Texture description and segmentation through fractal geometry

A Review on Traditional and Artificial Intelligence-Based Preservation Techniques for Oil Painting Artworks

Oil paintings represent significant cultural heritage, as they embody human creativity and historical narratives. The preservation of these invaluable artifacts requires effective maintenance practices to ensure their longevity and integrity. Despite their inherent durability, oil paintings are susceptible to mechanical damage and chemical deterioration, necessitating rigorous conservation efforts. Traditional preservation techniques that have been developed over centuries involve surface treatment, structural stabilization, and gel-based cleaning to maintain both the integrity and aesthetic appeal of these artworks. Recent advances in artificial intelligence (AI)-powered predictive maintenance techniques offer innovative solutions to predict and prevent deterioration. By integrating image analysis and environmental monitoring, AI-based models provide valuable insights into painting preservation. This review comprehensively analyzes traditional and AI-based techniques for oil painting maintenance, highlighting the importance of adopting innovative approaches. By integrating traditional expertise with AI technology, conservators can enhance their capacity to maintain and preserve these cultural treasures for future generations.

Restored texture segmentation using Markov random fields

Texture segmentation plays a crucial role in the domain of image analysis and its recognition. Noise is inextricably linked to images, just like it is with every signal received by sensing, which has an impact on how well the segmentation process performs in general. Recent literature reveals that the research community has started recognizing the domain of noisy texture segmentation for its work towards solutions for the automated quality inspection of objects, decision support for biomedical images, facial expressions identification, retrieving image data from a huge dataset and many others. Motivated by the latest work on noisy textures, during our work being presented here, Brodatz and Prague texture images are contaminated with Gaussian and salt-n-pepper noise. A three-phase approach is developed for the segmentation of textures contaminated by noise. In the first phase, these contaminated images are restored using techniques with excellent performance as per the recent literature. In the remaining two phases, segmentation of the restored textures is carried out by a novel technique developed using Markov Random Fields (MRF) and objective customization of the Median Filter based on segmentation performance metrics. When the proposed approach is evaluated on Brodatz textures, an improvement of up to 16% segmentation accuracy for salt-n-pepper noise with 70% noise density and 15.1% accuracy for Gaussian noise (with a variance of 50) has been made in comparison with the benchmark approaches. On Prague textures, accuracy is improved by 4.08% for Gaussian noise (with variance 10) and by 2.47% for salt-n-pepper noise with 20% noise density. The approach in the present study can be applied to a diversified class of image analysis applications spanning a wide spectrum such as satellite images, medical images, industrial inspection, geo-informatics, etc.

Spatial and Texture Analysis of Root System distribution with Earth mover's Distance (STARSEED)

PURPOSE

Root system architectures are complex and challenging to characterize effectively for agronomic and ecological discovery.

METHODS

We propose a new method, Spatial and Texture Analysis of Root SystEm distribution with Earth mover's Distance (STARSEED), for comparing root system distributions that incorporates spatial information through a novel application of the Earth Mover's Distance (EMD).

RESULTS

We illustrate that the approach captures the response of sesame root systems for different genotypes and soil moisture levels. STARSEED provides quantitative and visual insights into changes that occur in root architectures across experimental treatments.

CONCLUSION

STARSEED can be generalized to other plants and provides insight into root system architecture development and response to varying growth conditions not captured by existing root architecture metrics and models. The code and data for our experiments are publicly available: https://github.com/GatorSense/STARSEED .

Application of Fractal Image Analysis by Scale-Space Filtering in Experimental Mechanics

Increasingly complex numerical analyses require more and more precise, accurate and varied input parameters in order to achieve results that are as realistic and reliable as possible. Therefore, experimental analyses for material parameter identification are of high importance and a driving force for further developments. In this work, opportunities by applying fractal analysis to optical measurement data of a shear cutting process are investigated. The fractal analysis is based on a modification of the concept of scale-space filtering. Scale exponent fields are calculated for the image sequences of the shear cutting process that are taken by a mobile microscope. A least-square approximation is used for the automated evaluation of the local scale exponent values. In order to determine the change of the scale exponent of individual material points, a digital image correlation is applied.

