Fractal Dimension of Dog Kidney Proximal Convoluted Tubuli Sections by Mean Box-Counting Algorithm

Gil, Joaquín Navarro; Gimeno, Miguel; Laborda, Jesús; Nuviala, Javier

doi:10.4067/s0717-95022006000500005

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…Y que al disminuir el tamaño de caja se necesitan más cajas para cubrir al objeto. Por lo tanto, el método Boxcounting involucra cubrir el objeto por un conjunto de cajas de lado Ԑ; el número de cajas N(Ԑ) es proporcional a la escala en la forma N(Ԑ) N(Ԑ)α1 d /Ԑ^d donde, d es la dimensión del objeto (Gil et al 2006). Considerando que en el caso de una imagen digital el tamaño de caja corresponde al número de pixeles por pulgada cuadrada.…”

Section: Materiales Y Métodosunclassified

Caracterización morfométrica de estructuras florales de Tagetes erecta L. y Tagetes patula L. (Asteraceae) utilizando análisis digital de imágenes y dimensión fractal

Quintanilla-Carvajal

Arenas-Ocampo²,

Mendiola³

et al. 2015

Gayana Bot.

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Caracterización morfométrica de estructuras florales de Tagetes erecta L. y Tagetes patula L. (Asteraceae) utilizando análisis digital de imágenes y dimensión fractal RESUMENLas flores Tagetes erecta L. y Tagetes patula L. tienen usos ornamentales en México, y también algunas industrias las utilizan en la coloración de carne. El género Tagetes presenta especies y variedades con diferentes colores y tonalidades en sus flores. Por lo que, una forma de distinción rápida y objetiva de estas variedades sería útil para la industria. En este trabajo se desarrolló un método para distinguir y caracterizar la diversidad en dos variedades de T. erecta y T. patula a través de la caracterización de las estructuras florales, utilizando técnicas de análisis digital de imágenes y análisis fractal. Para esto, se capturaron imágenes de lígulas y capítulos florales, que posteriormente fueron binarizadas para obtener imágenes de objetos separados (lígulas y capítulos florales). El análisis de estas imágenes se realizó determinando diferentes parámetros morfométricos, tales como perímetro, área proyectada, longitud máxima, factor de forma y compacidad. Adicionalmente, se determinó la dimensión fractal de contorno, de perímetro y de área. Los resultados mostraron que la dimensión fractal y el factor de forma son los parámetros que detectan con mayor sensibilidad las diferencias entre lígulas y entre capítulos florales, por lo que se proponen como parámetro adecuados para caracterizar estructuras florales. Palabras clave:Tagetes erecta, T. patula, estructuras florales, análisis digital de imágenes, análisis fractal. ABSTRACTTagetes erecta L. and Tagetes patula L. flowers have ornamental uses in Mexico, but also some industries used in the coloring of meat. The genus Tagetes presents species and varieties with different colors and shades in their flowers. Therefore a rapid and objective form of distinction of these varieties would be useful for the industry. In this research was developed a method to distinguish and characterize the diversity in two varieties of the T. erecta and T. patula through the characterization of the floral structures, using techniques of digital image analysis and fractal analysis. Images of ligules and flower heads were captured and binarized to produce images of separate objects (ligules and flower heads). The analysis of these images was performed by determining different morphometric parameters such as perimeter, projected area, maximum length, shape factor and compactness. Additionally, the boundary fractal dimension, perimeter fractal dimension and area fractal dimension were determined. The results showed that the fractal dimension and form factor were the parameters in petals and flower head with higher sensitivity to detect differences between and among varieties and so are proposed as suitable parameter to characterize floral structures.

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Section: Materiales Y Métodosunclassified

Caracterización morfométrica de estructuras florales de Tagetes erecta L. y Tagetes patula L. (Asteraceae) utilizando análisis digital de imágenes y dimensión fractal

Quintanilla-Carvajal

Arenas-Ocampo²,

Mendiola³

et al. 2015

Gayana Bot.

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“…In the study of frequency distribution histogram, a large proportion of the lymphocytes of hairy cell leukemia patients had a fractal dimension exceeding 1.28 [8]. The fractal dimension calculated by applying the Box-counting method for the proximal convoluted tubule of the dog kidney was obtained as 1.33 ± 0.18 with 95 % security coefficient [14]. The metastases of colorectal cancer with fractal dimensions greater than 1.35 were associated with poor survival rate [15].…”

Section: Linear Regression and Statistical Methodsmentioning

confidence: 99%

Digital Mammogram and Tumour Detection Using Fractal-Based Texture Analysis: A Box-Counting Algorithm

Latha

Valarmathi

Sulthana

et al. 2014

Advances in Intelligent Systems and Computing

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Mammography and X-ray imaging of the breast are considered as the mainstay of breast cancer screening. In the past several years, there has been tremendous interest in image processing and analysis techniques in mammography. The fractal is an irregular geometric object with an infinite nesting of structure of different sizes. Fractals can be used to make models of any objects. The most important properties of fractals are self-similarity, chaos, and non-integer fractal dimension. The fractal dimension analysis has been applied to study the wide range of objects in biology and medicine and has been used to detect small tumors, microcalcification in mammograms, tumors in brain, and to diagnose blood cells and human cerebellum. Fractal theory also provides an appropriate platform to build oncological-related software program because the ducts within human breast tissue have fractal properties. Fractal analysis of mammogram was used for the breast parenchymal density assessment. The fractal dimension of the surface is determined by utilizing the Boxcounting method. The Mammograms were collected from HCG Hospital, Bangalore. In this study, a method was developed in the Visual Basic for extracting the suspicious

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“…We used the Box counting technique to calculate fractal dimensions, as previously used in works on kidney (Gil et al, 2006) and the bronchial tree (Canals et al, …”

Section: Macroscopic Studymentioning

confidence: 99%

Anatomy of corpus callosum in prenatally malnourished rats

et al. 2012

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The effect of prenatal malnutrition on the anatomy of the corpus callosum was assessed in adult rats (45-52 days old). In the prenatally malnourished animals we observed a signifi cant reduction of the corpus callosum total area, partial areas, and perimeter, as compared with normal animals. In addition, the splenium of corpus callosum (posterior fi fth) showed a signifi cant decrease of fi ber diameters in the myelinated fi bers without changing density. There was also a signifi cant decrease in diameter and a signifi cant increase in density of unmyelinated fi bers. Measurements of perimeter's fractal dimensions from sagittal sections of the brain and corpus callosum did not show signifi cant differences between malnourished and control animals. These fi ndings indicate that cortico-cortical connections are vulnerable to the prenatal malnutrition, and suggest this may affect interhemispheric conduction velocity, particulary in visual connections (splenium).

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Fractal Dimension of Dog Kidney Proximal Convoluted Tubuli Sections by Mean Box-Counting Algorithm

Cited by 5 publications

References 7 publications

Caracterización morfométrica de estructuras florales de Tagetes erecta L. y Tagetes patula L. (Asteraceae) utilizando análisis digital de imágenes y dimensión fractal

Caracterización morfométrica de estructuras florales de Tagetes erecta L. y Tagetes patula L. (Asteraceae) utilizando análisis digital de imágenes y dimensión fractal

Digital Mammogram and Tumour Detection Using Fractal-Based Texture Analysis: A Box-Counting Algorithm

Anatomy of corpus callosum in prenatally malnourished rats

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