A comparative study on multiscale fractal dimension descriptors

Fractal theory presents a large number of applications to image and signal analysis. Although the fractal dimension can be used as an image object descriptor, a multiscale approach, such as multiscale fractal dimension (MFD), increases the amount of information extracted from an object. MFD provides a curve which describes object complexity along the scale. However, this curve presents much redundant information, which could be discarded without loss in performance. Thus, it is necessary the use of a descriptor technique to analyze this curve and also to reduce the dimensionality of these data by selecting its meaningful descriptors. This paper shows a comparative study among different techniques for MFD descriptors generation. It compares the use of well-known and state-of-the-art descriptors, such as Fourier, Wavelet, Polynomial Approximation (PA), Functional Data Analysis (FDA), Principal Component Analysis (PCA), Symbolic Aggregate Approximation (SAX), kernel PCA, Independent Component Analysis (ICA), geometrical and statistical features. The descriptors are evaluated in a classification experiment using Linear Discriminant Analysis over the descriptors computed from MFD curves from two data sets: generic shapes and rotated fish contours. Results indicate that PCA, FDA, PA and Wavelet Approximation provide the best MFD descriptors for recognition and classification tasks. (C) 2012 Elsevier B.V. All rights reserved.

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.

Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images

Image analysis could be a useful tool for investigating the spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to define apparent soil moisture patterns from vertical planes of Vertisol pit images and (ii) to describe the scaling of apparent soil moisture distribution using fractal parameters. Twelve soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. Six of them were excavated in April/2011 and six pits were established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. Each soil image was analyzed using two fractal scaling exponents, box counting (capacity) dimension (DBC) and interface fractal dimension (Di), and three prefractal scaling coefficients, the total number of boxes intercepting the foreground pattern at a unit scale (A), fractal lacunarity at the unit scale (Λ1) and Shannon entropy at the unit scale (S1). All the scaling parameters identified significant differences between both sets of spatial patterns. Fractal lacunarity was the best discriminator between apparent soil moisture patterns. Soil image interpretation with fractal exponents and prefractal coefficients can be incorporated within a site-specific agriculture toolbox. While fractal exponents convey information on space filling characteristics of the pattern, prefractal coefficients represent the investigated soil property as seen through a higher resolution microscope. In spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used in connection with traditional soil moisture sampling, which always renders punctual estimates

Fractal scaling of apparent soil moisture estimated from vertical planesof Vertisol pit images

Image analysis could be a useful tool for investigating the spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to define apparent soil moisture patterns from vertical planes of Vertisol pit images and (ii) to describe the scaling of apparent soil moisture distribution using fractal parameters. Twelve soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. Six of them were excavated in April/2011 and six pits were established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak? digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ?373 ?m of the photographed soil pit. Each soil image was analyzed using two fractal scaling exponents, box counting (capacity) dimension (DBC) and interface fractal dimension (Di), and three prefractal scaling coefficients, the total number of boxes intercepting the foreground pattern at a unit scale (A), fractal lacunarity at the unit scale (?1) and Shannon entropy at the unit scale (S1). All the scaling parameters identified significant differences between both sets of spatial patterns. Fractal lacunarity was the best discriminator between apparent soil moisture patterns. Soil image interpretation with fractal exponents and prefractal coefficients can be incorporated within a site-specific agriculture toolbox. While fractal exponents convey information on space filling characteristics of the pattern, prefractal coefficients represent the investigated soil property as seen through a higher resolution microscope. In spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used in connection with traditional soil moisture sampling, which always renders punctual estimates.

Characterization of rock joints by fractal analysis

From a physical perspective, a joint experiences fracturing processes that affect the rock at both microscopic and macroscopic levels. The result is a behaviour that follows a fractal structure. In the first place, for saw-tooth roughness profiles, the use of the triadic Koch curve appears to be adequate and by means of known correlations the JRC parameter is obtained from the angle measured on the basis of the height and length of the roughnesses. Therefore, JRC remains related to the geometric pattern that defines roughness by fractal analysis. In the second place, to characterise the geometry of irregularities with softened profiles, consequently, is proposed a characterisation of the fractal dimension of the joints with a circumference arc generator that is dependent on an average contact angle with regard to the mid-plane. The correlation between the JRC and the fractal dimension of the model is established with a defined statistical ratio.

