Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer

Background: Prostate cancer is a serious public health problem that affects quality of life and has a significant mortality rate. The aim of the present study was to quantify the fractal dimension and Shannon’s entropy in the histological diagnosis of prostate cancer. Methods: Thirty-four patients with prostate cancer aged 50 to 75 years having been submitted to radical prostatectomy participated in the study. Histological slides of normal (N), hyperplastic (H) and tumor (T) areas of the prostate were digitally photographed with three different magnifications (40x, 100x and 400x) and analyzed. The fractal dimension (FD), Shannon’s entropy (SE) and number of cell nuclei (NCN) in these areas were compared. Results: FD analysis demonstrated the following significant differences between groups: T vs. N and H vs. N groups (p < 0.05) at a magnification of 40x; T vs. N (p < 0.01) at 100x and H vs. N (p < 0.01) at 400x. SE analysis revealed the following significant differences groups: T vs. H and T vs. N (p < 0.05) at 100x; and T vs. H and T vs. N (p < 0.001) at 400x. NCN analysis demonstrated the following significant differences between groups: T vs. H and T vs. N (p < 0.05) at 40x; T vs. H and T vs. N (p < 0.0001) at 100x; and T vs. H and T vs. N (p < 0.01) at 400x. Conclusions: The quantification of the FD and SE, together with the number of cell nuclei, has potential clinical applications in the histological diagnosis of prostate cancer.

Effects of specimen geometry and loading mode on crack growth resistance curves of a high-strength pipeline girth weld

This work presents an investigation of the ductile tearing properties for a girth weld made of an API 5L X80 pipeline steel using experimentally measured crack growth resistance curves. Use of these materials is motivated by the increasing demand in the number of applications for manufacturing high strength pipes for the oil and gas industry including marine applications and steel catenary risers. Testing of the pipeline girth welds employed side-grooved, clamped SE(T) specimens and shallow crack bend SE(B) specimens with a weld centerline notch to determine the crack growth resistance curves based upon the unloading compliance (UC) method using the single specimen technique. Recently developed compliance functions and η-factors applicable for SE(T) and SE(B) fracture specimens with homogeneous material and overmatched welds are introduced to determine crack growth resistance data from laboratory measurements of load-displacement records.

Characterization of nanostructured material images using fractal descriptors

This work presents a methodology to the morphology analysis and characterization of nanostructured material images acquired from FEG-SEM (Field Emission Gun-Scanning Electron Microscopy) technique. The metrics were extracted from the image texture (mathematical surface) by the volumetric fractal descriptors, a methodology based on the Bouligand-Minkowski fractal dimension, which considers the properties of the Minkowski dilation of the surface points. An experiment with galvanostatic anodic titanium oxide samples prepared in oxalyc acid solution using different conditions of applied current, oxalyc acid concentration and solution temperature was performed. The results demonstrate that the approach is capable of characterizing complex morphology characteristics such as those present in the anodic titanium oxide.

Texture analysis by multi-resolution fractal descriptors

This work proposes a novel texture descriptor based on fractal theory. The method is based on the Bouligand- Minkowski descriptors. We decompose the original image recursively into four equal parts. In each recursion step, we estimate the average and the deviation of the Bouligand-Minkowski descriptors computed over each part. Thus, we extract entropy features from both average and deviation. The proposed descriptors are provided by concatenating such measures. The method is tested in a classification experiment under well known datasets, that is, Brodatz and Vistex. The results demonstrate that the novel technique achieves better results than classical and state-of-the-art texture descriptors, such as Local Binary Patterns, Gabor-wavelets and co-occurrence matrix.

Multiscale fractal descriptors applied to nanoscale images

This work proposes the application of fractal descriptors to the analysis of nanoscale materials under different experimental conditions. We obtain descriptors for images from the sample applying a multiscale transform to the calculation of fractal dimension of a surface map of such image. Particularly, we have used the Bouligand-Minkowski fractal dimension. We applied these descriptors to discriminate between two titanium oxide films prepared under different experimental conditions. Results demonstrate the discrimination power of proposed descriptors in such kind of application.

Combining fractal and deterministic walkers for texture analysis and classification

In this paper,we present a novel texture analysis method based on deterministic partially self-avoiding walks and fractal dimension theory. After finding the attractors of the image (set of pixels) using deterministic partially self-avoiding walks, they are dilated in direction to the whole image by adding pixels according to their relevance. The relevance of each pixel is calculated as the shortest path between the pixel and the pixels that belongs to the attractors. The proposed texture analysis method is demonstrated to outperform popular and state-of-the-art methods (e.g. Fourier descriptors, occurrence matrix, Gabor filter and local binary patterns) as well as deterministic tourist walk method and recent fractal methods using well-known texture image datasets.