Modeling and analysis of fractal transformation of distorted images of the Earth’s surface obtained by optoelectronic surveillance systems

The results of a study of methods for processing optoelectronic images of the Earth’s surface are presented. The application of fractal transformations to solve the problems of automated and automatic analysis of terrain images, ensuring the separation of natural and anthropogenic objects without the use of machine learning, is shown. The analysis of existing works has shown the absence of studies linking the result of fractal transformation with the image quality recorded in real conditions of optoelectronic photography. There is no justification for choosing a specific fractal transformation for the applied processing of images with certain typical distortions. The purpose of this work was to identify the dependence of the signal-to-noise ratio of fractal dimension on the quality of the source images, to determine the type of fractal transformation that is most resistant to the effects of the considered negative factors. Methods of fractal transformations for thematic image processing are defined, which include the prism method and the differential cube counting method, and their description is presented. To study the selected methods, real images of the Earth’s surface were used, simulating distorted images of the terrain. Image distortions determined by the instability of shooting conditions and the properties of the optoelectronic complex are considered: defocusing, smudging and noise. The mathematical models used to describe them are summarized. A technique for analyzing the signal-to-noise ratio of fractal transformation is described, involving the processing of reference and distorted images of the terrain. The aspects of distortion modeling and indicators characterizing the level of image distortion are indicated. To implement the experiment, images of the area were selected characterized by various plots. For each plot, the dependences of the signal-to-noise ratio on the indicators characterizing the studied distortions are obtained. By estimating the signal-tonoise ratio, the analysis of the influence of distorting factors on the fractal dimension field being formed was performed. The results of the experiment confirmed the possibility of using fractal transformations for thematic processing of distorted optoelectronic images. It is shown that the dependence of the signal-to-noise ratio on the distortion index has a pronounced nonlinear character. It is established that for distortions of the defocusing and smearing type, the prism method is more stable, and in the presence of noise, the differential cube method is more stable. For processing images of an area represented mainly by images of forest vegetation, the best result is shown by using the differential cube counting method

Investigation on Non-Segmentation Based Algorithms for Microvasculature Quantification in OCTA Images

Optical Coherence Tomography Angiography (OCTA) is an imaging modality that provides three-dimensional information of the retinal microvasculature and therefore promises early diagnosis and sufficient monitoring in ophthalmology. However, there is considerable variability between experts analysing this data. Measures for quantitative assessment of the vasculature need to be developed and established, such as fractal dimension. Fractal dimension can be used to assess the complexity of vessels and has been shown to be independently associated with neovascularization, a symptom of diseases such as diabetic retinopathy. This investigation assessed the performance of three fractal dimension algorithms: Box Counting Dimension (BCD), Information Dimension (ID), and Differential Box Counting (DBC). Two of those, BCD and ID, rely on previous vessel segmentation. Assessment of the added value or disturbance regarding the segmentation step is a second aim of this study. The investigation was performed on a data set composed of 9 in vivo human eyes. Since there is no ground truth available, the performance of the methods in differentiating the Superficial Vascular Complex (SVC) and Deep Vascular Complex (DVC) layers apart and the consistency of measurements of the same layer at different time-points were tested. The performance parameters were the ICC and the Mann-Whitney U tests. The three applied methods were suitable to tell the different layers apart and showed consistent values applied in the same slab. Within the consistency test, the non-segmentation-based method, DBC, was found to be less accurate, expressed in a lower ICC value, compared to its segmentation-based counterparts. This result is thought to be due to the DBC’s higher sensitivity when compared to the other methods. This higher sensitivity might help detect changes in the microvasculature, like neovascularization, but is also more likely prone to noise and artefacts

2D Fourier Fractal Analysis of Optical Coherence Tomography Images of Basal Cell Carcinomas and Melanomas

The optical coherence tomography (OCT) technique is applied in the diagnosis of the skin tissue. In general, quantitative imaging features obtained from OCT images have already been used as biomarkers to categorize skin tumors. Particularly, the fractal dimension (FD) could be capable of providing an efficient approach for analyzing OCT images of skin tumors. The 2D Fourier fractal analysis (FFA) as well as the differential box counting method (DBCM) was used in this paper to classify the basal cell carcinomas (BCC), melanomas, and benign melanocytic nevi. Generalized estimating equations were used to test for differences between skin tumors. Our results showed that the significant decrease of the 2D FD was detected in the benign melanocytic nevi and basal cell carcinomas as compared with the melanomas. Our results also suggested that the 2D FFA could provide a more efficient way to calculating FD to differentiate the basal cell carcinomas, melanomas, and benign melanocytic nevi as compared to the 2D DBCM

Suitability of lacunarity measure for blind steganalysis

Blind steganalysis performance is influenced by several factors including the features used for classification. This paper investigates the suitability of using lacunarity measure as a potential feature vectorfor blind steganalysis. Differential Box Counting (DBC) based lacunarity measure has been employed using the traditional sequential grid (SG) and a new radial strip (RS) approach. The performance of the multi-class SVM based classifier was unfortunately not what was expected. However, the findings show that both the SG and RS lacunarity produce enough discriminating features that warrant further research

