Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

Topological characterization of antireflective and hydrophobic rough surfaces: are random process theory and fractal modeling applicable?

The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study provides a deep critical comparison on this matter, providing some insight into the capabilities and limitations in applying RPT and fractal modeling to antireflective and hydrophobic rough surfaces, two important types of textured surfaces. A multi-resolution experimental campaign by using a confocal profilometer with different lenses is carried out and a comprehensive software for the statistical description of rough surfaces is developed. It is found that the topology of the analyzed textured surfaces cannot be fully described according to RPT and fractal modeling. The following complexities emerge: (i) the presence of cut-offs or bi-fractality in the power-law power-spectral density (PSD) functions; (ii) a more pronounced shift of the PSD by changing resolution as compared to what expected from fractal modeling; (iii) inaccuracy of the RPT in describing the joint PDFs of asperity heights and curvatures of textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured surfaces in case of special surface treatments, not accounted by fractal modeling.Comment: 21 pages, 13 figure

Complexity and biourbanism: thermodynamical architectural and urban models integrated in modern geographic mapping

The paper was presented on 5th April 2012 by Eleni Tracada in Theoretical Currents II conference in the University of Lincoln.Abstract Vital elements in urban fabric have been often suppressed for reasons of ‘style’. Recent theories, such as Biourbanism, suggest that cities risk becoming unstable and deprived of healthy social interactions. Our paper aims at exploring the reasons for which, fractal cities, which have being conceived as symmetries and patterns, can have scientifically proven and beneficial impact on human fitness of body and mind. During the last few decades, modern urban fabric lost some very important elements, only because urban design and planning turned out to be stylistic aerial views or new landscapes of iconic technological landmarks. Biourbanism attempts to re-establish lost values and balance, not only in urban fabric, but also in reinforcing human-oriented design principles in either micro or macro scale. Human life in cities and beyond emerges during ‘connectivity’ via geometrical continuity of grids and fractals, via path connectivity among highly active nodes, via exchange/movement of people and, finally via exchange of information (networks). All these elements form a hypercomplex system of several interconnected layers of a dynamic structure, all influencing each other in a non-linear manner. Sometimes networks of communication at all levels may suffer from sudden collapse of dynamic patterns, which have been proved to be vital for a long time either to landscapes and cityscapes. We are now talking about negotiating boundaries between human activities, changes in geographic mapping and, mainly about sustainable systems to support continuous growth of communities. We are not only talking about simple lives (‘Bios’) as Urban Syntax (bio and socio-geometrical synthesis), but also about affinities between developing topographies created by roadways and trajectories and the built environment. We shall also have the opportunity to show recent applications of these theories in our postgraduate students’ work, such as a 3D model as a new method of cartography of the Island of Mauritius, with intend to highlight developments in topography and architecture through a series of historical important events and mutating socio-political and economical geographies. This model may be able to predict failures in proposed and/or activated models of expansion, which do not follow strictly morphogenetic and physiological design processes. The same kind of modelling is capable to enable recognition of ‘optimal forms’ at different feedback scales, which, through morphogenetic processes, guarantee an optimal systemic efficiency, and therefore quality of life.ADT funds, university of Derby

Diffusion-based Holistic Texture Rectification and Synthesis

We present a novel framework for rectifying occlusions and distortions in degraded texture samples from natural images. Traditional texture synthesis approaches focus on generating textures from pristine samples, which necessitate meticulous preparation by humans and are often unattainable in most natural images. These challenges stem from the frequent occlusions and distortions of texture samples in natural images due to obstructions and variations in object surface geometry. To address these issues, we propose a framework that synthesizes holistic textures from degraded samples in natural images, extending the applicability of exemplar-based texture synthesis techniques. Our framework utilizes a conditional Latent Diffusion Model (LDM) with a novel occlusion-aware latent transformer. This latent transformer not only effectively encodes texture features from partially-observed samples necessary for the generation process of the LDM, but also explicitly captures long-range dependencies in samples with large occlusions. To train our model, we introduce a method for generating synthetic data by applying geometric transformations and free-form mask generation to clean textures. Experimental results demonstrate that our framework significantly outperforms existing methods both quantitatively and quantitatively. Furthermore, we conduct comprehensive ablation studies to validate the different components of our proposed framework. Results are corroborated by a perceptual user study which highlights the efficiency of our proposed approach.Comment: SIGGRAPH Asia 2023 Conference Pape

Microstructure reconstruction of 2D/3D random materials via diffusion-based deep generative models

Microstructure reconstruction serves as a crucial foundation for establishing Process-Structure-Property (PSP) relationship in material design. Confronting the limitations of variational autoencoder and generative adversarial network within generative modeling, this study adopted the denoising diffusion probability model (DDPM) to learn the probability distribution of high-dimensional raw data and successfully reconstructed the microstructures of various composite materials, such as inclusion materials, spinodal decomposition materials, chessboard materials, fractal noise materials, and so on. The quality of generated microstructure was evaluated using quantitative measures like spatial correlation functions and Fourier descriptor. On this basis, this study also successfully achieved the regulation of microstructure randomness and the generation of gradient materials through continuous interpolation in latent space using denoising diffusion implicit model (DDIM). Furthermore, the two-dimensional microstructure reconstruction is extended to three-dimensional framework and integrates permeability as a feature encoding embedding. This enables the conditional generation of three-dimensional microstructures for random porous materials within a defined permeability range. The permeabilities of these generated microstructures were further validated through the application of the Boltzmann method