Fractal analysis of pyramidal cells in the visual cortex of the galago (Otolemur garnetti): Regional variation in dendritic branching patterns between visual areas

Previously it has been shown that the branching pattern of pyramidal cells varies markedly between different cortical areas in simian primates. These differences are thought to influence the functional complexity of the cells. In particular, there is a progressive increase in the fractal dimension of pyramidal cells with anterior progression through cortical areas in the occipitotemporal (OT) visual stream, including the primary visual area (V1), the second visual area (V2), the dorsolateral area (DL, corresponding to the fourth visual area) and inferotemporal cortex (IT). However, there are as yet no data on the fractal dimension of these neurons in prosimian primates. Here we focused on the nocturnal prosimian galago (Otolemur garnetti). The fractal dimension (D), and aspect ratio (a measure of branching symmetry), was determined for I I I layer III pyramidal cells in V1, V2, DL and IT. We found, as in simian primates, that the fractal dimension of neurons increased with anterior progression from V1 through V2, DL, and IT. Two important conclusions can be drawn from these results: (1) the trend for increasing branching complexity with anterior progression through OT areas was likely to be present in a common primate ancestor, and (2) specialization in neuron structure more likely facilitates object recognition than spectral processing.

Vascular Pattern In Enchondroma And Chondrosarcoma: Clinical And Immunohistologic Study.

Although cartilaginous tumors have low microvascular density, vessels are important for the provision of nutrition so that the tumor can grow and generate metastasis. The aim of this study was to assess the value of the vascular pattern classification as a prognostic tool in chondrosarcomas (CSs) and its relation with vascular endothelial growth factor (VEGF) expression. This was a retrospective study of 21 enchondromas and 57 conventional CSs. Clinical data and outcome were retrieved from medical files. CSs histologic grades (on a scale of 1 to 3) were determined according to the World Health Organization classification. The vascular pattern (on a scale of A to C) was assessed through CD34, according to Kalinski. CD105 and VEGF were also evaluated. Poor outcome was significantly associated with vascular pattern groups B and C. Higher vascular pattern were 6.5 times more frequent in moderate-grade and high-grade CSs than in grade 1 CS. On multivariate analysis, a clear correlation was found between VEGF overexpression and B/C vascular patterns. Only 18 (benign and malignant) tumors stained for CD105. The results point to the use of the vascular pattern classification as a prognostic tool in CSs and to differentiate low-grade from moderate-grade/high-grade CSs. Vascular pattern might be also used to complement histologic grade, VEGF immunostaining, and microvascular density, for indicating a patient's prognosis. Low-grade CSs develop under low neoangiogenesis, which conforms to the slow growth rate of these tumors.

Primary Relapse Site Pattern In Women With Triple-negative Breast Cancer.

Despite the remarkable improvements in breast cancer (BC) characterization, accurate prediction of BC clinical behavior is often still difficult to achieve. Some studies have investigated the association between the molecular subtype, namely the basal-like BC and the pattern of relapse, however only few investigated the association between relapse pattern and immunohistochemical defined triple-negative breast cancers (TNBCs). The aim of this study was to evaluate the pattern of relapse in patients with TNBC, namely the primary distant relapse site. One-hundred twenty nine (129) invasive breast carcinomas with follow-up information were classified according to the molecular subtype using immunohistochemistry for ER, PgR and Her2. The association between TNBC and distant relapse primary site was analyzed by logistic regression. Using multivariate logistic regression analysis patients with TNBC displayed only 0.09 (95% CI: 0.00-0.74; p=0.02) the odds of the non-TNBC patients of developing bone primary relapse. Regarding visceral and lymph-node relapse, no differences between in this cohort were found. Though classically regarded as aggressive tumors, TNBCs rarely development primary relapse in bone when compared to non-TNBC, a clinical relevant fact when investigating a metastasis of an occult or non-sampled primary BC.

The Inadequacy Of The Y-axis Of Growth (sngn) For The Vertical Pattern Assessment In Patients With Sagittal Discrepancies.

The aim of this cephalometric study was to evaluate the influence of the sagittal skeletal pattern on the 'Y-axis of growth' measurement in patients with different malocclusions. Lateral head films from 59 patients (mean age 16y 7m, ranging from 11 to 25 years) were selected after a subjective analysis of 1630 cases. Sample was grouped as follows: Group 1 - class I facial pattern; group 2 - class II facial pattern; and Group 3 - class III facial pattern. Two angular measurements, SNGoGn and SNGn, were taken in order to determine skeletal vertical facial pattern. A logistic regression with errors distributed according to a binomial distribution was used to test the influence of the sagittal relationship (Class I, II, III facial patterns) on vertical diagnostic measurement congruence (SNGoGn and SNGn). RESULTS show that the probability of congruence between the patterns SNGn and SNGoGn was relatively high (70%) for group 1, but for groups II (46%) and III (37%) this congruence was relatively low. The use of SNGn appears to be inappropriate to determine the vertical facial skeletal pattern of patients, due to Gn point shifting throughout sagittal discrepancies. Clinical Significance: Facial pattern determined by SNGn must be considered carefully, especially when severe sagittal discrepancies are present.

Chronic Telogen Effluvium And Female Pattern Hair Loss Are Separate And Distinct Forms Of Alopecia: A Histomorphometric And Immunohistochemical Analysis.