Fractality of Borsa Istanbul during the COVID-19 Pandemic

Forecasting price changes is very important for the process of estimating and managing market risk in financial markets. Price changes in financial markets may also depend on non-market factors. Considering this situation, the study investigates the effect of the COVID-19 pandemic on Borsa Istanbul. It tackles changes in the fractal dimensions of the time series obtained with the daily closing prices of stocks traded on Borsa Istanbul (BIST). According to the results of the sector-based analysis, we found that fractal dimension changes were quite effective in price estimation.

Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy

The differential box-counting (DBC) method is useful for determining the fractal dimension of grayscale images. It is simple to learn and implement and has been extensively utilized. However, this approach has several problems, such as over- or undercounting the number of boxes due to inappropriate parameter choices, limiting the calculation accuracy. Many studies have been conducted to increase the algorithm’s computational accuracy by improving the calculating parameters of the differential box-counting method. The grid size is a crucial parameter for the DBC method. Generally, there are two typical ways for selecting the grid size in relevant studies: consecutive integer and divisors of image size. However, both methods for grid size selection are problematic. The consecutive integer method cannot partition the image entirely and will result in the undercounting of boxes; the divisors of image size can partition the image completely. However, this method uses fewer grid sizes to compute fractal dimensions and has a relatively huge distance error (DE). To address the shortcomings of the above-mentioned two approaches, this research presents an improved grid size selection strategy. The improved method enhances computational accuracy by computing the discarded image edge areas in the consecutive integer method, allowing the original image information to be used as thoroughly as the divisor strategy. Based on fractional Brownian motion (FBM), Brodatz, and Aerials image sets, the accuracy of the three grid size selection techniques (consecutive integer method, divisors of image size method, and the improved algorithm) to compute the fractal dimension is then compared. The results reveal that, compared to the two prior techniques, the revised algorithm described in this study minimizes the distance error and increases the accuracy of the fractal dimension computation.

Colour and Texture Descriptors for Visual Recognition: A Historical Overview

Colour and texture are two perceptual stimuli that determine, to a great extent, the appearance of objects, materials and scenes. The ability to process texture and colour is a fundamental skill in humans as well as in animals; therefore, reproducing such capacity in artificial (‘intelligent’) systems has attracted considerable research attention since the early 70s. Whereas the main approach to the problem was essentially theory-driven (‘hand-crafted’) up to not long ago, in recent years the focus has moved towards data-driven solutions (deep learning). In this overview we retrace the key ideas and methods that have accompanied the evolution of colour and texture analysis over the last five decades, from the ‘early years’ to convolutional networks. Specifically, we review geometric, differential, statistical and rank-based approaches. Advantages and disadvantages of traditional methods vs. deep learning are also critically discussed, including a perspective on which traditional methods have already been subsumed by deep learning or would be feasible to integrate in a data-driven approach.

Texture Analysis and its Applications in Biomedical Imaging: A Survey

Texture analysis describes a variety of image analysis techniques that quantify the variation in intensity and pattern. This paper provides an overview of several texture analysis approaches addressing the rationale supporting them, their advantages, drawbacks, and applications. This surveys emphasis is in collecting and categorising over five decades of active research on texture analysis. Brief descriptions of different approaches are presented along with application examples. From a broad range of texture analysis applications, this surveys final focus is on biomedical image analysis. An up-to-date list of biological tissues and organs in which disorders produce texture changes that may be used to spot disease onset and progression is provided. Finally, the role of texture analysis methods as biomarkers of disease is summarised.

Multi-marker quantitative radiomics for mass characterization in dedicated breast CT imaging

Purpose

To develop and evaluate the diagnostic performance of an algorithm for multi‐marker radiomic‐based classification of breast masses in dedicated breast computed tomography (bCT) images.

