Recently, several high-throughput phenotyping facilities have been established that allow for an automated collection of multiple view images of a large number of plants over time. One of the key problems in phenotyping is identifying individual plant organs such as leaves, stems, or roots. We introduced a novel algorithm that uses a 3D segmented plant on its input by using a voxel carving algorithm, and separates the plant into leaves and stems. Our algorithm first uses voxel thinning that generates a first approximation of the plant 3D skeleton. The skeleton is transformed into a mathematical tree by comparing and assessing paths from each leaf or stem tip to the plant root and pruned by using biologically inspired features, fed into a machine learning classifier, leading to a skeleton that corresponds to the input plant. The final skeleton is then used to identify the plant organs and segment voxels. We validated our system on 20 different plants, each represented in a voxel array of a resolution $512^3$, and the segmentation was executed in under one minute, making our algorithm suitable for the processing of large amounts of plants.

Sorghum Segmentation by Skeleton Extraction

A novel approach to generating watertight, manifold boundary representations from noisy binary image masks of MRI or CT scans is presented. The method samples an input segmented image and locally approximates the material boundary. Geometric error metrics between the voxelated boundary and an approximating template surface are minimized, and boundary point/normals are correspondingly generated. Voronoi partitioning is employed to perform surface reconstruction on the resulting oriented point cloud. The method performs competitively against other approaches, both in comparisons of shape and volume error metrics to a canonical image mask, and in qualitative comparisons using noisy image masks from real scans. The framework readily admits enhancements for capturing sharp edges and corners. The approach robustly produces high-quality b-reps that may be inserted into an image-based meshing pipeline for purposes of physics-based simulation. 

A robust workflow for b-rep generation from image masks

Herb Voelcker and his research team laid the foundations of Solid Modelling, on which Computer-Aided Design is based. He founded the ambitious Production Automation Project, that included Constructive Solid Geometry (CSG) as the basic 3D geometric representation. CSG trees were compact and robust, saving a memory space that was scarce in those times. But the main computational problem was Boundary Evaluation: the process of converting CSG trees to Boundary Representations (BReps) with explicit faces, edges and vertices for manufacturing and visualization purposes. This paper presents some glimpses of the history and evolution of some ideas that started with Herb Voelcker. We briefly describe the path from “localization and boundary evaluation” to “localization and printing”, with many intermediate steps driven by hardware, software and new mathematical tools: voxel and volume representations, triangle meshes, and many others, observing also that in some applications, voxel models no longer require Boundary Evaluation. In this last case, we consider the current research challenges and discuss several avenues for further research. 

Solid Modelling for Manufacturing: From Voelcker's Boundary Evaluation to Discrete Paradigms

Classes of curves like par-regularity, $$\mu $$ -reach, locally turn boundedness, quasi-regularity (and their generalizations) have been defined so as to guarantee geometrical or topological properties under discretization. An overview of their inter-relations is given. A focus is made on the Locally Turn Bounded (LTB) curves, a class having good discretization properties. It has already been shown that being LTB implies quasi-regularity. In this paper, it is shown that the LTB curves have a positive $$\mu $$ -reach. Moreover, we show that a LTB curve having a Lipschitz turn is par-regular. 

A Survey on 2D Euclidean Curve Classes in Discrete Geometry with New Results

Defining consistent calculus frameworks on discrete meshes is useful for processing the geometry of meshes or model numerical simulations and variational problems onto them. However digital surfaces (boundary of voxels) cannot benefit directly from the classical mesh calculus frameworks, since their vertex and face geometry is too poor to capture the geometry of the underlying smooth Euclidean surface well enough. This paper proposes two new calculus frameworks dedicated to digital surfaces, which exploit a corrected normal field, in a manner similar to the recent digital calculus of [3]. First we build a corrected interpolated calculus by defining inner products with position and normal interpolation in the Grassmannian. Second we present a corrected finite element method which adapts the standard Finite Element Method with a corrected metric per element. Experiments show that these digital calculus frameworks seem to converge toward the continuous calculus, offer a valid alternative to classical mesh calculus, and induce effective tools for digital surface processing tasks. 

Digital Calculus Frameworks and Comparative Evaluation of Their Laplace-Beltrami Operators

Voxel based modeling is a very attractive way to represent complex multi-material objects. Beside artistic choices of pixel/voxel arts, representing objects as voxels allows efficient and dynamic interactions with the scene. For geometry processing purposes, many applications in material sciences, medical imaging or numerical simulation rely on a regular partitioning of the space with labeled voxels. In this article, we consider a variational approach to reconstruct interfaces in multi-labeled digital images. This approach efficiently produces piecewise smooth quadrangulated surfaces with some theoretical stability guarantee. Non-manifold parts at intersecting interfaces are handled naturally by our model. We illustrate the strength of our tool for digital surface regularization, as well as voxel art regularization by transferring colorimetric information to regularized quads and computing isotropic geodesic on digital surfaces.

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Digital Surface Regularization With Guarantees

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Digital Surface Regularization With Guarantees

DGtal-team/DGtal: Release 1.0