The Fractal Dimension of Architecture

Ostwald, Michael J.; Vaughan, Josephine

doi:10.1007/978-3-319-32426-5

Cited by 51 publications

(59 citation statements)

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“…Microvessel fractal dimension is a metric used to quantify the structural complexity of a vascular network. The box counting method [ 33 ] was employed to calculate mvFD using the binary image through the following six steps as shown in the diagram in Fig. 1 : 1) the binary image was padded with zeros to make its dimensions to a power of 2; 2) the box size ( S ) was set to the size of the binary image; 3) the number of boxes ( N S ) needed to cover all vessels (non-zero pixels) in the binary image were counted; 4) S was set to S /2 and step 3 was repeated only if S > size of a pixel, otherwise, the process continues to step 5; 5) a first-order polynomial fit was applied to the pairs, (

, log( N S )); 6) the slope of the fitted line was obtained as mvFD:

…”

Section: Methodsmentioning

confidence: 99%

Quantitative Biomarkers for Cancer Detection Using Contrast-Free Ultrasound High-Definition Microvessel Imaging: Fractal Dimension, Murray’s Deviation, Bifurcation Angle & Spatial Vascularity Pattern

Ternifi

Wang

Polley

et al. 2021

IEEE Trans. Med. Imaging

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A growing body of evidence indicates that there is a strong correlation between microvascular morphological features and malignant tumors. Therefore, quantification of these features might allow more accurate differentiation of benign and malignant tumors. The main objective of this research project is to improve the quantification of microvascular networks depicted in contrast-free ultrasound microvessel images. To achieve this goal, a new series of quantitative microvessel morphological parameters are introduced for differentiation of breast masses using contrast-free ultrasound-based high-definition microvessel imaging (HDMI). Using HDMI, we quantified and analyzed four new parameters: 1) microvessel fractal dimension (mvFD), a marker of tumor microvascular complexity, 2) Murray's deviation (MD), the diameter mismatch, defined as the deviation from Murray's law, 3) Bifurcation angle (BA), abnormally decreased angle, and 4) spatial vascular pattern (SVP), indicating tumor vascular distribution pattern, either intratumoral or peritumoral. The new biomarkers have been tested on 60 patients with breast masses. Validation of the feature's extraction algorithm was performed using a synthetic data set. All the proposed parameters had the power to discriminate the breast lesion malignancy (p < 0.05), displaying BA as the most sensitive test, with a sensitivity of 90.6%, and mvFD as the most specific test, with a specificity of 92%. The results of all four new biomarkers showed an AUC=0.889, sensitivity of 80% and specificity of 91.4% In conclusion, the added value of the proposed quantitative morphological parameters, as new biomarkers of angiogenesis within breast masses, paves the way for more accurate breast cancer detection with higher specificity.

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, log( N S )); 6) the slope of the fitted line was obtained as mvFD:

…”

Section: Methodsmentioning

confidence: 99%

Quantitative Biomarkers for Cancer Detection Using Contrast-Free Ultrasound High-Definition Microvessel Imaging: Fractal Dimension, Murray’s Deviation, Bifurcation Angle & Spatial Vascularity Pattern

Ternifi

Wang

Polley

et al. 2021

IEEE Trans. Med. Imaging

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“…• Measuring building facades and street silhouettes: In the book 'The Fractal Dimension of Architecture', the plans and facades of traditional, modern and postmodern houses were analyzed. While there is a decrease in plan and facade complexity from traditional to modern, minimalist plans have been found to have a higher complexity than expected (Ostwald and Vaughan, 2016). In another study, the visual layers such as form, material and ornament of the Süleymaniye Mosque facades were analyzed.…”

Section: Literature Reviewmentioning

confidence: 96%

Fractality and Lacunarity of Turkish Cities

İlhan¹,

Gürsakal²

2021

GRID - Architecture, Planning and Design Journal

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Article InformationFor the first time in this article, fractal dimensions and lacunarity coefficients of all the cities in Turkey are calculated using an open-source software ImageJ and a plugin FracLac. According to these values, 81 Turkish cities are grouped into 10 clusters. While the distribution of the lacunarity coefficients pass the goodness of fit test for the normal distribution; the distribution of fractal dimensions did not pass this test, since it is a two-moded distribution. From the results obtained, we understand that there is a weak, negative, significant (5% significance level) correlation between fractal dimension and lacunarity; a weak, positive significant (1% significance level) relationship between fractal dimension and population; and also there is a moderate, positive significant (1% significance level) relation between fractal dimension and gross domestic product per capita by provinces. No significant relationship was found between lacunarity and population. Although it has been stated that, "in the mean, the larger cities are alike", when we examine the similarities of Turkish cities in multivariate context using fractal dimensions and lacunarity coefficients, small cities were found to be more alike.

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“…Sala [20] applied Bovill's method to Frank Lloyd Wright's Robie house. Architectural works of multiple well-known architects such as Le Corbusier, Frank Lloyd Wright, Eileen Gray, Peter Eisenman, Glenn Murcutt and Kazuyo Sejima were analysed using fractal dimension [2,22,23]. Stamps [11] and Ostwald and Vaughan [2] also compared nature and architecture using the fractal dimension to analyse relationships between architecture and its setting.…”

Section: Fractal Analysis Of Built Environmentsmentioning

confidence: 99%

Between 2D and 3D: Studying Structural Complexity of Urban Fabric Using Voxels and LiDAR-Derived DSMs

2021

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Cities are complex systems and their physical forms are the manifestation of cultural, social and economic processes shaped by the geometry of natural and man-made elements. Digital Surface Models (DSM) using LiDAR provide an efficient volumetric transformation of urban fabric including all built and natural elements which allows the study of urban complexity through the lens of fractal dimension (D). Founded on the “box-counting” method, we reveal a voxelization technique developed in GIS (Geographic Information System) to estimate D values of ten DSM samples across central Melbourne. Estimated D values of surface models (between 2 and 3) provide a measure to interpret the structural complexity of different urban characters defined by the pattern of developments and densities. The correlations between D values with other DSM properties such as elevation, volume, solar radiation and surface roughness, showed a strong relationship between DSM volume and mean elevation. Lower strength correlations were recorded with solar radiation and surface roughness. The proposed method provides opportunities for fractal research to study pressing issues in complex urban environments such as declining physical fitness, mental health and urban biodiversity.

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The Fractal Dimension of Architecture

Cited by 51 publications

References 0 publications

Quantitative Biomarkers for Cancer Detection Using Contrast-Free Ultrasound High-Definition Microvessel Imaging: Fractal Dimension, Murray’s Deviation, Bifurcation Angle & Spatial Vascularity Pattern

Quantitative Biomarkers for Cancer Detection Using Contrast-Free Ultrasound High-Definition Microvessel Imaging: Fractal Dimension, Murray’s Deviation, Bifurcation Angle & Spatial Vascularity Pattern

Fractality and Lacunarity of Turkish Cities

Between 2D and 3D: Studying Structural Complexity of Urban Fabric Using Voxels and LiDAR-Derived DSMs

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