Algorithm 2: Registration optimization based on neighboring meshes

Input: different frames point clouds of plant after denoising and smoothing

Output: one frame of complete plant point cloud

Setting: global transformation matrix $M_{glo}$

(1) Registration: At the beginning, the first two frames are selected for processing. Fast global registration [41], which is more efficient than FPFH, is applied for rough registration, and ICP is applied for fine alignment, producing the temporary matrix $M_{temp}$. $$M_{glo}=M_{glo}\ast M_{temp}$$

(2) Meshing: Greedy projection triangulation is used to form triangular patches for these two frames.

(3) Searching neighboring patches: Calculating the patches’ geometric center and getting two center point clouds $p_{c1}$ and $p_{c2}$. For each point in $p_{c1}$, searching the neighboring points of selected point in $p_{c2}$ based on the k-d tree. The center point corresponds to the patch, so the neighboring patches of the patch $△abc$ of $p_{c1}$ are a set $T=\{△mn{q}_i | i=1,2,3\dots \dots \}$

(4) Calculating the relationship between the patches: For each patch in set T, calculating the relationship between this patch and patch $△abc$. After projection, the new patch will take the place of the old one.

(5) Iteration and repetition: If ${\mathsf{\alpha }}_{tri}$ is less than the minimum angle threshold ${\mathsf{\alpha }}_{min}$, or ${\mathrm{d}}_{pro}$ is less than the minimum distance threshold ${\mathrm{d}}_{min}$, the optimization of these pairs of patches is completed. Repeating Steps 3–5 for all patches in the first frame.

(6) Down-sampling: After optimization, these two frames are combined into one frame, which is set as the new first frame. Due to repeated points, down-sampling is applied to reduce the point-cloud density.

(7) Applying to all frames: Taking the next frame from memory as the new second frame and then repeating the above operations until all frames are used.