Getting shapes into numbers

January 20, 2021

In nature, many things have evolved that differ in size, color and, above all, in shape. While the color or size of an object can be easily described, the description of a shape is more complicated. In a study now published in Nature Communications, Jacqueline Nowak of the Max Planck Institute of Molecular Plant Physiology and her colleagues have outlined a new and improved way to describe shapes based on a network representation that can also be used to reassemble and compare shapes.

Jacqueline Nowak designed a novel approach that relies on a network-based shape representation, named visibility graph, along with a tool for analyzing shapes, termed GraVis. The visibility graph represents the shape of an object that is defined by its surrounding contour and the mathematical structure behind GraVis is specified by a set of nodes equidistantly placed around the contour. The nodes are then connected with each other by edges, that do not cross or align with the shape boundary.As a result, testing the connection between all pairs of nodes specifies the visibility graph for the analyzed shape.

In this study, Jacqueline Nowak used the visibility graphs and the GraVis tool to compare different shapes. To test the power of the new approach, visibility graphs of simple triangular, rectangular and circular shapes, but also complex shapes of sand grains, fish shapes and leaf shapes were compared with each other.

By using different machine learning approaches, they demonstrated that the approach can be used to distinguish shapes according to their complexity. Furthermore, visibility graphs enable to distinguish the complexity of shapes as it was shown for epidermal pavement cells in plants, which have a similar shape to pieces of jigsaw puzzle. For these cells, distinct shape parameters like lobe length, neck width or cell area can be accurately quantified with GraVis. "The quantification of the lobe number of epidermal cells with GraVis outperforms existing tools, showing that it is a powerful tool to address particular questions relevant to shape analysis", says Zoran Nikoloski, GraVis project leader, head of the research group "Systems biology and Mathematical Modelling" at the Max Planck Institute of Molecular Plant Physiology and Professor of Bioinformatics at University of Potsdam.

In future, the scientists want to apply visibility graphs of epidermal cells and entire leaves to gain biological insights of key cellular processes that impact shape. In addition, shape features of different plant cells quantified by GraVis can facilitate genetic screens to determine the genetic basis of morphogenesis. Finally, the application of GraVis will help to gain deeper understanding of the interrelation between cells and organ shapes in nature.
-end-
Original publication

Jacqueline Nowak, Ryan Christopher Eng, Timon Matz, Matti Waack, Staffan Persson, Arun Sampathkumar, Zoran Nikoloski
A network-based framework for shape analysis enables accurate characterization and classification of leaf epidermal cells
Nature Communications, Published: 19 January 2021

Max-Planck-Gesellschaft

Related Nature Articles from Brightsurf:

Future climate changes in nature reserves
The Earth's nature reserves are set to be affected by future climate change in very different ways.

Tailored light inspired by nature
An international research team with Prof. Cornelia Denz from the Institute of Applied Physics at the University of M√ľnster (Germany) develop for the first time light fields using caustics that do not change during propagation.

Accounting for nature in economies
Gross Domestic Product, the standard metric for measuring national economies, doesn't account for the valuable services provided by nature.

Nature unveiling herself before science
21st century societal challenges such as demographic developments and an ageing population demand for new functional materials, such as for bone prostheses.

Energized by enzymes -- nature's catalysts
Scientists at Pacific Northwest National Laboratory are using a custom virtual reality app to design an artificial enzyme that converts carbon dioxide to formate, a kind of fuel.

Mother nature and child development
A world first review of the importance of nature play could transform children's play spaces, supporting investment in city and urban parks, while also delivering important opportunities for children's physical, social and emotional development.

How nature tells us its formulas
A team from TU Wien and the University of Heidelberg has developed methods with which these models can be directly obtained from experimental measurements.

Reconnecting with nature key for sustainability
People who live in more built up areas and spend less free-time in nature are also less likely to take actions that benefit the environment, such as recycling, buying eco-friendly products, and environmental volunteering.

Limiting the loss of nature
With only about half of Earth's terrestrial surface remaining as natural vegetation, a University of Queensland-led team has proposed an international goal to halt its continued loss.

Combatting air pollution with nature
Air pollution is composed of particles and gases that can have negative impacts on both the environment and human health.

Read More: Nature News and Nature Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.