In [0]:

```
# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
```

In this tutorial, we learn to deform an initial generic shape (e.g. sphere) to fit a target shape.

We will cover:

- How to
**load a mesh**from an`.obj`

file - How to use the PyTorch3D
**Meshes**datastructure - How to use 4 different PyTorch3D
**mesh loss functions** - How to set up an
**optimization loop**

Starting from a sphere mesh, we learn the offset to each vertex in the mesh such that the predicted mesh is closer to the target mesh at each optimization step. To achieve this we minimize:

`chamfer_distance`

, the distance between the predicted (deformed) and target mesh, defined as the chamfer distance between the set of pointclouds resulting from**differentiably sampling points**from their surfaces.

However, solely minimizing the chamfer distance between the predicted and the target mesh will lead to a non-smooth shape (verify this by setting `w_chamfer=1.0`

and all other weights to `0.0`

).

We enforce smoothness by adding **shape regularizers** to the objective. Namely, we add:

`mesh_edge_length`

, which minimizes the length of the edges in the predicted mesh.`mesh_normal_consistency`

, which enforces consistency across the normals of neighboring faces.`mesh_laplacian_smoothing`

, which is the laplacian regularizer.

If `torch`

, `torchvision`

and `pytorch3d`

are not installed, run the following cell:

In [0]:

```
!pip install torch torchvision
!pip install 'git+https://github.com/facebookresearch/[email protected]'
```

In [0]:

```
import os
import torch
from pytorch3d.io import load_obj, save_obj
from pytorch3d.structures import Meshes
from pytorch3d.utils import ico_sphere
from pytorch3d.ops import sample_points_from_meshes
from pytorch3d.loss import (
chamfer_distance,
mesh_edge_loss,
mesh_laplacian_smoothing,
mesh_normal_consistency,
)
import numpy as np
from tqdm import tqdm_notebook
%matplotlib notebook
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib as mpl
mpl.rcParams['savefig.dpi'] = 80
mpl.rcParams['figure.dpi'] = 80
# Set the device
device = torch.device("cuda:0")
```

Download the target 3D model of a dolphin. It will be saved locally as a file called `dolphin.obj`

.

In [1]:

```
!wget https://dl.fbaipublicfiles.com/pytorch3d/data/dolphin/dolphin.obj
```

In [0]:

```
# Load the dolphin mesh.
trg_obj = os.path.join('dolphin.obj')
```

In [0]:

```
# We read the target 3D model using load_obj
verts, faces, aux = load_obj(trg_obj)
# verts is a FloatTensor of shape (V, 3) where V is the number of vertices in the mesh
# faces is an object which contains the following LongTensors: verts_idx, normals_idx and textures_idx
# For this tutorial, normals and textures are ignored.
faces_idx = faces.verts_idx.to(device)
verts = verts.to(device)
# We scale normalize and center the target mesh to fit in a sphere of radius 1 centered at (0,0,0).
# (scale, center) will be used to bring the predicted mesh to its original center and scale
# Note that normalizing the target mesh, speeds up the optimization but is not necessary!
center = verts.mean(0)
verts = verts - center
scale = max(verts.abs().max(0)[0])
verts = verts / scale
# We construct a Meshes structure for the target mesh
trg_mesh = Meshes(verts=[verts], faces=[faces_idx])
```

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```
# We initialize the source shape to be a sphere of radius 1
src_mesh = ico_sphere(4, device)
```

In [0]:

```
def plot_pointcloud(mesh, title=""):
# Sample points uniformly from the surface of the mesh.
points = sample_points_from_meshes(mesh, 5000)
x, y, z = points.clone().detach().cpu().squeeze().unbind(1)
fig = plt.figure(figsize=(5, 5))
ax = Axes3D(fig)
ax.scatter3D(x, z, -y)
ax.set_xlabel('x')
ax.set_ylabel('z')
ax.set_zlabel('y')
ax.set_title(title)
ax.view_init(190, 30)
plt.show()
```

In [75]:

```
# %matplotlib notebook
plot_pointcloud(trg_mesh, "Target mesh")
plot_pointcloud(src_mesh, "Source mesh")
```

In [0]:

```
# We will learn to deform the source mesh by offsetting its vertices
# The shape of the deform parameters is equal to the total number of vertices in src_mesh
deform_verts = torch.full(src_mesh.verts_packed().shape, 0.0, device=device, requires_grad=True)
```

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```
# The optimizer
optimizer = torch.optim.SGD([deform_verts], lr=1.0, momentum=0.9)
```

In [78]:

```
# Number of optimization steps
Niter = 2000
# Weight for the chamfer loss
w_chamfer = 1.0
# Weight for mesh edge loss
w_edge = 1.0
# Weight for mesh normal consistency
w_normal = 0.01
# Weight for mesh laplacian smoothing
w_laplacian = 0.1
# Plot period for the losses
plot_period = 250
loop = tqdm_notebook(range(Niter))
chamfer_losses = []
laplacian_losses = []
edge_losses = []
normal_losses = []
%matplotlib inline
for i in loop:
# Initialize optimizer
optimizer.zero_grad()
# Deform the mesh
new_src_mesh = src_mesh.offset_verts(deform_verts)
# We sample 5k points from the surface of each mesh
sample_trg = sample_points_from_meshes(trg_mesh, 5000)
sample_src = sample_points_from_meshes(new_src_mesh, 5000)
# We compare the two sets of pointclouds by computing (a) the chamfer loss
loss_chamfer, _ = chamfer_distance(sample_trg, sample_src)
# and (b) the edge length of the predicted mesh
loss_edge = mesh_edge_loss(new_src_mesh)
# mesh normal consistency
loss_normal = mesh_normal_consistency(new_src_mesh)
# mesh laplacian smoothing
loss_laplacian = mesh_laplacian_smoothing(new_src_mesh, method="uniform")
# Weighted sum of the losses
loss = loss_chamfer * w_chamfer + loss_edge * w_edge + loss_normal * w_normal + loss_laplacian * w_laplacian
# Print the losses
loop.set_description('total_loss = %.6f' % loss)
# Save the losses for plotting
chamfer_losses.append(loss_chamfer)
edge_losses.append(loss_edge)
normal_losses.append(loss_normal)
laplacian_losses.append(loss_laplacian)
# Plot mesh
if i % plot_period == 0:
plot_pointcloud(new_src_mesh, title="iter: %d" % i)
# Optimization step
loss.backward()
optimizer.step()
```

In [79]:

```
fig = plt.figure(figsize=(13, 5))
ax = fig.gca()
ax.plot(chamfer_losses, label="chamfer loss")
ax.plot(edge_losses, label="edge loss")
ax.plot(normal_losses, label="normal loss")
ax.plot(laplacian_losses, label="laplacian loss")
ax.legend(fontsize="16")
ax.set_xlabel("Iteration", fontsize="16")
ax.set_ylabel("Loss", fontsize="16")
ax.set_title("Loss vs iterations", fontsize="16")
```

Out[79]:

Text(0.5, 1.0, 'Loss vs iterations')

In [0]:

```
# Fetch the verts and faces of the final predicted mesh
final_verts, final_faces = new_src_mesh.get_mesh_verts_faces(0)
# Scale normalize back to the original target size
final_verts = final_verts * scale + center
# Store the predicted mesh using save_obj
final_obj = os.path.join('./', 'final_model.obj')
save_obj(final_obj, final_verts, final_faces)
```

In this tutorial we learnt how to load a mesh from an obj file, initialize a PyTorch3D datastructure called **Meshes**, set up an optimization loop and use four different PyTorch3D mesh loss functions.