Higuchi Dimension of Digital Images

There exist several methods for calculating the fractal dimension of objects represented as 2D digital images. For example, Box counting, Minkowski dilation or Fourier analysis can be employed. However, there appear to be some limitations. It is not possible to calculate only the fractal dimension of an irregular region of interest in an image or to perform the calculations in a particular direction along a line on an arbitrary angle through the image. The calculations must be made for the whole image. In this paper, a new method to overcome these limitations is proposed. 2D images are appropriately prepared in order to apply 1D signal analyses, originally developed to investigate nonlinear time series. The Higuchi dimension of these 1D signals is calculated using Higuchi's algorithm, and it is shown that both regions of interests and directional dependencies can be evaluated independently of the whole picture. A thorough validation of the proposed technique and a comparison of the new method to the Fourier dimension, a common two dimensional method for digital images, are given. The main result is that Higuchi's algorithm allows a direction dependent as well as direction independent analysis. Actual values for the fractal dimensions are reliable and an effective treatment of regions of interests is possible. Moreover, the proposed method is not restricted to Higuchi's algorithm, as any 1D method of analysis, can be applied

Analysis of anal intraepithelial neoplasia images using 1d and 2d higuchi's fractal dimension methods

The ILF (Image Landscapes' Fractal Dimension) method and DF2d method obtained by a 2D generalization of Higuchi's algorithm were applied to a set of 120 digital histological images of Anal Intraepithelial Neoplasia (AIN). The main goal of this research was to examine accuracy that means sensitivity and specificity of these methods and compare the applicability of both methods in the quantitative characterization and differentiation of clinical cases of AIN. Histological examination by an experienced pathologist revealed three grades of AIN tumors in the 120 histological slices: 36 of AIN1, 56 of AIN2 and 28 of AIN3. Statistical tests showed significant differences between calculated fractal dimension values in three datasets (AIN1, AIN2 and AIN3) using ILF and DF2d methods at the level of significance of 0.05. Application of the ILF and DF2d methods has an advantage when it comes to speed, accuracy, simplicity and time necessary for analysis. Both methods can be successfully applied for differentiation between AIN stages giving practically the same results. They can easily be adapted to other histological specimen

CAN COMPLEXITY MEASURES WITH HIERARCHICAL CLUSTER ANALYSIS IDENTIFY OVERPAINTED ARTWORK?

Exploring the attribution of sub-painted layers in overpainted artworks created with various pigments on canvas/wood has received limited attention. Previously this problem of underpainting inhered limitations. This study addresses the palimpsest-like stratigraphy of such artworks using an innovative and validated statistical approach. To replicate the process, painted and overpainted panels were meticulously constructed following historical recipes for preparation and pigment selection. Spectral data in the near-infrared (NIR) range (400-1000nm) were captured using a multispectral NIR camera, employing reflected light under normal illumination conditions. A total of 45 pigments, representing 45 colors, were employed in the creation of three sets of overpainted layers: upper Egyptian blue, cadmium red, and cadmium yellow. Several parameters influencing the experimental setup were considered, including capturing conditions and imaged areas. A normalization procedure was applied to ensure consistent capturing conditions across all images. The standardized set of spectral images was subjected to appropriate agglomerative hierarchical clustering methods (Average Linkage, Complete Linkage, Ward Linkage, and Ward D2 Linkage), as well as principal component analysis (PCA) with accompanying statistical tests to validate clustering (Silhouette, Box plots, K-means, Wilks). Additionally, complex and entropy measures were employed. By integrating traditional statistical multivariate methods with modern complexity measures, consistent interpretation of the data was achieved. PCA combined with clustering methods enabled referencing of spectral data with the Mahalanobis connection distance, highlighting clusters directly associated with differences in intensity along the NIR range for each panel's segmented spectral cubes. It is non-destructive method and offers a unique data base for future research. The novelty of this study is therefore utilizing the experimental database and applying innovative corroborated mathematical techniques. This approach facilitated the identification of overpainted panels based on their similar NIR spectral characteristics and successfully identified an unknown painted panel within this initial three-color database with highly satisfactory results

Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems.

Significant advancements in imaging technology and the dramatic increase in computer power over the last few years broke the ground for the construction of anatomically realistic models of the heart at an unprecedented level of detail. To effectively make use of high-resolution imaging datasets for modeling purposes, the imaged objects have to be discretized. This procedure is trivial for structured grids. However, to develop generally applicable heart models, unstructured grids are much preferable. In this study, a novel image-based unstructured mesh generation technique is proposed. It uses the dual mesh of an octree applied directly to segmented 3-D image stacks. The method produces conformal, boundary-fitted, and hexahedra-dominant meshes. The algorithm operates fully automatically with no requirements for interactivity and generates accurate volume-preserving representations of arbitrarily complex geometries with smooth surfaces. The method is very well suited for cardiac electrophysiological simulations. In the myocardium, the algorithm minimizes variations in element size, whereas in the surrounding medium, the element size is grown larger with the distance to the myocardial surfaces to reduce the computational burden. The numerical feasibility of the approach is demonstrated by discretizing and solving the monodomain and bidomain equations on the generated grids for two preparations of high experimental relevance, a left ventricular wedge preparation, and a papillary muscle