Is a two-dimensional generalization of the Higuchi algorithm really necessary?

Fractals in the Neurosciences: A Translational Geographical Approach

The chapter presents three new fractal indices (fractal fragmentation index, fractal tentacularity index, and fractal anisotropy index) and normalized Kolmogorov complexity with proven applicability in geographic research, developed by the authors, and the possibility of their future use in neuroscience. The research demonstrates the relevance of fractal analysis in different fields and the basic concepts and principles of fractal geometry being sufficient for the development of models relevant to the studied reality. Also, the research highlighted the need to continue interdisciplinary research based on known fractal indicators, as well as the development of new analysis methods with the translational potential between fields.

ComsystanJ: A collection of Fiji/ImageJ2 plugins for nonlinear and complexity analysis in 1D, 2D and 3D

Complex systems such as the global climate, biological organisms, civilisation, technical or social networks exhibit diverse behaviours at various temporal and spatial scales, often characterized by nonlinearity, feedback loops, and emergence. These systems can be characterized by physical quantities such as entropy, information, chaoticity or fractality rather than classical quantities such as time, velocity, energy or temperature. The drawback of these complexity quantities is that their definitions are not always mathematically exact and computational algorithms provide estimates rather than exact values. Typically, evaluations can be cumbersome, necessitating specialized tools. We are therefore introducing ComsystanJ, a novel and user-friendly software suite, providing a comprehensive set of plugins for complex systems analysis, without the need for prior programming knowledge. It is platform independent, end-user friendly and extensible. ComsystanJ combines already known algorithms and newer methods for generalizable analysis of 1D signals, 2D images and 3D volume data including the generation of data sets such as signals and images for testing purposes. It is based on the framework of the open-source image processing software Fiji and ImageJ2. ComsystanJ plugins are macro recordable and are maintained as open-source software. ComsystanJ includes effective surrogate analysis in all dimensions to validate the features calculated by the different algorithms. Future enhancements of the project will include the implementation of parallel computing for image stacks and volumes and the integration of artificial intelligence methods to improve feature recognition and parameter calculation.

Accessibility of the surface fractal dimension during film growth

Fractal properties on self-affine surfaces of films growing under nonequilibrium conditions are important in understanding the corresponding universality class. However, measurement of the surface fractal dimension has been intensively investigated and is still very problematic. In this work, we report the behavior of the effective fractal dimension in the context of film growth involving lattice models believed to belong to the Kardar-Parisi-Zhang (KPZ) universality class. Our results, which are presented for growth in a d-dimensional substrate (d=1,2) and use the three-point sinuosity (TPS) method, show universal scaling of the measure M, which is defined in terms of discretization of the Laplacian operator applied to the height of the film surface, M=t^{δ}g[Θ], where t is the time, g[Θ] is a scale function, δ=2β, Θ≡τt^{-1/z}, β, and z are the KPZ growth and dynamical exponents, respectively, and τ is a spatial scale length used to compute M. Importantly, we show that the effective fractal dimensions are consistent with the expected KPZ dimensions for d=1,2, if Θ≲0.3, which include a thin film regime for the extraction of the fractal dimension. This establishes the scale limits in which the TPS method can be used to accurately extract effective fractal dimensions that are consistent with those expected for the corresponding universality class. As a consequence, for the steady state, which is inaccessible to experimentalists studying film growth, the TPS method provided effective fractal dimension consistent with the KPZ ones for almost all possible τ, i.e., 1≲τ<L/2, where L is the lateral size of the substrate on which the deposit is grown. In the growth of thin films, the true fractal dimension can be observed in a narrow range of τ, the upper limit of which is of the same order of magnitude as the correlation length of the surface, indicating the limits of self-affinity of a surface in an experimentally accessible regime. This upper limit was comparatively lower for the Higuchi method or the height-difference correlation function. Scaling corrections for the measure M and the height-difference correlation function are studied analytically and compared for the Edwards-Wilkinson class at d=1, yielding similar accuracy for both methods. Importantly, we extend our discussion to a model representing diffusion-dominated growth of films and find that the TPS method achieves the corresponding fractal dimension only at steady state and in a narrow range of the scale length, compared to that found for the KPZ class.

Directionally Sensitive Fractal Radiomics Compatible With Irregularly Shaped Magnetic Resonance Tumor Regions of Interest: Association With Osteosarcoma Chemoresistance

BACKGROUND

Computational analysis of routinely acquired MRI has potential to improve the tumor chemoresistance prediction and to provide decision support in precision medicine, which may extend patient survival. Most radiomic analytical methods are compatible only with rectangular regions of interest (ROIs) and irregular tumor shape is therefore an important limitation. Furthermore, the currently used analytical methods are not directionally sensitive.

PURPOSE

To implement a tumor analysis that is directionally sensitive and compatible with irregularly shaped ROIs.

STUDY TYPE

Retrospective.

