Learning Generative Models of the Geometry and Topology of Tree-like 3D Objects

How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and computing geodesic deformations between the shapes of such tree-like 3D objects. A hierarchical organization of subtrees characterizes these objects -- each subtree has the main branch with some side branches attached -- and one needs to match these structures across objects for meaningful comparisons. We propose a novel representation that extends the Square-Root Velocity Function (SRVF), initially developed for Euclidean curves, to tree-shaped 3D objects. We then define a new metric that quantifies the bending, stretching, and branch sliding needed to deform one tree-shaped object into the other. Compared to the current metrics, such as the Quotient Euclidean Distance (QED) and the Tree Edit Distance (TED), the proposed representation and metric capture the full elasticity of the branches (i.e., bending and stretching) as well as the topological variations (i.e., branch death/birth and sliding). It completely avoids the shrinkage that results from the edge collapse and node split operations of the QED and TED metrics. We demonstrate the utility of this framework in comparing, matching, and computing geodesics between biological objects such as neurons and botanical trees. The framework is also applied to various shape analysis tasks: (i) symmetry analysis and symmetrization of tree-shaped 3D objects, (ii) computing summary statistics (means and modes of variations) of populations of tree-shaped 3D objects, (iii) fitting parametric probability distributions to such populations, and (iv) finally synthesizing novel tree-shaped 3D objects through random sampling from estimated probability distributions.Comment: under revie

Spatial Reconstruction of Biological Trees from Point Cloud

Trees are complex systems in nature whose topology and geometry ar

Characterizing neuromorphologic alterations with additive shape functionals

The complexity of a neuronal cell shape is known to be related to its function. Specifically, among other indicators, a decreased complexity in the dendritic trees of cortical pyramidal neurons has been associated with mental retardation. In this paper we develop a procedure to address the characterization of morphological changes induced in cultured neurons by over-expressing a gene involved in mental retardation. Measures associated with the multiscale connectivity, an additive image functional, are found to give a reasonable separation criterion between two categories of cells. One category consists of a control group and two transfected groups of neurons, and the other, a class of cat ganglionary cells. The reported framework also identified a trend towards lower complexity in one of the transfected groups. Such results establish the suggested measures as an effective descriptors of cell shape

From Models to Simulations

This book analyses the impact computerization has had on contemporary science and explains the origins, technical nature and epistemological consequences of the current decisive interplay between technology and science: an intertwining of formalism, computation, data acquisition, data and visualization and how these factors have led to the spread of simulation models since the 1950s. Using historical, comparative and interpretative case studies from a range of disciplines, with a particular emphasis on the case of plant studies, the author shows how and why computers, data treatment devices and programming languages have occasioned a gradual but irresistible and massive shift from mathematical models to computer simulations

Multiscale Framework for Modeling and Analyzing Light Interception by Trees

International audienceThis paper presents a new framework for modeling light interception by isolated trees which makes it possible to analyze the influence of structural tree organization on light capture. The framework is based on a multiscale representation of the plant organization. Tree architecture is decomposed into a collection of components representing clusters of leaves at different scales in the tree crown. The components are represented by porous envelopes automatically generated as convex hulls containing components at a finer scale. The component opacity is defined as the interception probability of a light beam going through its envelope. The role of tree organization on light capture was assessed by running different scenarii where the components at any scale were either randomly distributed or localized to their actual 3D position. The modeling framework was used with three-dimensional digitized fruit trees, namely peach and mango trees. A sensitivity analysis was carried out to assess the effect of the spatial organization in each scale on light interception. This modeling framework makes it possible to identify a level of tree description that achieves a good compromise between the amount of measurement required to describe the tree architecture and the quality of the resulting light interception model

Root system markup language: toward an unified root architecture description language

The number of image analysis tools supporting the extraction of architectural features of root systems has increased over the last years. These tools offer a handy set of complementary facilities, yet it is widely accepted that none of these software tool is able to extract in an efficient way growing array of static and dynamic features for different types of images and species. We describe the Root System Markup Language (RSML) that has been designed to overcome two major challenges: (i) to enable portability of root architecture data between different software tools in an easy and interoperable manner allowing seamless collaborative work, and (ii) to provide a standard format upon which to base central repositories which will soon arise following the expanding worldwide root phenotyping effort. RSML follows the XML standard to store 2D or 3D image metadata, plant and root properties and geometries, continuous functions along individual root paths and a suite of annotations at the image, plant or root scales, at one or several time points. Plant ontologies are used to describe botanical entities that are relevant at the scale of root system architecture. An xml-schema describes the features and constraints of RSML and open-source packages have been developed in several languages (R, Excel, Java, Python, C#) to enable researchers to integrate RSML files into popular research workflow

Reconstructing Plant Architecture from 3D Laser scanner data

International audienceAutomatic acquisition of plant phenotypes constitutes a major bottleneck in the construction of quantitative models of plant development. This issue needs to be addressed to build accurate models of plant, useful for instance in agronomic and forestry applications. In this work, we present a method for reconstructing plant architecture from laser scanner data. A dedicated evaluation procedure based on a detailed comparison between expert and automatic reconstruction was developed to quantify accurately the quality of the reconstruction method

Modelagem e simulação de padrões arquiteturais de plantas.

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MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models

International audienceConstruction of architectural databases over years is time consuming and cannot easily capture the event dynamics, especially when both tr ee topology and geometry are considered. The present project aimed to bring together models of topology and geometry in a single simulation such that the architecture of an apple t ree may emerge from process interactions. This integration was performed using L-systems. A m ixed approach was developed based on stochastic models to simulate plant topology and me chanistic model for the geometry. The succession of growth units (GUs) along axes and the ir branching structure were jointly modeled by a hierarchical hidden Markov model. A bi omechanical model, derived from previous studies, was used to calculate stem form a t the metamer scale, taking into account the intra-year dynamics of primary, secondary and f ruit growth. Outputs consist of 3D mock- ups geometric models representing the progression o f tree form over time. To asses these models, a sensitivity analysis was performed and de scriptors were compared between simulated and digitized trees, including the total number of GUs in the entire tree, descriptors of shoot geometry (basal diameter, length), and des criptors of axis geometry (inclination, curvature). In conclusion, in spite of some limitat ions MAppleT constitutes a useful tool for simulating development of apple trees in interactio n with gravity