# 1. Distance

## 1.1. Point-to-surface distance (P2F)

measures the minimum distance from the sampled points of the predicted to the surface of the ground truth.

point-wise distance.

## 1.2. Chamfer distance (CD)

measures the bidirectional shortest distance between the point samples of the predicted and the ground truth.

point-wise distance.





## 1.3. Earth Mover Distance





## 1.4. F-score





# 2. Voxel IoU scores (IoU)

used in sketch to shape reconstruction

# 3. Visual quality

## 3.1. Light filed distance (LFD)

measures the visual similarity in rendered images of the predicted and the ground truth at different views.

measures the visual quality of object surfaces.

## 3.2. Frechet Inception Distance (FID)

render the 3D shapes into 2D images and report the FID between the rendered images and the ground-truth samples.

It is introduced by Heusel et al in 2017.

It calculates the distance between the feature vectors of real images and the feature vectors of fake images(generated by the generator). The lower FID score represents that the quality of images generated by the generator is higher and similar to the real ones.

• Use the Inception V2 pre-trained model to extract the feature vectors of real images and fake images(Generated by the generator)
• Calculate the feature-wise mean of the feature vectors generated in step 1
• Generate the covariance matrices of the feature vectors — C, C_w
• Calculate trace(The sum of the elements along the main diagonal of the square matrix) of (C+C_w-2(CCₓ)¹/2)
• Calculate the squared difference of the mean vectors calculated in step 2 — ||m-m_w||² Finally, add the output of step 4 and step 5