SurfDist: Interpretable Three-Dimensional Instance Segmentation Using Curved Surface Patches

TL;DR

SurfDist advances 3D instance segmentation by predicting closed surfaces composed of curved patches, using bicubic Bézier triangles to form smooth, interpretable meshes that decouple surface parameterization from voxel resolution. The method defines a per-voxel loss with per-voxel radial directions sampled from the predicted surface, enabling arbitrary-resolution surface upsampling without voxel artifacts. Across synthetic and real biomedical datasets, SurfDist matches or exceeds StarDist-3D performance on blob-like objects while using fewer parameters, though training is slower and performance can vary with dataset-specific labeling artifacts. The work highlights a promising direction at the intersection of computational geometry and deep learning for 3D segmentation and points to avenues for speedups, handling more complex topologies, and improving data quality for evaluation.

Abstract

We present SurfDist, a convolutional neural network architecture for three-dimensional volumetric instance segmentation. SurfDist enables prediction of instances represented as closed surfaces composed of smooth parametric surface patches, specifically bicubic Bézier triangles. SurfDist is a modification of the popular model architecture StarDist-3D which breaks StarDist-3D's coupling of instance parameterization dimension and instance voxel resolution, and it produces predictions which may be upsampled to arbitrarily high resolutions without introduction of voxelization artifacts. For datasets with blob-shaped instances, common in biomedical imaging, SurfDist can outperform StarDist-3D with more compact instance parameterizations. We detail SurfDist's technical implementation and show one synthetic and one real-world dataset for which it outperforms StarDist-3D. These results demonstrate that interpretable instance surface models can be learned effectively alongside instance membership.

Figures (7)

• Figure 1: Representative StarDist and SplineDist instance models from mandal2021splinedist.
• Figure 2: A generic bicubic Bézier triangle from lee2016bezier. Control points are annotated with gray spheres, vertex control points are annotated with red spheres, vertex normals are annotated with red arrows, the control mesh is shown in blue, and the smooth triangular surface parameterized by the control points is rendered in gray.
• Figure 3: A StarDist-3D versus a SurfDist model instance. The models use the same number of mesh vertices and triangular faces, but the SurfDist model is better suited to reproducing smooth instance surfaces.
• Figure 4: StarDist-3D vs. SurfDist reconstruction error for a voxelized sphere. With fewer parameters, SurfDist better models large spheres than StarDist-3D.
• Figure 5: IoU distributions for matched predicted and true validation instances for dataset Worm across all trained models detailed in \ref{['table:worm_metrics']}. Models of type SurfDist 6 use 6 rays, 8 triangular faces, and 38 total free parameters per instance. Models of type SurfDist 12 use 12 rays, 20 triangular faces, and 92 total free parameters per instance. Models of type StarDist-3D 96 use 96 rays, 188 triangular faces, and 96 total free parameters per instance.