Estimation of fractal dimension and fractal curvatures from digital images
نویسندگان
چکیده
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several geometric characteristics, namely all the intrinsic volumes (i.e. volume, surface area, Euler characteristic etc.) of the parallel sets of a fractal. Motivated by recent results on their limiting behaviour, we use these functionals to estimate the fractal dimension of sets from digital images. Simultaneously, we also obtain estimates of the fractal curvatures of these sets, some fractal counterpart of intrinsic volumes, allowing a finer classification of fractal sets than by means of fractal dimension only. We show the consistency of our estimators and test them on some digital images of self-similar sets.
منابع مشابه
Diagnosis of B-CLL Leukemia Using Fractal Dimension
Background:Leukemia is cancer of blood and bone marrow cells. In general, there are four types of leukemia: chronic myelogenous leukemia (CML), acute myeloid leukemia (AML), B-cell chronic lymphocytic leukemia (CLL) and acute lymphoblastic leukemia (ALL). Fractal geometry can be introduced as one of the effective ways to detect this type of cancer. In this study, with introduc...
متن کاملFractal Study on Nuclear Boundary of Cancer Cells in Urinary Smears
Background & Objectives: Cancer is a serious problem for human being and is becoming a serious problem day-by-day .A prerequisite for any therapeutic modality is early diagnosis. Automated cancer diagnosis by automatic image feature extraction procedures can be used as a feature extraction in the field of fractal dimension. The aim of this survey was to introduce a quantitative and objective...
متن کاملAssessment the Effect of Exposure Conditions and Geometry Parameters on Calculated Fractal Dimension of Mandibular Bone
Introduction: One of the fractal analysis methods to examine the structure of a texture is fractal dimension (F.D.) measurement. F.D is a quantitative method to show the complexity of a structure using a number. The aim of this study was to determine the effect of different exposure conditions, voltages and angle of x-ray tube on F.D. values of mandibular bone. Methods: This lab-trial analytic...
متن کاملComparison Density and Fractal Dimension of Drainage Networks in Different Scales and Precision Different (Case Study: Ilam Watersheds)
Every phenomena in the nature, despite the complexity of the subject, has certain rules and regulations. River pattern and behavior as one of the most complex natural phenomena to this is not an exception. Depending on geomorphologic, climatic, topographic and erosive conditions, the waterways exhibit different patterns and behaviors. One of the parameters which can be achieved using the comple...
متن کاملEffect of Noise in Estimation of Fractal Dimension of Digital Images
In present paper the effect of noise on fractal dimension of digital images has been tested. Since fractal dimension is a measure of texture which is property of neighbourhood, it is interesting to check how noise affects the values of fractal dimension. For this purpose, three standard digital images have been used and Gaussian noise, salt and pepper noise and speckle noise have been applied t...
متن کامل