Textural analysis of skin cancer tumors on OCT images

In this paper, we propose a report about our two years investigations in skin cancer texture analysis on OCT images from different tissues. We suggest method compiled from Haralick texture features, fractal dimension, complex directional field features and Markov random field method. Additionally, boosting has been used for the quality enhancing of the diagnosis method. We obtained precision about 90% for two classes cases and about 75% for four classes case.This research was supported by the Ministry of Education and Science of the Russian Federation. Authors are thankful to Dr. Wei Gao from Ningbo University of Technology for Matlab code providing for denoising and fractal dimension calculating

Implementación de algoritmos fractales para la clasificación no supervisada de imágenes raster

El presente artículo abarca la utilización de la geometría fractal y la estimación de la dimensión fractal como parámetro para clasificar una ima- gen digital por medio del método no supervisado. Existen múltiples métodos para estimar la dimen- sión fractal como el Método Fraccional Brownia- no (fBm, por sus siglas en inglés), los métodos de conteo de cajas y los métodos de determinación de áreas. A la hora de realizar una clasificación de imágenes digitales se utiliza como parámetro de clasificación la textura presente en las imágenes; esta textura es usualmente calculada por el mé- todo GLCM (Matriz de Co-ocurrencias de niveles de gris), la dimensión fractal es una alternativa a la hora de extraer esta característica de las imáge- nes. Se tomó el método de conteo de cajas dife- rencial (DBC, por sus siglas en inglés) mejorado como base en la determinación de la dimensión fractal y posterior clasificación de las imágenes raster. Las imágenes raster escogidas son imáge- nes de radar SAR debido a que es en este tipo de imágenes donde se obtiene mayor provecho del análisis de texturas, fuente de información pa- ra realizar la clasificación no supervisada, esto debido a la característica textural que puede ser capturada por medio de este tipo de sensores.

Investigating Tissue Optical Properties and Texture Descriptors of the Retina in Patients with Multiple Sclerosis

PURPOSE: To assess the differences in texture descriptors and optical properties of retinal tissue layers in patients with multiple sclerosis (MS) and to evaluate their usefulness in the detection of neurodegenerative changes using optical coherence tomography (OCT) image segmentation. PATIENTS AND METHODS: 38 patients with MS were examined using Stratus OCT. The raw macular OCT data were exported and processed using OCTRIMA software. The enrolled eyes were divided into two groups, based on the presence of optic neuritis (ON) in the history (MSON+ group, n = 36 and MSON- group, n = 31). Data of 29 eyes of 24 healthy subjects (H) were used as controls. A total of seven intraretinal layers were segmented and thickness as well as optical parameters such as contrast, fractal dimension, layer index and total reflectance were measured. Mixed-model ANOVA analysis was used for statistical comparisons. RESULTS: Significant thinning of the retinal nerve fiber layer (RNFL), ganglion cell/inner plexiform layer complex (GCL+IPL) and ganglion cell complex (GCC, RNFL+GCL+IPL) was observed between study groups in all comparisons. Significant difference was found in contrast in the RNFL, GCL+IPL, GCC, inner nuclear layer (INL) and outer plexiform layer when comparing MSON+ to the other groups. Higher fractal dimension values were observed in GCL+IPL and INL layers when comparing H vs. MSON+ groups. A significant difference was found in layer index in the RNFL, GCL+IPL and GCC layers in all comparisons. A significant difference was observed in total reflectance in the RNFL, GCL+IPL and GCC layers between the three examination groups. CONCLUSION: Texture and optical properties of the retinal tissue undergo pronounced changes in MS even without optic neuritis. Our results may help to further improve the diagnostic efficacy of OCT in MS and neurodegeneration

An Information Theoretic Approach For Feature Selection And Segmentation In Posterior Fossa Tumors

Posterior Fossa (PF) is a type of brain tumor located in or near brain stem and cerebellum. About 55% - 70 % pediatric brain tumors arise in the posterior fossa, compared with only 15% - 20% of adult tumors. For segmenting PF tumors we should have features to study the characteristics of tumors. In literature, different types of texture features such as Fractal Dimension (FD) and Multifractional Brownian Motion (mBm) have been exploited for measuring randomness associated with brain and tumor tissues structures, and the varying appearance of tissues in magnetic resonance images (MRI). For selecting best features techniques such as neural network and boosting methods have been exploited. However, neural network cannot descirbe about the properties of texture features. We explore methods such as information theroetic methods which can perform feature selection based on properties of texture features. The primary contribution of this dissertation is investigating efficacy of different image features such as intensity, fractal texture, and level - set shape in segmentation of PF tumor for pediatric patients. We explore effectiveness of using four different feature selection and three different segmentation techniques respectively to discriminate tumor regions from normal tissue in multimodal brain MRI. Our research suggest that Kullback - Leibler Divergence (KLD) measure for feature ranking and selection and Expectation Maximization (EM) algorithm for feature fusion and tumor segmentation offer the best performance for the patient data in this study. To improve segmentation accuracy, we need to consider abnormalities such as cyst, edema and necrosis which surround tumors. In this work, we exploit features which describe properties of cyst and technique which can be used to segment it. To achieve this goal, we extend the two class KLD techniques to multiclass feature selection techniques, so that we can effectively select features for tumor, cyst and non tumor tissues. We compute segemntation accuracy by computing number of pixels segemented to total number of pixels for the best features. For automated process we integrate the inhomoheneity correction, feature selection using KLD and segmentation in an integrated EM framework. To validate results we have used similarity coefficients for computing the robustness of segmented tumor and cyst