Variogram Based Estimator of Fractal Dimension for the Analysis of Cell Nuclei from the Papanicolaou Smears

2013 ◽  
pp. 47-54 ◽  
Author(s):  
Dorota Oszutowska–Mazurek ◽  
Przemysław Mazurek ◽  
Kinga Sycz ◽  
Grażyna Waker–Wójciuk
Keyword(s):  
Fractal Dimension ◽  
Cell Nuclei ◽  
Papanicolaou Smears

scholarly journals From the slit-island method to the Ising model: Analysis of irregular grayscale objects

2014 ◽  
Vol 24 (1) ◽  
pp. 49-63 ◽  
Author(s):  
Przemysław Mazurek ◽  
Dorota Oszutowsk A-M Ażurek
Keyword(s):  
Image Analysis ◽  
Fractal Dimension ◽  
Ising Model ◽  
Image Data ◽  
Input Image ◽  
Cell Nuclei ◽  
Cervical Cell ◽  
Atypical Cells ◽  
Model Context ◽  
Slit Island Method

Abstract The Slit Island Method (SIM) is a technique for the estimation of the fractal dimension of an object by determining the area- perimeter relations for successive slits. The SIM could be applied for image analysis of irregular grayscale objects and their classification using the fractal dimension. It is known that this technique is not functional in some cases. It is emphasized in this paper that for specific objects a negative or an infinite fractal dimension could be obtained. The transformation of the input image data from unipolar to bipolar gives a possibility of reformulated image analysis using the Ising model context. The polynomial approximation of the obtained area-perimeter curve allows object classification. The proposed technique is applied to the images of cervical cell nuclei (Papanicolaou smears) for the preclassification of the correct and atypical cells.

scholarly journals The Fractal Dimension of Nuclear Chromatin as a Prognostic Factor in Acute Precursor B Lymphoblastic Leukemia

2006 ◽  
Vol 28 (1-2) ◽  
pp. 55-59
Author(s):  
Randall L. Adam ◽  
Rosana C. Silva ◽  
Fernanda G. Pereira ◽  
Neucimar J. Leite ◽  
Irene Lorand-Metze ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Prognostic Factor ◽  
Goodness Of Fit ◽  
Cox Regression ◽  
Lymphoblastic Leukemia ◽  
Three Dimensions ◽  
Cell Nuclei ◽  
Biologically Relevant ◽  
Relevant Prognostic Factor ◽  
Prognostic Importance

The fractal nature of the DNA arrangement has been postulated to be a common feature of all cell nuclei. We investigated the prognostic importance of the fractal dimension (FD) of chromatin in blasts of patients with acute precursor B lymphoblastic leukemia (B-ALL). In 28 patients, gray scale transformed pseudo-3D images of 100 nuclei (May–Grünwald–Giemsa stained bone marrow smears) were analyzed. FD was determined by the Minkowski–Bouligand method extended to three dimensions. Goodness-of-fit of FD was estimated by the R2 values in the log-log plots. Whereas FD presented no prognostic relevance, patients with higher R2 values showed a prolonged survival. White blood cell count (WBC), age and mean fluorescence intensity of CD45 (MFICD45) were all unfavorable prognostic factors in univariate analyses. In a multivariate Cox-regression, R2, WBC, and MFICD45, entered the final model, which showed to be stable in a bootstrap resampling study. Blasts with lower R2 values, equivalent to accentuated “coarseness” of the chromatin pattern, which may reflect profound changes of the DNA methylation, indicated a poor prognosis. In conclusion the goodness-of-fit of the Minkowski–Bouligand dimension of chromatin can be regarded as a new and biologically relevant prognostic factor for patients with B-ALL.

scholarly journals Diagnosis System for Hepatocellular Carcinoma Based on Fractal Dimension of Morphometric Elements Integrated in an Artificial Neural Network

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Dan Ionuț Gheonea ◽  
Costin Teodor Streba ◽  
Cristin Constantin Vere ◽  
Mircea Șerbănescu ◽  
Daniel Pirici ◽  
...  
Keyword(s):  
Neural Network ◽  
Hepatocellular Carcinoma ◽  
Artificial Neural Network ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Cell Nuclei ◽  
Normal Tissues ◽  
Vascular Elements ◽  
Artificial Neural ◽  
Human Operators

Background and Aims. Hepatocellular carcinoma (HCC) remains a leading cause of death by cancer worldwide. Computerized diagnosis systems relying on novel imaging markers gained significant importance in recent years. Our aim was to integrate a novel morphometric measurement—the fractal dimension (FD)—into an artificial neural network (ANN) designed to diagnose HCC.Material and Methods.The study included 21 HCC and 28 liver metastases (LM) patients scheduled for surgery. We performed hematoxylin staining for cell nuclei and CD31/34 immunostaining for vascular elements. We captured digital images and used an in-house application to segment elements of interest; FDs were calculated and fed to an ANN which classified them as malignant or benign, further identifying HCC and LM cases.Results.User intervention corrected segmentation errors and fractal dimensions were calculated. ANNs correctly classified 947/1050 HCC images (90.2%), 1021/1050 normal tissue images (97.23%), 1215/1400 LM (86.78%), and 1372/1400 normal tissues (98%). We obtained excellent interobserver agreement between human operators and the system.Conclusion. We successfully implemented FD as a morphometric marker in a decision system, an ensemble of ANNs designed to differentiate histological images of normal parenchyma from malignancy and classify HCCs and LMs.

