Modeling the time-varying 3D appearance of plants during their growth poses unique challenges: unlike many dynamic scenes, plants generate new geometry over time as they expand, branch, and differentiate. Recent motion modeling techniques are ill-suited to this problem setting. For example, deformation fields cannot introduce new geometry, and 4D Gaussian splatting constrains motion to a linear trajectory in space and time and cannot track the same set of Gaussians over time. Here, we introduce a 3D Gaussian flow field representation that models plant growth as a time-varying derivative over Gaussian parameters -- position, scale, orientation, color, and opacity -- enabling nonlinear and continuous-time growth dynamics. To initialize a sufficient set of Gaussian primitives, we reconstruct the mature plant and learn a process of reverse growth, effectively simulating the plant's developmental history in reverse. Our approach achieves superior image quality and geometric accuracy compared to prior methods on multi-view timelapse datasets of plant growth, providing a new approach for appearance modeling of growing 3D structures.

翻译：对植物生长过程中随时间变化的三维外观进行建模面临独特挑战：与多数动态场景不同，植物在扩展、分枝和分化过程中会随时间生成新的几何结构。现有运动建模技术难以适用于此问题场景：例如变形场无法引入新几何结构，而四维高斯溅射法将运动约束为时空线性轨迹，且无法随时间追踪同一组高斯单元。本文提出一种三维高斯流场表示方法，将植物生长建模为高斯参数（位置、尺度、取向、颜色及不透明度）随时间变化的导数场，从而实现对非线性连续时间生长动力学的建模。为初始化充足的高斯基元集合，我们重建成熟植株并学习逆向生长过程，有效逆向模拟植物的发育历史。在植物生长多视角时序数据集上的实验表明，相较于现有方法，本方法在图像质量与几何精度方面均取得更优结果，为生长中三维结构的外观建模提供了新途径。