 147 (2) (2004), 171-199. Actually a soft ditopological space is a soft set with two independent structures on it - a soft topology and a soft co-topology. The first one is used to describe openness-type properties of a space while the second one deals with its closedness-type properties. We study basic properties of such spaces and accordingly defined continuous mappings between such spaces.

Trends in Continuity and Interpolation for Computer Graphics.

In every computer graphics oriented application today, it is a common practice to texture 3D models as a way to obtain realistic material. As part of this process, mesh texturing, deformation, and visualization are all key parts of the computer graphics field. This PhD dissertation was completed in the context of these three important and related fields in computer graphics. The article presents techniques that improve on existing state-of-the-art approaches related to continuity and interpolation in texture space (texturing), object space (deformation), and screen space (rendering).

Lebesgue quasi-uniformity on textures

This is a continuation of the work where the notions<br /> of Lebesgue uniformity and Lebesgue quasi uniformity in a<br />texture space were introduced. It is well known that the quasi<br />uniform space with a compact topology has the Lebesgue property.<br />This result is extended to direlational quasi uniformities and<br />dual dicovering quasi uniformities. Additionally we discuss the<br />completeness of lebesgue di-uniformities and dual dicovering<br />lebesgue di-uniformities.

4D Model Flow: Precomputed Appearance Alignment for Real-time 4D Video Interpolation

We introduce the concept of 4D model flow for the precomputed alignment of dynamic surface appearance across 4D video sequences of different motions reconstructed from multi-view video. Precomputed 4D model flow allows the efficient parametrization of surface appearance from the captured videos, which enables efficient real-time rendering of interpolated 4D video sequences whilst accurately reproducing visual dynamics, even when using a coarse underlying geometry. We estimate the 4D model flow using an image-based approach that is guided by available geometry proxies. We propose a novel representation in surface texture space for efficient storage and online parametric interpolation of dynamic appearance. Our 4D model flow overcomes previous requirements for computationally expensive online optical flow computation for data-driven alignment of dynamic surface appearance by precomputing the appearance alignment. This leads to an efficient rendering technique that enables the online interpolation between 4D videos in real time, from arbitrary viewpoints and with visual quality comparable to the state of the art.

Continuity and Interpolation Techniques for Computer Graphics

AbstractContinuity and interpolation have been crucial topics for computer graphics since its very beginnings. Every time we want to interpolate values across some area, we need to take a set of samples over that interpolating region. However, interpolating samples faithfully allowing the results to closely match the underlying functions can be a tricky task as the functions to sample could not be smooth and, in the worst case, it could be even impossible when they are not continuous. In those situations bringing the required continuity is not an easy task, and much work has been done to solve this problem. In this paper, we focus on the state of the art in continuity and interpolation in three stages of the real‐time rendering pipeline. We study these problems and their current solutions in texture space (2D), object space (3D) and screen space. With this review of the literature in these areas, we hope to bring new light and foster research in these fundamental, yet not completely solved problems in computer graphics.

A textural view of soft fuzzy rough sets

This paper aims to give a new insight for soft fuzzy sets. Firstly, using textural soft fuzzy direlations on a soft fuzzy lattice, we obtain a soft fuzzy rough set algebra where the inverse soft fuzzy relation and inverse soft fuzzy corelation are the upper approximation and lower approximation, respectively. On the other hand, we consider Alexandroff soft fuzzy topology and we prove that there exists a one-to-one correspondence between the Alexandroff topologies and the reflexive and transitive direlations on a texture space.

An improved texture-related vertex clustering algorithm for model simplification

As an important data source in 3D GIS, 3D landmark models are built to simulate the real-world scenario. However, due to the enormous volume and complexity of 3D models, the data transmission under limited bandwidth and the real-time rendering have always been an open problem. In order to improve the visualization and the efficiency, this paper proposes a novel model simplification algorithm in consideration of texture after the analysis of the existing model simplification approaches. Differing from the previous research, our approach defines a new error metric related to the model texture, which extends the vertex clustering scheme in 3D geometry space and 2D texture space independently. Since the uneven distribution of vertices is taken into account, the clustering unit is divided adaptively in consideration of both geometry and texture information. In view of reducing the memory overhead and improving the algorithm efficiency, we don’t create new vertices by iterative calculations, but use the inherent vertices in the initial meshes as the characteristic vertices. To demonstrate the feasibility and effectiveness of our strategy, a series of simplification experiments have been carried out on the platform of DirectX 3D, a widely used 3D application programming interface. The results show that the simplified models in consideration of texture preserve more texture details than those traditional ones. It apparently makes a good balance between the reduction rate and visual effects.

B-G-Compactness in Ditopological Texture Spaces

The main goal of this paper is to introduce and study new notions of continuity, compactness and stability in ditopological texture spaces based on the notions of b-g-open and b-g-closed sets and some of their characterizations are obtained.

