Modeling and visualization of leaf venation patterns

Abstract

We introduce a class of biologically−motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree−like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research. Reference Modeling and visualization of leaf venation patterns AbstractWe introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodesandauxinsources.Inaddition,aveinconnectiongraphis maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree-like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.

Leaf Extraction and Analysis Framework Graphical User Interface: Segmenting and Analyzing the Structure of Leaf Veins and Areoles

“…Alternatively, Banavar and colleagues (1999) suggested power law relationships between network volume and length determined by leaf dimension. These are two examples from a growing number of recent theoretical attempts in need of empirical validation (Banavar et al, 1999;Couder et al, 2002;Runions et al, 2005;Dimitrov and Zucker, 2006;Dodds, 2010;Katifori et al, 2010). However, as mentioned above, to date there has been very limited data with which to test these theories.…”

The origin of the diversity of leaf venation pattern

“…Lobed leaves, for example, maple, display the palmate pattern wherein the primary veins elongate radially towards the lobe apexes. Although the effects of leaf shape (Dengler and Kang, 2001;Runions et al, 2005) and leaf expansion (Sachs, 2003;Runions et al, 2005) on leaf venation patterns have been discussed, the mechanism underlying the diversity of venation patterns is not yet elucidated.…”

More of the same: Synthesizing a variety by structural layering

“…Photorealistic results were demonstrated by techniques which offered a way to botanicaly model the evolution of the leaves venation [24]. However, those methods also suffer from the same problems as the tree modeling techniques, which are domain expertise and significant manual effort.…”