Methods

Over 1000 radiomic descriptors aimed at quantifying mass and border heterogeneity, morphology, and margin sharpness were developed and implemented. These included well‐established texture and shape feature descriptors, which were supplemented with additional approaches for contour irregularity quantification, spicule and lobe detection, characterization of degree of infiltration, and differences in peritumoral compartments. All descriptors were extracted from a training set of 202 bCT masses (133 benign and 69 malignant), and their individual diagnostic performance was investigated in terms of area under the receiver operating characteristics (ROC) curve (AUC) of single‐feature‐based linear discriminant analysis (LDA) classifiers. Subsequently, the most relevant descriptors were selected through a multiple‐step feature selection process (including stability analysis, statistical significance, evaluation of feature interaction, and dimensionality reduction), and used to develop a final LDA radiomic model for classification of benign and malignant masses, which was then tested on an independent test set of 82 cases (45 benign and 37 malignant).

Results

The majority of the individual radiomic descriptors showed, on the training set, an AUC value deriving from a linear decision boundary higher than 0.65, with the lower limit of the associated 95% confidence interval (C.I.) not overlapping with random chance (AUC = 0.5). The final LDA radiomic model resulted in a test set AUC of 0.90 (95% C.I. 0.80–0.96).

Conclusions

The proposed multi‐marker radiomic approach achieved high diagnostic accuracy in bCT mass classification, using a radiomic signature based on different feature types. While future studies with larger datasets are needed to further validate these results, quantitative radiomics applied to bCT shows potential to improve the breast cancer diagnosis pipeline.

A Class-Independent Texture-Separation Method Based on a Pixel-Wise Binary Classification

Texture segmentation is a challenging problem in computer vision due to the subjective nature of textures, the variability in which they occur in images, their dependence on scale and illumination variation, and the lack of a precise definition in the literature. This paper proposes a method to segment textures through a binary pixel-wise classification, thereby without the need for a predefined number of textures classes. Using a convolutional neural network, with an encoder–decoder architecture, each pixel is classified as being inside an internal texture region or in a border between two different textures. The network is trained using the Prague Texture Segmentation Datagenerator and Benchmark and tested using the same dataset, besides the Brodatz textures dataset, and the Describable Texture Dataset. The method is also evaluated on the separation of regions in images from different applications, namely remote sensing images and H&E-stained tissue images. It is shown that the method has a good performance on different test sets, can precisely identify borders between texture regions and does not suffer from over-segmentation.

Individual Tree Detection from UAV Imagery Using Hölder Exponent

This article explores the application of Hölder exponent analysis for the identification and delineation of single tree crowns from very high-resolution (VHR) imagery captured by unmanned aerial vehicles (UAV). Most of the present individual tree crown detection (ITD) methods are based on canopy height models (CHM) and are very effective as far as an accurate digital terrain model (DTM) is available. This prerequisite is hard to accomplish in some environments, such as alpine forests, because of the high tree density and the irregular topography. Indeed, in such conditions, the photogrammetrically derived DTM can be inaccurate. A novel image processing method supports the segmentation of crowns based only on the parameter related to the multifractality description of the image. In particular, the multifractality is related to the deviation from a strict self-similarity and can be treated as the information about the level of inhomogeneity of considered data. The multifractals, even if well established in image processing and recognized by the scientific community, represent a relatively new application in VHR aerial imagery. In this work, the Hölder exponent (one of the parameters related to multifractal description) is applied to the study of a coniferous forest in the Western Alps. The infrared dataset with 10 cm pixels is captured by a UAV-mounted optical sensor. Then, the tree crowns are detected by a basic workflow. This consists of the thresholding of the image on the basis of the Hölder exponent. Then, the single crowns are segmented through a multiresolution segmentation approach. The ITD segmentation was validated through a two-level validation analysis that included a visual evaluation and the computing of quantitative measures based on 200 reference crowns. The results were checked against the ITD performed in the same area but using only spectral, textural, and elevation information. Specifically, the visual assessment included the estimation of the producer’s and user’s accuracies and the F1 score. The quantitative measures considered are the root mean square error (RMSE) (for the area, the perimeter, and the distance between centroids) and the over-segmentation and under-segmentation indices, the Jaccard index, and the completeness index. The F1 score indicates positive results (over 73%) as well as the completeness index that does not exceed 0.23 on a scale of 0 to 1, taking 0 as the best result possible. The RMSE of the extension of crowns is 3 m2, which represents only 14% of the average extension of reference crowns. The performance of the segmentation based on the Hölder exponent outclasses those based on spectral, textural, and elevation information. Despite the good results of the segmentation, the method tends to under-segment rather than over-segment, especially in areas with sloping. This study lays the groundwork for future research into ITD from VHR optical imagery using multifractals.

