Accuracy in Quantitative 3D Image Analysis

Quantitative 3D imaging is becoming an increasingly popular and powerful approach to investigate plant growth and development. With the increased use of 3D image analysis, standards to ensure the accuracy and reproducibility of these data are required. This commentary highlights how image acquisition and postprocessing can introduce artifacts into 3D image data and proposes steps to increase both the accuracy and reproducibility of these analyses. It is intended to aid researchers entering the field of 3D image processing of plant cells and tissues and to help general readers in understanding and evaluating such data.Advances in digital imaging have led to the generation of an increasing number of 3D data sets (Truernit et al., 2008; Fernandez et al., 2010; Kierzkowski et al., 2012; Roeder et al., 2012). Whole-mount and time-lapse imaging enable all cells in an organ to be analyzed in 3D over time, providing a comprehensive analysis of plant growth and development (Roeder et al., 2011).The generation of these 3D image data sets has led to the development of novel computational approaches to facilitate their analysis (Cunha et al., 2010; Kierzkowski et al., 2012; Bassel et al., 2014; Yoshida et al., 2014). With the development of these new methods comes a need for quality control and standard measures to ensure the accurate analysis of data sets. An overall objective of this approach is the accurate capture and quantification of the 3D geometry of biological objects. The inaccurate abstraction of shape data and introduction of artifacts during image acquisition and postprocessing must be kept to a minimum.Following imaging, typically using confocal microscopy, 3D objects can be identified through the process of segmentation (Roeder et al., 2012). This can be achieved using automatic seeding through a watershed approach or by inflating “balloons” with defined seeds in individual cells (Federici et al., 2012). Vertices and meshes that describe cell surfaces may then be generated using an algorithm such as marching cubes (Lorensen and Cline, 1987). Vertices at defined spacings can be placed on the surface of unique segments, and the surfaces describing these geometric shapes are represented by the triangles connecting adjacent vertices constituting a polygonal mesh.The mesh describing segment surfaces is ultimately what defines the shape of an object in question. Rough and irregular features are often represented by meshes owing to the imperfect nature of data collection from biological samples (Desbrun et al., 1999; Taubin, 2000). In the context of plant cells whose surfaces are naturally smooth, the segmentations and meshes describing them are in practice noisy and contain undesirable geometric irregularities. The lower the quality of the original image being segmented, the greater the irregularities in the mesh that describe the shape.In order to improve the quality of irregularly triangulated polygonal meshes, smoothing operations can be performed. In this way, the roughness of the surface can be reduced, improving the texture and representation of a segmented object.A straightforward and easy to implement operation to remove noise in 3D meshes is Laplacian smoothing (Field, 1988). This process repositions vertices to an average position (barycentre) along a mesh surface to create a smoothed effect. However, Laplacian smoothing has the side effect of slightly shrinking the object in question (Taubin, 2000). While this shrinkage effect is well documented among computer scientists who develop algorithms to modify polygonal meshes, it is perhaps less well understood and discussed by the end user biological community.Smoothing of meshes has the positive effect of making surfaces smoother and removing noise, while enhancing the visual aesthetic of segmented objects providing the appearance that their geometry has been captured accurately (Figures 1A and 1B). In cases where objects have been poorly segmented, the need to remove the jagged appearance of meshes is greater, and additional smoothing steps are often used. This repeated Laplacian smoothing leads to additional smoothing-induced shrinkage and greater abstraction of the object being analyzed. Given that the mesh itself is intended to represent the 3D geometry of an object in question, changing its overall size by smoothing represents a perturbation and manipulation of data that inaccurately reflects the quantitative capture of geometry. The need to remove rough edges in meshes due to noise needs to be balanced with the accuracy that the mesh represents an object in question.Open in a separate windowFigure 1.Effect of Laplacian Smoothing on the Cellular Structure of a 3D Segmented Arabidopsis Radicle.(A) Surface rendering of a mesh following generation using marching cubes with a cube size of 2 μm and no smoothing. Bar = 10 μm.(B) Same as (A) following one Laplacian smoothing pass. (C) Same as (A) following six smoothing passes. (D) Same as (A) following nine smoothing passes. (E) An original confocal stack showing cell walls in green and the multicolored segmented stack before generating the mesh using marching cubes. (F) Smoothing of the mesh in (A) using the Taubin λ/μ algorithm with λ = 0.5, μ = −0.53, and nine smoothing steps. An example of an unsmoothed mesh representing the cells of 3D segmented plant organ can in seen in Figure 1A. The rough edges and irregularities of this primary unsmoothed mesh, coming from a suboptimal noisy confocal image stack, do not accurately represent the surface of these plant cells. The mesh in Figure 1B, which has been smoothed once, appears to be a more accurate representation of cell shape than the unsmoothed mesh in Figure 1A and has not been shrunk dramatically.In the context of plant organ cellular segmentations, additional Laplacian smoothing steps create even smoother cells, but also exaggerated gaps between adjacent cells due to cell shrinkage (Figures 1C and 1D). These spaces do not reflect reality as adjacent cells are physically appressed against their cell walls, which are rarely more than several microns thick. This example demonstrates the abstraction of cell shape that can occur following multiple Laplacian smoothing steps, and the gaps between cells are a hallmark of data that have been postprocessed to the point of inaccuracy.Other factors can affect the response of 3D segmented cells to Laplacian smoothing. These include mesh triangle size, with larger triangles being more susceptible to shrinkage (Desbrun et al., 1999), and cell size, with smaller cells being more susceptible to smoothing-based shrinking than larger cells (Figure 1D).If the purpose of 3D segmentation is strictly qualitative, smoothing-based shrinkage may not present a problem. However, if quantitative analyses are applied to shrunken meshes, this will result in inaccurate data.