A Critical Appraisal of the Box Counting Method to Assess the Fractal Dimension of Tree Crowns

Silva, D. Da; Boudon, Frédéric; Godin, Christophe; Puech, Olivier; Smith, Cole L.; Sinoquet, Hervé

doi:10.1007/11919476_75

Cited by 19 publications

(30 citation statements)

References 20 publications

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“…A weakness of such approaches is that exact space-filling properties, such as the fractal dimension, are sensitive to the incompleteness of the excavated root network (Nielsen et al, , 1999. In particular, the box counting method was criticized for above-ground branching networks of tree crowns (Da Silva et al, 2006). The same critiques apply to root systems, because fine secondary or tertiary roots can be lost or cutoff or can adhere to each other during the cleaning process, making it impossible to analyze the entire network.…”

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confidence: 99%

Image-Based High-Throughput Field Phenotyping of Crop Roots

et al. 2014

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Current plant phenotyping technologies to characterize agriculturally relevant traits have been primarily developed for use in laboratory and/or greenhouse conditions. In the case of root architectural traits, this limits phenotyping efforts, largely, to young plants grown in specialized containers and growth media. Hence, novel approaches are required to characterize mature root systems of older plants grown under actual soil conditions in the field. Imaging methods able to address the challenges associated with characterizing mature root systems are rare due, in part, to the greater complexity of mature root systems, including the larger size, overlap, and diversity of root components. Our imaging solution combines a field-imaging protocol and algorithmic approach to analyze mature root systems grown in the field. Via two case studies, we demonstrate how image analysis can be utilized to estimate localized root traits that reliably capture heritable architectural diversity as well as environmentally induced architectural variation of both monocot and dicot plants. In the first study, we show that our algorithms and traits (including 13 novel traits inaccessible to manual estimation) can differentiate nine maize (Zea mays) genotypes 8 weeks after planting. The second study focuses on a diversity panel of 188 cowpea (Vigna unguiculata) genotypes to identify which traits are sufficient to differentiate genotypes even when comparing plants whose harvesting date differs up to 14 d. Overall, we find that automatically derived traits can increase both the speed and reproducibility of the trait estimation pipeline under field conditions.

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confidence: 99%

Image-Based High-Throughput Field Phenotyping of Crop Roots

et al. 2014

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“…(e.g., BUCZKOWSKI et al, 1998;CHEN et al, 1993;DASILVA et al, 2006;FOROUTAN-POUR et al, 1999;KELLER et al, 1987;JELINEK, FERNANDEZ, 1998). Entre os pontos indicados pelos pesquisadores como importantes na implementação do método, encontramse os seguintes: a resolução da imagem original (ela deve ser bastante fina, para conter os detalhes de escalas espaciais analisadas), a escolha do tamanho de caixas (as escalas maiores e menores normalmente são desconsideradas), e a relação entre coberturas sucessivas (a variação do tamanho de caixas deve ser gradual, não abrupta).…”

Section: Pós-pós V21 N36 • São Paulo • Dez Embro 2014unclassified

Sobre dimensões fractais de ambientes construídos e naturais

Naoumova

Bourchtein

2015

Pós. Rev. Programa Pós-Grad. Arquit. Urban. FAUUSP

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In this study, fractal analysis is applied in the evaluation of the visual complexity of historic buildings and the surrounding natural environment. The fractal dimension and its approximations, quantified through the box-counting method, are used to define the general and local complexity of digital images of houses and landscapes. The essential properties of the box-counting method are discussed and an optimized version of the method is proposed. The hypothesis of the existence of a relationship between the complexity levels of built sites and natural landscapes is analyzed in the well-known case of the city of Amasya, and also for two historical cities in Brazil, Ouro Preto and Pelotas. The findings reveal a strong relationship between the spatial dynamics of fractal dimensions of built and natural environments.

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“…Iterative function systems (Sinoquet et al 2005) or Lsystems (Lindenmayer Systems; Prusinkiewicz and Lindenmayer, 2004) have gained traction as algorithms to construct graphics that exhibit self-similarity across a range of scales. L-systems have been widely used in plant modelling and are well suited to the study of light transport in heterogeneous media (Sinoquet et al 2005(Sinoquet et al , 2007Da Silva et al 2006;Cote et al 2011). The fractal dimension of these forms can either be derived from theory (Sinoquet er al.…”

Section: Introductionmentioning

confidence: 99%

A Box-Counting Method to Characterize Degrees of Foliage Clumping Using Airborne and Simulated Lidar Data

Leeuwen

Aardt

Kampe

et al. 2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Monitoring forest productivity and health is key to sustainable ecosystem management and informed decision making. A key parameter used in monitoring forest resources is the leaf area index (LAI), which is defined as the one-sided leaf area per unit ground area and is used to describe the canopy radiation regime, among other forest biophysical dynamics. Traditional optics-based methods to estimate LAI rely on the measurement of canopy transmission and foliage clumping. Extending optical methods to LiDAR data has been challenging and studies have reported effective LAI assessments, with no further quantification of foliage clumping. This study investigates the use of the box-counting method to assess the fractal dimension of point cloud data for contrasting forest types and along a gradient of foliage dispersal. We demonstrate the box-counting method on simulated 'range-to-hit', as well as acquired airborne discrete LiDAR data. Coherent results obtained from the different test cases hint at the potential of the box-counting fractal dimension to characterize foliage clumping and bode well for the use of clumping assessments in support of airborne, wall-to-wall estimates of LAI.

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A Critical Appraisal of the Box Counting Method to Assess the Fractal Dimension of Tree Crowns

Cited by 19 publications

References 20 publications

Image-Based High-Throughput Field Phenotyping of Crop Roots

Image-Based High-Throughput Field Phenotyping of Crop Roots

Sobre dimensões fractais de ambientes construídos e naturais

A Box-Counting Method to Characterize Degrees of Foliage Clumping Using Airborne and Simulated Lidar Data

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