SUBJECTS

A total of 54 patients with histopathologic diagnosis of primary osteosarcoma on tubular long bones and with prechemotherapy MRI.

FIELD STRENGTH/SEQUENCE

A 1.5 T, T2-weighted-short-tau-inversion-recovery-fast-spin-echo.

ASSESSMENT

A model to explore associations with osteosarcoma chemo-responsiveness included MRI data obtained before OsteoSa MAP neoadjuvant cytotoxic chemotherapy. Osteosarcoma morphology was analyzed in the MRI data by calculation of the nondirectional two-dimensional (2D) and directional and nondirectional one-dimensional (1D) Higuchi dimensions (Dh). MAP chemotherapy response was assessed by histopathological necrosis.

STATISTICAL TESTS

The area under the receiver operating characteristic (ROC) curve (AUC) evaluated the association of the calculated features with the actual chemoresponsiveness, using tumor histopathological necrosis (95%) as the endpoint. Least absolute shrinkage and selection operator (LASSO) machine learning and multivariable regression were used for feature selection. Significance was set at <0.05.

RESULTS

The nondirectional 1D Dh reached an AUC of 0.88 in association with the 95% tumor necrosis, while the directional 1D analysis along 180 radial lines significantly improved this association according to the Hanley/McNeil test, reaching an AUC of 0.95. The model defined by variable selection using LASSO reached an AUC of 0.98. The directional analysis showed an optimal predictive range between 90° and 97° and revealed structural osteosarcoma anisotropy manifested by its directionally dependent textural properties.

DATA CONCLUSION

Directionally sensitive radiomics had superior predictive performance in comparison to the standard nondirectional image analysis algorithms with AUCs reaching 0.95 and full compatibility with irregularly shaped ROIs.

EVIDENCE LEVEL

3 TECHNICAL EFFICACY: Stage 1.

Skin Lesion Classification Based on Surface Fractal Dimensions and Statistical Color Cluster Features Using an Ensemble of Machine Learning Techniques

Simple Summary

This study aimed to investigate the efficacy of implementation of novel skin surface fractal dimension features as an auxiliary diagnostic method for melanoma recognition. We therefore examined the skin lesion classification accuracy of the kNN-CV algorithm and of the proposed Radial basis function neural network model. We found an increased accuracy of classification when the fractal analysis is added to the classical color distribution analysis. Our results indicate that by using a reliable classifier, more opportunities exist to detect timely cancerous skin lesions.

Abstract

(1) Background: An approach for skin cancer recognition and classification by implementation of a novel combination of features and two classifiers, as an auxiliary diagnostic method, is proposed. (2) Methods: The predictions are made by k-nearest neighbor with a 5-fold cross validation algorithm and a neural network model to assist dermatologists in the diagnosis of cancerous skin lesions. As a main contribution, this work proposes a descriptor that combines skin surface fractal dimension and relevant color area features for skin lesion classification purposes. The surface fractal dimension is computed using a 2D generalization of Higuchi’s method. A clustering method allows for the selection of the relevant color distribution in skin lesion images by determining the average percentage of color areas within the nevi and melanoma lesion areas. In a classification stage, the Higuchi fractal dimensions (HFDs) and the color features are classified, separately, using a kNN-CV algorithm. In addition, these features are prototypes for a Radial basis function neural network (RBFNN) classifier. The efficiency of our algorithms was verified by utilizing images belonging to the 7-Point, Med-Node, and PH2 databases; (3) Results: Experimental results show that the accuracy of the proposed RBFNN model in skin cancer classification is 95.42% for 7-Point, 94.71% for Med-Node, and 94.88% for PH2, which are all significantly better than that of the kNN algorithm. (4) Conclusions: 2D Higuchi’s surface fractal features have not been previously used for skin lesion classification purpose. We used fractal features further correlated to color features to create a RBFNN classifier that provides high accuracies of classification.

Particularities of Forest Dynamics Using Higuchi Dimension. Parâng Mountains as a Case Study

The legal or illegal losses and the natural disturbance regime of forest areas in Romania generate major imbalances in territorial systems. The main purpose of the current research was to examine the dynamics of the complexity of forests under the influence of forest loss but also to compare the applicability of Higuchi dimension. In this study, two fractal algorithms, Higuchi 1D (H1D) and Higuchi 2D (H2D), were used to determine qualitative and quantitative aspects based on images obtained from a Geographic Information System (GIS) database. The H1D analysis showed that the impact of forest loss has led to increased fragmentation of the forests, generating a continuous increase in the complexity of forest areas. The H2D analysis identified the complexity of forest morphology by the relationship between each pixel and the neighboring pixels from analyzed images, which allowed us to highlight the local characteristics of the forest loss. The H1D and H2D methods showed that they have the speed and simplicity required for forest loss analysis. Using this methodology complementary to GIS analyses, a relevant status of how forest loss occurred and their impact on tree-cover dynamics was obtained.

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.