Parametric mapping of cellular morphology in plant tissue sections by gray level granulometry

BACKGROUND

The cellular morphology of plant organs is strongly related to other physical properties such as shape, size, growth, mechanical properties or chemical composition. Cell morphology often vary depending on the type of tissue, or on the distance to a specific tissue. A common challenge in quantitative plant histology is to quantify not only the cellular morphology, but also its variations within the image or the organ. Image texture analysis is a fundamental tool in many areas of image analysis, that was proven efficient for plant histology, but at the scale of the whole image.

RESULTS

This work presents a method that generates a parametric mapping of cellular morphology within images of plant tissues. It is based on gray level granulometry from mathematical morphology for extracting image texture features, and on Centroidal Voronoi Diagram for generating a partition of the image. Resulting granulometric curves can be interpreted either through multivariate data analysis or by using summary features corresponding to the local average cell size. The resulting parametric maps describe the variations of cellular morphology within the organ.

CONCLUSIONS

We propose a methodology for the quantification of cellular morphology and of its variations within images of tissue sections. The results should help understanding how the cellular morphology is related to genotypic and / or environmental variations, and clarify the relationships between cellular morphology and chemical composition of cell walls.

Reliability of MRI tumor size measurements for minimal invasive treatment selection in small breast cancers

INTRODUCTION

Due to the shift towards minimal invasive treatment, accurate tumor size estimation is essential for small breast cancers. The purpose of this study was to determine the reliability of MRI-based tumor size measurements with respect to clinical, histological and radiomics characteristics in small invasive or in situ carcinomas of the breast to select patients for minimal invasive therapy.

MATERIALS AND METHODS

All consecutive cases of cT1 invasive breast carcinomas that underwent pre-operative MRI, treated in two hospitals between 2005 and 2016, were identified retrospectively from the Dutch cancer registry and cross-correlated with local databases. Concordance between MRI-based measurements and final pathological size was analyzed. The influence of clinical, histological and radiomics characteristics on the accuracy of MRI size measurements were analyzed.

RESULTS

Analysis included 343 cT1 breast carcinomas in 336 patients (mean age, 55 years; range, 25-81 years). Overall correlation of MRI measurements with pathology was moderately strong (ρ = 0.530, P < 0.001), in 42 cases (12.2%) MRI underestimated the size with more than 5 mm. Underestimation occurs more often in grade 2 and grade 3 disease than in low grade invasive cancers. In DCIS the frequency of underestimation is higher than in invasive breast cancer. Unfortunately, none of the patient, imaging or biopsy characteristics appeared predictive for underestimation.

CONCLUSION

Size measurements of small breast cancers on breast MRI are within 5 mm of pathological size in 88% of patients. Nevertheless, underestimation cannot be adequately predicted, particularly for grade 2 and grade 3 tumors, which may hinder patient selection for minimal invasive therapy.

Color Image Complexity versus Over-Segmentation: A Preliminary Study on the Correlation between Complexity Measures and Number of Segments

It is said that image segmentation is a very difficult or complex task. First of all, we emphasize the subtle difference between the notions of difficulty and complexity. Then, in this article, we focus on the question of how two widely used color image complexity measures correlate with the number of segments resulting in over-segmentation. We study the evolution of both the image complexity measures and number of segments as the image complexity is gradually decreased by means of low-pass filtering. In this way, we tackle the possibility of predicting the difficulty of color image segmentation based on image complexity measures. We analyze the complexity of images from the point of view of color entropy and color fractal dimension and for color fractal images and the Berkeley data set we correlate these two metrics with the segmentation results, more specifically the number of quasi-flat zones and the number of JSEG regions in the resulting segmentation map. We report on our experimental results and draw conclusions.

