The Fractal Dimension Suggests Two Chromatin Configurations in Small Cell Neuroendocrine Lung Cancer and Is an Independent Unfavorable Prognostic Factor for Overall Survival.

Experimental studies have shown that in small cell neuroendocrine lung carcinomas (SCLC) global opening of the chromatin structure is associated with a higher transcription activity and increase of tumor aggressiveness and metastasis. The study of the fractal characteristics (FD) of nuclear chromatin has been widely used to describe the cell nuclear texture and its changes correspond to changes in nuclear metabolic and transcription activity. Hence, we investigated whether the nuclear fractal dimension could be a prognostic factor in SCLC. Hematoxylin-eosin stained brush cytology slides from 49 patients with SCLC were retrieved from our files. The chromatin (FD) was calculated in digitalized and interactively segmented nuclei using a differential box-counting method. The 3,575 nuclei studied showed a bimodal distribution (peaks at FD1 = 2.115 and FD2 = 2.180). The 75 percentile of the FD was an independent unfavorable prognostic factor for overall survival when tested together with ECOG (Eastern Cooperative Oncology Group) performance status, tumor extension, and therapy in a multivariate Cox regression. Our study corroborates the concept of two main chromatin configurations in small cell neuroendocrine carcinomas and that globally more open chromatin indicates a higher risk of metastasis and therefore a shorter survival of the patient.

The fractal dimension of chromatin - a potential molecular marker for carcinogenesis, tumor progression and prognosis.

INTRODUCTION: Fractality is omnipresent in medicine and life sciences. In particular, the fractal principle is found simultaneously at different organization levels of the cell nucleus. The aim of this review is to show whether fractal characteristics of chromatin could be related to tumor pathology and pathophysiology. Areas covered: This review provides an overview of the application of fractal measurements of chromatin or DNA for the characterization of physiological or pathological processes, in particular for the detection of preneoplastic changes, the characterization of tumor progression, the differential diagnosis between neoplasms and for prognosis. We used a network-based literature research strategy, i.e. after a systematic investigation by key-words, we looked for all citations (and the citations to these citations) of the selected papers in Scopus and Webofscience. Expert opinion: The fractal dimension (FD) increases during carcinogenesis, thus permitting the diagnosis of malignancy. In various malignant tumors, a higher FD or diminished goodness-of-fit of its regression line indicates a more aggressive behavior and worse prognosis. Applying new spectral techniques, the chromatin FD can be estimated at scales below the light microscopic resolution. The latter also permits the examination of live cells and studies on field carcinogenesis and chemoprophylaxis.

Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors.

The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification.

Fractal descriptors in the Fourier domain applied to color texture analysis.

The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists of two steps. First, we apply a linear transform in the color space of the image aiming at highlighting spatial structuring relations among the color of pixels. Second, we apply a multiscale approach to the calculus of fractal dimension based on Fourier transform. From this multiscale operation, we extract the descriptors that are used to discriminate the texture represented in digital images. The accuracy of the method is verified in the classification of two color texture datasets, by comparing the performance of the proposed technique to other classical and state-of-the-art methods for color texture analysis. The results showed an advantage of almost 3% of the proposed technique over the second best approach.

Mumford-Shah algorithm applied to videokeratography image processing and consequences to refractive power values.

There are many corneal diseases that can be detected using an eye-care device called videokeratograph. The videokeratograph is based on the principle of an apparatus called Placido disc and is used to precisely measure the anterior surface of the cornea. This disc contains rings alternately white and black, which are reflected on the patient's cornea during the examination. The device can find anomalies by analyzing the reflected image, using image-processing algorithms. Although the efficiency of most commercial videokeratographs is acceptable, manufacturers do not disseminate to the scientific community the technique used in the image analysis algorithms. This makes it difficult for the specialized researcher in order to find better algorithms for the image-processing and, consequently, increase the instrument's precision. In this work we have segmented the Placido disc in polar coordinates by implementing a diagonal section of the image, in the radial direction. The objective is to find the inflection points in the signal obtained. In this paper the signal is studied by using the Mumford-Shah segmentation method. The results are compared to those obtained with other classic methods in the literature, e.g. Marr-Hildreth filters, numerical derivative, Fourier derivative, morphological Laplacian and Canny derivative. The best result was achieved by using the Mumford-Shah functional. Using this technique it was possible to find the inflection positions with higher accuracy. The method did not detect any false inflection. Mumford-Shah's method demonstrated also a high precision in the task of eliminating noises from the original signal.