A Texture Segmentation Model Driven by the Simplified Cauchy-Schwarz Divergence *

This paper addresses a new segmentation model for texture image based on active contour and the model is driven by the simplified Cauchy-Schwarz divergence. First, we define a new texture descriptor with the Gauss curvature and the mean curvature of the textural region to represent the textural image space. Then, a novel active contour model has been developed to distinguish between object of interest and background by computing the simplified Cauchy-Schwarz divergence of the probability density functions. Finally, an alternative minimization procedure and the Chambolle's fast duality projection algorithm are adopted in order to efficiently solve this model. Experimental results show that our model has better segmentation performance than the traditional models driven by the Kullback-Leiber divergence and the Bhattacharyya distance for both synthetic and natural texture image.

Visual perception of procedural textures: identifying perceptual dimensions and predicting generation models.

Procedural models are widely used in computer graphics for generating realistic, natural-looking textures. However, these mathematical models are not perceptually meaningful, whereas the users, such as artists and designers, would prefer to make descriptions using intuitive and perceptual characteristics like "repetitive," "directional," "structured," and so on. To make up for this gap, we investigated the perceptual dimensions of textures generated by a collection of procedural models. Two psychophysical experiments were conducted: free-grouping and rating. We applied Hierarchical Cluster Analysis (HCA) and Singular Value Decomposition (SVD) to discover the perceptual features used by the observers in grouping similar textures. The results suggested that existing dimensions in literature cannot accommodate random textures. We therefore utilized isometric feature mapping (Isomap) to establish a three-dimensional perceptual texture space which better explains the features used by humans in texture similarity judgment. Finally, we proposed computational models to map perceptual features to the perceptual texture space, which can suggest a procedural model to produce textures according to user-defined perceptual scales.

Selection properties of texture structures

The aim of this paper is to begin with study of selection principles in texture and ditopological texture spaces and to establish relationships between these selection principles and other covering properties of texture or ditopological spaces. We also investigate the behavior of the properties under consideration under standard operations with ditopological spaces.

A categorical view of textural approximation spaces

The basic motivation of the theory of textures is to find a convenient point-set based setting for fuzzy sets. Recent works on textures show that they also provide a useful model for rough set theory. In this paper, we show that i-c spaces (interior-closure texture spaces) can be regarded as a textural rough set systems on a single universe. Then we consider the approaches containing direlations and dicovers for textural rough sets and we give some basic results related to direlations and dicovers. Considering the discrete textures we discuss on these results for rough sets based on relations and coverings. Finally, we prove that the category of topological spaces and continuous functions is isomorphic to the category of (covering) approximation spaces and continuous functions.

Connections between realcompactifications in various categories

The author gives a detailed analysis of the relation between the theories of realcompactifications and compactifications in the category of ditopological texture spaces and in the categories of bitopological spaces and topological spaces.

Exploring the Space of Abstract Textures by Principles and Random Sampling

Exemplar-based texture synthesis methods try to emulate textures observed in our visual world. Yet the field of all possible textures (natural or not) has been little explored. Indeed, existing abstract synthesis methods focus on a single generation rule and generate a rather limited set of textures. This limitation can be overcome by combining randomly various generation principles and rule parameters. Doing so gives access to a vast and still unexplored set of possible images. In this paper, we introduce an image sampling method combining the main painting techniques of abstract art. This sampler synthesizes what we call multi-layered textures. The underlying image model extends three abstract image synthesis models: the dead leaves model, the spot noise, and fractal generators. By respecting minimal self-similarity rules keeping Gestalt theory grouping principles at each texture layer, the abstract textures remain understandable to human perception. The complexity of the generated textures derives from the systematic and randomized use of shape interaction principles taken from abstract art such as occlusion, transparency, exclusion, inclusion, and tessellation.

Strong Forms of Generalized Closed Sets in Ditopological Texture Spaces

The purpose of this paper is to introduce the new concepts namely, α-g-closed, pre-g-closed, semi-g-closed, b-g-closed, β-g-closed, α-g-open, pre-g-open, semi-g-open, b-g-open and β-g-open sets in ditopological texture spaces. The relationships between these classes of sets are also obtained. Also some properties and several characterizations are investigated.

Near Compactness of Ditopological Texture Spaces

The authors consider the notions of near compactness, near cocompactness, near stability, near costability and near dicompactness in the setting of ditopological texture spaces. In particular preservation of these properties under surjective R-dimaps, co-R-dimaps and bi-R-dimaps is investigated and non-trivial characterizations of near dicompactness are given which generalize those for dicompactness. The notions of semiregularization, semicoregularization and semibiregularization are defined and used to give generalizations of Mrowka’s Theorem for near compactness and near cocompactness, and of Tychonoff’s Theorem for near compactness, near cocompactness and near dicompactness. Also, results related to pseudo-open and pseudo-closed sets are presented. Finally, examples are given of co-T1 nearly dicompact ditopologies on textures which are not nearly plain and an open question is posed. 2000 AMS Classification: 54A05, 54C 10.

Completeness types for uniformity theory on textures

In this paper the author considers the various types of completeness for di-uniform texture spaces and especially for complemented ones. Following that, the relationships between completeness of uniform spaces and these types of completeness for complemented di-uniform texture spaces are investigated in a categorical setting, just as interrelations between quasi-uniform spaces and di-uniform texture spaces are pointed out insofar as completeness is concerned. Additionally, useful requirements among the various types of completeness of a di-uniformity and real dicompactness of the uniform ditopological space generated by that di-uniformity are presented as a diagram.