A survey of exemplar-based texture synthesis

Exemplar-based texture synthesis is the process of generating, from an input sample, new texture images of arbitrary size and which are perceptually equivalent to the sample. The two main approaches are statistics-based methods and patch re-arrangement methods. In the first class, a texture is characterized by a statistical signature; then, a random sampling conditioned to this signature produces genuinely different texture images. The second class boils down to a clever "copy-paste" procedure, which stitches together large regions of the sample. Hybrid methods try to combine ideas from both approaches to avoid their hurdles. The recent approaches using convolutional neural networks fit to this classification, some being statistical and others performing patch re-arrangement in the feature space. They produce impressive synthesis on various kinds of textures. Nevertheless, we found that most real textures are organized at multiple scales, with global structures revealed at coarse scales and highly varying details at finer ones. Thus, when confronted with large natural images of textures the results of state-of-the-art methods degrade rapidly, and the problem of modeling them remains wide open.Comment: v2: Added comments and typos fixes. New section added to describe FRAME. New method presented: CNNMR

Master Texture Space: An Efficient Encoding for Projectively Mapped Objects

Projectively textured models are used in an increasingly large number of applicationsthat dynamically combine images with a simple geometric surface in a viewpoint dependentway. These models can provide visual fidelity while retaining the effects affordedby geometric approximation such as shadow casting and accurate perspective distortion.However, the number of stored views can be quite large and novel views must be synthesizedduring the rendering process because no single view may correctly texture the entireobject surface. This work introduces the Master Texture encoding and demonstrates thatthe encoding increases the utility of projectively textured objects by reducing render-timeoperations. Encoding involves three steps; 1) all image regions that correspond to the samegeometric mesh element are extracted and warped to a facet of uniform size and shape,2) an efficient packing of these facets into a new Master Texture image is computed, and3) the visibility of each pixel in the new Master Texture data is guaranteed using a simplealgorithm to discard occluded pixels in each view. Because the encoding implicitly representsthe multi-view geometry of the multiple images, a single texture mesh is sufficientto render the view-dependent model. More importantly, every Master Texture image cancorrectly texture the entire surface of the object, removing expensive computations suchas visibility analysis from the rendering algorithm. A benefit of this encoding is the supportfor pixel-wise view synthesis. The utility of pixel-wise view synthesis is demonstratedwith a real-time Master Texture encoded VDTM application. Pixel-wise synthesis is alsodemonstrated with an algorithm that distills a set of Master Texture images to a singleview-independent Master Texture image

Texture Structure Analysis

abstract: Texture analysis plays an important role in applications like automated pattern inspection, image and video compression, content-based image retrieval, remote-sensing, medical imaging and document processing, to name a few. Texture Structure Analysis is the process of studying the structure present in the textures. This structure can be expressed in terms of perceived regularity. Our human visual system (HVS) uses the perceived regularity as one of the important pre-attentive cues in low-level image understanding. Similar to the HVS, image processing and computer vision systems can make fast and efficient decisions if they can quantify this regularity automatically. In this work, the problem of quantifying the degree of perceived regularity when looking at an arbitrary texture is introduced and addressed. One key contribution of this work is in proposing an objective no-reference perceptual texture regularity metric based on visual saliency. Other key contributions include an adaptive texture synthesis method based on texture regularity, and a low-complexity reduced-reference visual quality metric for assessing the quality of synthesized textures. In order to use the best performing visual attention model on textures, the performance of the most popular visual attention models to predict the visual saliency on textures is evaluated. Since there is no publicly available database with ground-truth saliency maps on images with exclusive texture content, a new eye-tracking database is systematically built. Using the Visual Saliency Map (VSM) generated by the best visual attention model, the proposed texture regularity metric is computed. The proposed metric is based on the observation that VSM characteristics differ between textures of differing regularity. The proposed texture regularity metric is based on two texture regularity scores, namely a textural similarity score and a spatial distribution score. In order to evaluate the performance of the proposed regularity metric, a texture regularity database called RegTEX, is built as a part of this work. It is shown through subjective testing that the proposed metric has a strong correlation with the Mean Opinion Score (MOS) for the perceived regularity of textures. The proposed method is also shown to be robust to geometric and photometric transformations and outperforms some of the popular texture regularity metrics in predicting the perceived regularity. The impact of the proposed metric to improve the performance of many image-processing applications is also presented. The influence of the perceived texture regularity on the perceptual quality of synthesized textures is demonstrated through building a synthesized textures database named SynTEX. It is shown through subjective testing that textures with different degrees of perceived regularities exhibit different degrees of vulnerability to artifacts resulting from different texture synthesis approaches. This work also proposes an algorithm for adaptively selecting the appropriate texture synthesis method based on the perceived regularity of the original texture. A reduced-reference texture quality metric for texture synthesis is also proposed as part of this work. The metric is based on the change in perceived regularity and the change in perceived granularity between the original and the synthesized textures. The perceived granularity is quantified through a new granularity metric that is proposed in this work. It is shown through subjective testing that the proposed quality metric, using just 2 parameters, has a strong correlation with the MOS for the fidelity of synthesized textures and outperforms the state-of-the-art full-reference quality metrics on 3 different texture databases. Finally, the ability of the proposed regularity metric in predicting the perceived degradation of textures due to compression and blur artifacts is also established.Dissertation/ThesisPh.D. Electrical Engineering 201