**CornerNet** is an object detection model that detects an object bounding box as a pair of keypoints, the top-left corner and the bottom-right corner, using a single [convolution](https://paperswithcode.com/method/convolution) neural network. By detecting objects as paired keypoints, we eliminate the need for designing a set of anchor boxes commonly used in prior single-stage detectors. It also utilises [corner pooling](https://paperswithcode.com/method/corner-pooling), a new type of pooling layer than helps the network better localize corners.

**Matrix NMS**, or **Matrix Non-Maximum Suppression**,  performs [non-maximum suppression](https://paperswithcode.com/method/non-maximum-suppression) with parallel matrix operations in one shot. It is motivated by [Soft-NMS](https://paperswithcode.com/method/soft-nms). Soft-NMS decays the other detection scores as a monotonic decreasing function $f(iou)$ of their overlaps. By decaying the scores according to IoUs recursively, higher IoU detections will be eliminated with a minimum score threshold. However, such process is sequential like traditional Greedy NMS and can not be implemented in parallel.

Matrix NMS views this process from another perspective by considering how a predicted mask $m\_{j}$ being suppressed. For $m\_{j}$, its decay factor is affected by: (a) The penalty of each prediction $m\_{i}$ on $m\_{j}$ $\left(s\_{i}>s\_{j}\right)$, where $s\_{i}$ and $s\_{j}$ are the confidence scores; and (b) the probability of $m\_{i}$ being suppressed. For (a), the penalty of each prediction $m\_{i}$ on $m\_{j}$ could be easily computed by $f\left(\right.$ iou $\left.\_{i, j}\right)$. For (b), the probability of $m\_{i}$ being suppressed is not so elegant to be computed. However, the probability usually has positive correlation with the IoUs. So here we directly approximate the probability by the most overlapped prediction on $m\_{i}$ as

$$
f\left(\text { iou. }\_{, i}\right)=\min\_{\forall s\_{k}>s\_{i}} f\left(\text { iou }\_{k, i}\right)
$$

To this end, the final decay factor becomes

$$
\operatorname{decay}\_{j}=\min\_{\forall s\_{i}>s\_{j}} \frac{f\left(\text { iou }\_{i, j}\right)}{f\left(\text { iou }\_{\cdot, i}\right)}
$$

and the updated score is computed by $s\_{j}=s\_{j} \cdot$ decay $\_{j} .$ The authors consider the two most simple decremented functions, denoted as linear $f\left(\right.$ iou $\left.\_{i, j}\right)=1-$ iou $\_{i, j}$, and Gaussian $f\left(\right.$ iou $\left.\_{i, j}\right)=\exp \left(-\frac{i o u\_{i, j}^{2}}{\sigma}\right)$.

Matrix NMS

SOLOv2: Dynamic and Fast Instance Segmentation

CornerNet

CornerNet: Detecting Objects as Paired Keypoints

**Fourier Contour Embedding** is a text instance representation that allows networks to learn diverse text geometry variances. Most of existing methods model text instances in image spatial domain via masks or contour point sequences in the Cartesian or the polar coordinate system. However, the mask representation might lead to expensive post-processing, while the point sequence one may have limited capability to model texts with highly-curved shapes. This motivates modeling text instances in the Fourier domain.

Source	CornerNet: Detecting Objects as Paired Keypoints
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com