Chronic telogen effluvium (CTE), a poorly understood condition, can be confused with or may be a prodrome to female pattern hair loss (FPHL). The pathogenesis of both is related to follicle cycle shortening and possibly to blood supply changes. To analyze a number of histomorphometric and immunohistochemical findings through vascular endothelial growth factor (VEGF), Ki-67, and CD31 immunostaining in scalp biopsies of 20 patients with CTE, 17 patients with mild FPHL and 9 controls. Ki-67 index and VEGF optical density were analyzed at the follicular outer sheath using ImageJ software. CD31 microvessel density was assessed by a Chalkley grid. Significant follicle miniaturization and higher density of nonanagen follicles were found in FPHL, compared with patients with CTE and controls. Ki-67+ index correlated positively with FPHL histological features. The FPHL group showed the highest VEGF optical density, followed by the CTE and control groups. No differences were found in CD31 microvessel density between the three groups. Histomorphometric results establish CTE as a distinct disorder, separate from FPHL from its outset. Its pathogenic mechanisms are also distinct. These findings support the proposed mechanism of 'immediate telogen release' for CTE, leading to cycle synchronization. For FPHL, accelerated anagen follicular mitotic rates and, thus, higher Ki-67 and VEGF values, would leave less time for differentiation, resulting in hair miniaturization.

The Role Of Edaphic Environment And Climate In Structuring Phylogenetic Pattern In Seasonally Dry Tropical Plant Communities.

Seasonally dry tropical plant formations (SDTF) are likely to exhibit phylogenetic clustering owing to niche conservatism driven by a strong environmental filter (water stress), but heterogeneous edaphic environments and life histories may result in heterogeneity in degree of phylogenetic clustering. We investigated phylogenetic patterns across ecological gradients related to water availability (edaphic environment and climate) in the Caatinga, a SDTF in Brazil. Caatinga is characterized by semiarid climate and three distinct edaphic environments - sedimentary, crystalline, and inselberg -representing a decreasing gradient in soil water availability. We used two measures of phylogenetic diversity: Net Relatedness Index based on the entire phylogeny among species present in a site, reflecting long-term diversification; and Nearest Taxon Index based on the tips of the phylogeny, reflecting more recent diversification. We also evaluated woody species in contrast to herbaceous species. The main climatic variable influencing phylogenetic pattern was precipitation in the driest quarter, particularly for herbaceous species, suggesting that environmental filtering related to minimal periods of precipitation is an important driver of Caatinga biodiversity, as one might expect for a SDTF. Woody species tended to show phylogenetic clustering whereas herbaceous species tended towards phylogenetic overdispersion. We also found phylogenetic clustering in two edaphic environments (sedimentary and crystalline) in contrast to phylogenetic overdispersion in the third (inselberg). We conclude that while niche conservatism is evident in phylogenetic clustering in the Caatinga, this is not a universal pattern likely due to heterogeneity in the degree of realized environmental filtering across edaphic environments. Thus, SDTF, in spite of a strong shared environmental filter, are potentially heterogeneous in phylogenetic structuring. Our results support the need for scientifically informed conservation strategies in the Caatinga and other SDTF regions that have not previously been prioritized for conservation in order to take into account this heterogeneity.

Effect of different ferrule designs on the fracture resistance and failure pattern of endodontically treated teeth restored with fiber posts and all-ceramic crowns

OBJECTIVE: This study investigated the effect of different ferrule heights on endodontically treated premolars. MATERIAL AND METHODS: Fifty sound mandibular first premolars were endodontically treated and then restored with 7-mm fiber post (FRC Postec Plus #1 Ivoclar-Vivadent) luted with self-polymerized resin cement (Multilink, Ivoclar Vivadent) while the coronal section was restored with hybrid composite core build-up material (Tetric Ceram, Ivoclar-Vivadent), which received all-ceramic crown. Different ferrule heights were investigated: 1-mm circumferential ferrule without post and core (group 1 used as control), a circumferential 1-mm ferrule (group 2), non-uniform ferrule 2-mm buccally and 1-mm lingually (group 3), non-uniform ferrule 3-mm buccally and 2-mm lingually (group 4), and finally no ferrule preparation (group 5). The fracture load and failure pattern of the tested groups were investigated by applying axial load to the ceramic crowns (n=10). Data were analyzed statistically by one-way ANOVA and Tukey's post-hoc test was used for pair-wise comparisons (α=0.05). RESULTS: There were no significant differences among the failure load of all tested groups (P<0.780). The control group had the lowest fracture resistance (891.43±202.22 N) and the highest catastrophic failure rate (P<0.05). Compared to the control group, the use of fiber post reduced the percentage of catastrophic failure while increasing the ferrule height did not influence the fracture resistance of the restored specimens. CONCLUSIONS: Within the limitations of this study, increasing the ferrule length did not influence the fracture resistance of endodontically treated teeth restored with glass ceramic crowns. Insertion of a fiber post could reduce the percentage of catastrophic failure of these restorations under function.