Deep learning-based segmentation of breast masses in dedicated breast CT imaging: Radiomic feature stability between radiologists and artificial intelligence

A deep learning (DL) network for 2D-based breast mass segmentation in unenhanced dedicated breast CT images was developed and validated, and its robustness in radiomic feature stability and diagnostic performance compared to manual annotations of multiple radiologists was investigated. 93 mass-like lesions were extensively augmented and used to train the network (n = 58 masses), which was then tested (n = 35 masses) against manual ground truth of a qualified breast radiologist with experience in breast CT imaging using the Conformity coefficient (with a value equal to 1 indicating a perfect performance). Stability and diagnostic power of 672 radiomic descriptors were investigated between the computerized segmentation, and 4 radiologists' annotations for the 35 test set cases. Feature stability and diagnostic performance in the discrimination between benign and malignant cases were quantified using intraclass correlation (ICC) and multivariate analysis of variance (MANOVA), performed for each segmentation case (4 radiologists and DL algorithm). DL-based segmentation resulted in a Conformity of 0.85 ± 0.06 against the annotated ground truth. For the stability analysis, although modest agreement was found among the four annotations performed by radiologists (Conformity 0.78 ± 0.03), over 90% of all radiomic features were found to be stable (ICC>0.75) across multiple segmentations. All MANOVA analyses were statistically significant (p ≤ 0.05), with all dimensions equal to 1, and Wilks' lambda ≤0.35. In conclusion, DL-based mass segmentation in dedicated breast CT images can achieve high segmentation performance, and demonstrated to provide stable radiomic descriptors with comparable discriminative power in the classification of benign and malignant tumors to expert radiologist annotation.

Analysis and recognition of characteristics of digitized tongue pictures and tongue coating texture based on fractal theory in traditional Chinese medicine

Simple fractal dimensions have been proposed for use in the analysis of the characteristics of digitized tongue pictures and tongue coating texture, which could further the establishment of objectified classification criteria under the conditions of expanding sample size. However, detailed descriptions on simple fractal dimensions have been limited. Therefore, BP (back propagation) neural network model classifiers could be designed by further calculation of the multiple fractal spectrum characteristics of digitized tongue pictures in order to classify and recognize the thin/thick or greasy characteristics of tongue coating. The fractal dimensions of sample data of 587 digitized tongue pictures were collected in a standard environment. A statistical analysis was conducted on the calculation results of the sample data, and the sensitivity of the fractal dimensions to the thin/thick and greasy characteristics of digitized tongue pictures was observed. As the overlap region resulted from a range of values of a single parameter, another 8 characteristic parameters of the multiple fractal spectra of the digitized tongue pictures were further proposed as the elements in the input layer of the three-layers BP neural network. Automatic recognition classifiers were designed and trained for the characteristics of digitized tongue pictures and tongue coating textures. The simple fractal dimension was sensitive to the thin/thick and greasy characteristics of digitized tongue pictures and could better judge the characteristics of the thickness of the tongue coating. A classifier with characteristic parameters of multiple fractal spectra as the input vectors identified by the BP neural network models could effectively increase the accuracy rate judged by the characteristics of the tongue coating texture.

Comparative study on fractal analysis of interferometry images with application to tear film surface quality assessment

The purpose of this research was to evaluate the applicability of the fractal dimension (FD) estimators to assess lateral shearing interferometric (LSI) measurements of tear film surface quality. Retrospective recordings of tear film measured with LSI were used: 69 from healthy subjects and 41 from patients diagnosed with dry eye syndrome. Five surface quality descriptors were considered, four based on FD and a previously reported descriptor operating in a spatial frequency domain (M₂), presenting temporal kinetics of post-blink tear film. A set of 12 regression parameters has been extracted and analyzed for classification purposes. The classifiers are assessed in terms of receiver operating characteristics and areas under their curves (AUC). Also, the computational loads are estimated. The maximum AUC of 82.4% was achieved for M₂, closely followed by the binary box-counting (BBC) FD estimator with AUC=78.6%. For all descriptors, statistically significant differences between the subject groups were found (p<0.05). The BBC FD estimator was characterized with the highest empirical computational efficiency that was about 30% faster than that of M₂, while that based on the differential box-counting exhibited the lowest efficiency (4.5 times slower than the best one). Concluding, FD estimators can be utilized for quantitative assessment of tear film kinetics. They provide a viable alternative to previously used spectral counter parameters, and at the same time allow higher computational efficiency.

