*December 2020*

tl;dr: Locating objects with center points, but with a new loss function based on average Hausdorff distance.

#### Overall impression

This paper proposed a NMS-free method for object detection. The method by predicting a heat map is very similar to that of CenterNet and other anchor-free methods. However it proposes a new set-prediction loss based on the averaged Hausdorff distance.

Sometimes bbox of an object is not the optimal representation. Object localization is more appropriate where objects are very small, or substantially overlap. The bbox in crowded scenes may be infeasible to be used as GT.

#### Key ideas

- Chamfer distance or Earth Mover’s distance are closely related to and very similar to Hausdorff distance.
- Hausdorff function is highly sensitive to outliers, ergo the average Hausdorff distance.
$d_{AH}(X, Y) = \frac{1}{|X|} \sum_{x \in X} \min_{y \in Y} d(x, y) + \frac{1}{|Y|} \sum_{x \in Y} \min_{y \in X} d(x, y)$
- Average Hausdorff distance operates on coordinates, not heatmap. To use heatmap directly with the loss, a weighted Hausdorff loss is proposed.

#### Technical details

- Generalized mean function
$M_n[f(a)] = (\frac{1}{|A|} \sum_{a \in A} f(a)^n)^{1/n}$
- When n –> inf, then it is max function
- When n –> -inf, then it is min function
- When n = 1, it is mean function.

- Using a generalized mean will make min more smooth.

#### Notes

- I wonder how this will compare with the centerNet based keypoint approach.