Lacunarity Based Estimator for the Analysis of Cell Nuclei from the Papanicolaou Smears

2014 ◽  
pp. 486-493 ◽  
Author(s):  
Dorota Oszutowska-Mazurek ◽  
Przemysław Mazurek ◽  
Kinga Sycz ◽  
Grażyna Waker-Wójciuk
Keyword(s):  
Cell Nuclei ◽  
Papanicolaou Smears

AN “ASYMPTOTIC FRACTAL” APPROACH TO THE MORPHOLOGY OF MALIGNANT CELL NUCLEI

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 326-335 ◽  
Author(s):  
GABRIEL LANDINI ◽  
JOHN W. RIPPIN
Keyword(s):  
Fractal Dimension ◽  
Oral Cancer ◽  
Malignant Cell ◽  
Computer Memory ◽  
Cell Nuclei ◽  
Topological Dimension ◽  
Fractal Approach ◽  
Linear Discrimination ◽  
Boundary Length ◽  
Transmission Electron

To investigate quantitatively nuclear membrane irregularity, 672 nuclei from 10 cases of oral cancer (squamous cell carcinoma) and normal cells from oral mucosa were studied in transmission electron micrographs. The nuclei were photographed at ×1400 magnification and transferred to computer memory (1 pixel=35 nm). The perimeter of the profiles was analysed using the “yardstick method” of fractal dimension estimation, and the log-log plot of ruler size vs. boundary length demonstrated that there exists a significant effect of resolution on length measurement. However, this effect seems to disappear at higher resolutions. As this observation is compatible with the concept of asymptotic fractal, we estimated the parameters c, L and Bm from the asymptotic fractal formula Br=Bm {1+(r/L)c}−1, where Br is the boundary length measured with a ruler of size r, Bm is the maximum boundary for r→0, L is a constant, and c=asymptotic fractal dimension minus topological dimension (D−Dt) for r→∞. Analyses of variance showed c to be significantly higher in the normal than malignant cases (P<0.001), but log(L) and Bm to be significantly higher in the malignant cases (P<0.001). A multivariate linear discrimination analysis on c, log(L) and Bm re-classified 76.6% of the cells correctly (84.8% of the normal and 67.5% of the tumor). Furthermore, this shows that asymptotic fractal analysis applied to nuclear profiles has great potential for shape quantification in diagnosis of oral cancer.

Intranuclear Crystals in Regenerating Canine Kidneys

1973 ◽  
Vol 31 ◽  
pp. 412-413
Author(s):  
D.G. Osborne ◽  
L.J. McCormack ◽  
M.O. Magnusson ◽  
W.S. Kiser
Keyword(s):  
Epithelial Cell ◽  
Epithelial Cells ◽  
Tubular Epithelial Cell ◽  
Tubular Epithelial Cells ◽  
Cell Nuclei ◽  
Crystalline Structures ◽  
Small Crystals ◽  
Membrane Bound

During a project in which regenerative changes were studied in autotransplanted canine kidneys, intranuclear crystals were seen in a small number of tubular epithelial cells. These crystalline structures were seen in the control specimens and also in regenerating specimens; the main differences being in size and number of them. The control specimens showed a few tubular epithelial cell nuclei almost completely occupied by large crystals that were not membrane bound. Subsequent follow-up biopsies of the same kidneys contained similar intranuclear crystals but of a much smaller size. Some of these nuclei contained several small crystals. The small crystals occurred at one week following transplantation and were seen even four weeks following transplantation. As time passed, the small crystals appeared to fuse to form larger crystals.

Use of fractals to describe microstructures of porous thick-film platinum electrodes

1992 ◽  
Vol 50 (1) ◽  
pp. 314-315
Author(s):  
Steven D. Toteda
Keyword(s):  
Fractal Dimension ◽  
Power Plants ◽  
Electrical Response ◽  
Cubic Phase ◽  
Platinum Electrodes ◽  
Fine Grained ◽  
Impedance Response ◽  
Platinum Particles ◽  
Energy Surfaces ◽  
Highly Porous

Zirconia oxygen sensors, in such applications as power plants and automobiles, generally utilize platinum electrodes for the catalytic reaction of dissociating O2 at the surface. The microstructure of the platinum electrode defines the resulting electrical response. The electrode must be porous enough to allow the oxygen to reach the zirconia surface while still remaining electrically continuous. At low sintering temperatures, the platinum is highly porous and fine grained. The platinum particles sinter together as the firing temperatures are increased. As the sintering temperatures are raised even further, the surface of the platinum begins to facet with lower energy surfaces. These microstructural changes can be seen in Figures 1 and 2, but the goal of the work is to characterize the microstructure by its fractal dimension and then relate the fractal dimension to the electrical response. The sensors were fabricated from zirconia powder stabilized in the cubic phase with 8 mol% percent yttria. Each substrate was sintered for 14 hours at 1200°C. The resulting zirconia pellets, 13mm in diameter and 2mm in thickness, were roughly 97 to 98 percent of theoretical density. The Engelhard #6082 platinum paste was applied to the zirconia disks after they were mechanically polished ( diamond). The electrodes were then sintered at temperatures ranging from 600°C to 1000°C. Each sensor was tested to determine the impedance response from 1Hz to 5,000Hz. These frequencies correspond to the electrode at the test temperature of 600°C.

Comment on "On the fractal dimension of stream networks"

1990 ◽  
Vol 26 (9) ◽  
pp. 2243-2244 ◽  
Author(s):  
David G. Tarboton
Keyword(s):  
Fractal Dimension ◽  
Stream Networks
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