Quantitative Morphometry for Osteochondral Tissues Using Second Harmonic Generation Microscopy and Image Texture Information

Osteoarthritis (OA) is a chronic joint disorder involving degeneration of articular cartilage and subchondral bone in joints. We previously established a second harmonic generation (SHG) imaging technique for evaluating degenerative changes to articular cartilage in an OA mouse model. SHG imaging, an optical label-free technique, enabled observation of collagen fibrils, and characterized critical changes in the collagenous patterns of the joints. However, it still remains to be determined how morphological changes in the organization of tissue collagen fibrils should be quantified. In this study, we addressed this issue by employing an approach based on texture analysis. Image texture analysis using the gray level co-occurrence matrix was explored to extract image features. We investigated an image patch-based strategy, in which texture features were extracted on individual patches derived from original images to capture local structural patterns in them. We verified that this analysis enables discrimination of cartilaginous and osseous tissues in mouse joints. Moreover, we applied this method to OA cartilage pathology assessment, and observed improvements in the performance results compared with those obtained using an existing feature descriptor. The proposed approach can be applied to a wide range of conditions associated with collagen remodeling and diseases of cartilage and bone.

Pyramidal fractal dimension for high resolution images

Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension (D) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥1024×1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.

Fractal and Lacunarity Analyses: Quantitative Characterization of Hierarchical Surface Topographies

Biomimetic hierarchical surface structures that exhibit features having multiple length scales have been used in many technological and engineering applications. Their surface topographies are most commonly analyzed using scanning electron microscopy (SEM), which only allows for qualitative visual assessments. Here we introduce fractal and lacunarity analyses as a method of characterizing the SEM images of hierarchical surface structures in a quantitative manner. Taking femtosecond laser-irradiated metals as an example, our results illustrate that, while the fractal dimension is a poor descriptor of surface complexity, lacunarity analysis can successfully quantify the spatial texture of an SEM image; this, in turn, provides a convenient means of reporting changes in surface topography with respect to changes in processing parameters. Furthermore, lacunarity plots are shown to be sensitive to the different length scales present within a hierarchical structure due to the reversal of lacunarity trends at specific magnifications where new features become resolvable. Finally, we have established a consistent method of detecting pattern sizes in an image from the oscillation of lacunarity plots. Therefore, we promote the adoption of lacunarity analysis as a powerful tool for quantitative characterization of, but not limited to, multi-scale hierarchical surface topographies.

Bayesian estimation of the multifractality parameter for image texture using a whittle approximation

Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a challenge. This is due in the main to the fact that current estimation procedures consist of performing linear regressions across frequency scales of the 2D dyadic wavelet transform, for which only a few such scales are computable for images. The strongly non-Gaussian nature of multifractal processes, combined with their complicated dependence structure, makes it difficult to develop suitable models for parameter estimation. Here, we propose a Bayesian procedure that addresses the difficulties in the estimation of the multifractality parameter. The originality of the procedure is threefold. The construction of a generic semiparametric statistical model for the logarithm of wavelet leaders; the formulation of Bayesian estimators that are associated with this model and the set of parameter values admitted by multifractal theory; the exploitation of a suitable Whittle approximation within the Bayesian model which enables the otherwise infeasible evaluation of the posterior distribution associated with the model. Performance is assessed numerically for several 2D multifractal processes, for several image sizes and a large range of process parameters. The procedure yields significant benefits over current benchmark estimators in terms of estimation performance and ability to discriminate between the two most commonly used classes of multifractal process models. The gains in performance are particularly pronounced for small image sizes, notably enabling for the first time the analysis of image patches as small as 64 × 64 pixels.

MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS FOR IMAGE TEXTURE FEATURE REPRESENTATION

Multifractal theory has been widely used in different kinds of fields. In this paper, methods were proposed to extract two kinds of multifractal descriptors of gray series and two-dimensional surfaces for gray image based on the multifractal detrended fluctuation analysis. The proposed multifractal parameters can be well described by texture feature through the test of some textures. Three aspects of experiments have been conducted to verify the robustness of the proposed parameters, which include noise immunity, degree of image blurring and compression ratio. Comparisons were conducted between the proposed parameters and other kinds of texture feature parameters calculated by the standard multifractal analysis, the method of differential box counting and the methods of gray level co-occurrence matrix. Results demonstrate that the proposed exponents of H(2) and h(2) have great noise immunity and are robust to image compression and blurring.

Single-image superresolution of natural stochastic textures based on fractional Brownian motion

Texture enhancement presents an ongoing challenge, in spite of the considerable progress made in recent years. Whereas most of the effort has been devoted so far to enhancement of regular textures, stochastic textures that are encountered in most natural images, still pose an outstanding problem. The purpose of enhancement of stochastic textures is to recover details, which were lost during the acquisition of the image. In this paper, a texture model, based on fractional Brownian motion (fBm), is proposed. The model is global and does not entail using image patches. The fBm is a self-similar stochastic process. Self-similarity is known to characterize a large class of natural textures. The fBm-based model is evaluated and a single-image regularized superresolution algorithm is derived. The proposed algorithm is useful for enhancement of a wide range of textures. Its performance is compared with single-image superresolution methods and its advantages are highlighted.

Multi-Focus Image Fusion Using the Local Fractal Dimension

Abstract With the development of sensor and image-processing technology, image fusion has become a promising research field. Multi-focus image fusion is an important issue in multi-sensor image fusion. To make full use of the texture features of an image and take into account the inherent advantages of fractal theory in multi-focus image fusion, a new image fusion algorithm using the local fractal dimension (LFD) is proposed. The algorithm first calculates the LFD of each source image pixel-wise by using a blanket method and generates LFD maps of the source images. Then the local energy of each LFD is calculated to generate a decision map, in order to decide pixels of the fused image are from which source image. Finally, the fused image is reconstructed from the source images according to the decision map. Experimental results show that the proposed algorithm outperforms classic LP-based and DWT-based methods according to both visual and objective evaluations.

Epileptic seizure detection with linear and nonlinear features

Automatic seizure detection is significant in both diagnosis of epilepsy and relieving the heavy workload of inspecting prolonged EEG. This paper presents a new seizure detection method for multi-channel long-term EEG. The fractal intercept derived from fractal geometry is extracted as a novel nonlinear feature of EEG signals, and the relative fluctuation index is calculated as a linear feature. The feature vector, consisting of the two EEG descriptors, is fed into a single-layer neural network for classification. Extreme learning machine (ELM) algorithm is adopted to train the neural network. Finally, post-processing including smoothing, channel fusion, and collar technique is employed to obtain more accurate and stable results. Both the segment-based and event-based assessments are used for the performance evaluation of this method on the 21-patient Freiburg dataset. The segment-based sensitivity of 91.72% and specificity of 94.89% were achieved. For the event-based assessment, this method yielded a sensitivity of 93.85% with a false detection rate of 0.35/h.

ON THE USE OF MULTIFRACTAL ANALYSIS AND GENETIC ALGORITHMS FOR THE SEGMENTATION OF CERVICAL CELL IMAGES

This paper deals with the segmentation problem of cervical cell images. This segmentation consists of separating each cell into its core and its cytoplasm. The mentioned separation is part of a uterus cancer recognition system based on the morphology of both the cell core and the cell cytoplasm. In this paper, we propose to perform the above separation by using a multifractal algorithm. An important feature of the proposed algorithm is its low computation cost. To increase the quality of the segmentation, we propose an optimization step based on genetic algorithms. The proposed processing has been tested on several images. Herein, we present only the results obtained for three different cell images.

A METHOD FOR ESTIMATING FRACTAL DIMENSION OF TREE CROWNS FROM DIGITAL IMAGES

A new method for estimating fractal dimension of tree crowns from digital images is presented. Three species of trees, Japanese yew (Taxus cuspidata Sieb & Zucc), Hicks yew (Taxus × media), and eastern white pine (Pinus strobus L.), were studied. Fractal dimensions of Japanese yew and Hicks yew range from 2.26 to 2.70. Fractal dimension of eastern white pine range from 2.14 to 2.43. The difference in fractal dimension between Japanese yew and eastern white pine was statistically significant at 0.05 significance level as was the difference in fractal dimension between Hicks yew and eastern white pine. On average, the greater fractal dimensions of Japanese yew and Hicks yew were possibly related to uniform foliage distribution within their tree crowns. Therefore, fractal dimension may be useful for tree crown structure classification and for indexing tree images.

ARTIFICIAL LIFE: A NEW APPROACH TO TEXTURE CLASSIFICATION

This paper presents a novel approach to image texture classification, which involves a model of artificial organisms i.e. Artificial Crawlers (ACrawlers) and a series of evolution curves representing the features of the texture. The distributed ACrawlers locally interact with their living environment, i.e. textured regions, and each ACrawler acts according to a set of homogenous rules for isotropic motion, energy absorption and colony formation, etc. The ACrawlers evolve through natural selection, which produces the specific curves of agent evolution, habitant settlement and colony formation as well as the scale distribution of all colonies. The feasibility and effectiveness of the proposed method have been demonstrated by experiments.

ON TEXTURE CLASSIFICATION USING FRACTAL DIMENSION

The fractal dimension has been studied as a feature for texture analysis. It has been found that the fractal dimension is not an effective image texture measure but little is known about the reasons for the fractal dimension failing to be effective for texture analysis. This paper investigates into the underlying causes why the fractal dimension is not an effective image texture feature. Four mathematical properties have been identified which are responsible for the fractal dimension's ineffectiveness. The experimental results show that while the fractal dimension itself is hardly an effective feature for texture classification, it can considerably enhance other feature sets.

Fractal dimension of color fractal images

Fractal dimension is a very useful metric for the analysis of the images with self-similar content, such as textures. For its computation there exist several approaches, the probabilistic algorithm being accepted as the most elegant approach. However, all the existing methods are defined for 1-D signals or binary images, with extension to grayscale images. Our purpose is to propose a color version of the probabilistic algorithm for the computation of the fractal dimension. To validate this new approach, we also propose an extension of the existing algorithm for the generation of probabilistic fractals, in order to obtain color fractal images. Then we show the results of our experiments and conclude this paper.

Substrate-induced assembly of fibronectin into networks: influence of surface chemistry and effect on osteoblast adhesion

The influence of surface chemistry-substrates with controlled surface density of -OH groups-on fibronectin (FN) conformation and distribution is directly observed by atomic force microscopy (AFM). FN fibrillogenesis, which is known to be a process triggered by interaction with integrins, is shown in our case to be induced by the substrate (in absence of cells), which is able to enhance FN-FN interactions leading to the formation of a protein network on the material surface. This phenomenon depends both on surface chemistry and protein concentration. The level of the FN fibrillogenesis was quantified by calculating the fractal dimension of the adsorbed protein from image analysis of the AFM results. The total amount of adsorbed FN is obtained by making use of a methodology that employs Western blotting combined with image analysis of the corresponding protein bands, with the lowest sensitivity threshold equal to 15 ng of adsorbed protein. Further, FN adsorption is correlated to human osteoblast adhesion through morphology and actin cytoskeleton formation. Actin polymerization is in need of the formation of the protein network on the substrate's surface. Cell morphology is more rounded (as quantified by calculating the circularity of the cells by image analysis) when the degree of FN fibrillogenesis on the substrate is lower.