added readme for metrics

README.md

@@ -29,6 +29,10 @@ pip install panoptica
 
 For tutorials featuring various use cases, see: [BrainLesion/tutorials/panoptica](https://github.com/BrainLesion/tutorials/tree/main/panoptica)
 
+### Metrics
+
+Panoptica supports a large range of metrics. An overview of the supported metrics and their formulas can be found: [panoptica/metrics.md](https://github.com/BrainLesion/panoptica/metrics.md)
+
 ### Semantic Segmentation Input
 
 <img src="https://github.com/BrainLesion/panoptica/blob/main/examples/figures/semantic.png?raw=true" alt="semantic_figure" height="300"/>

metrics.md

@@ -0,0 +1,92 @@
+# Metrics
+
+A details list of all metrics currently supported by Panoptica.
+- DICE (DSC)
+- Intersection over Union (IoU)
+- Centerline Dice (clDSC)
+- Average Symmetric Surface Distance (ASSD)
+- Relative Volume Difference (RVD)
+
+For instance-wise metrics:
+- True Positives (tp)
+- False Positives (fp)
+- False Negatives (fn)
+
+And most importantly, the panoptic metrics:
+- Recognition Quality (rq)
+- Segmentation Quality (sq)
+- Panoptic Quality (pq)
+
+These three original come from [arXiv: Panoptic Segmentation](https://arxiv.org/abs/1801.00868).
+
+
+---
+### Missing a metric? Write us an [github: issue](https://github.com/BrainLesion/panoptica/issues/new?assignees=&labels=&projects=&template=feature_request.md&title=New_Metric:)
+Be sure to use the "metric" label.
+
+<br/>
+<br/>
+
+# Metric Formulas
+
+Formulas to calculate the different metrics
+
+## Dice
+
+$$
+\text{DSC}(X,Y) = \frac{2 | X \cap Y | }{ |X| + |Y|} \in [0,1]
+$$
+Represents an overlap score.
+
+## Intersection over Union
+
+$$
+\text{IoU}(X,Y) = \frac{| X \cap Y | }{ |X \cup Y|} \in [0,1]
+$$
+Represents an overlap score. Is related to DSC, so giving both metrics doesn't really make sense (you can compute one with the other).
+
+## Centerline Dice
+
+Originally from [arXiv: clDice](https://arxiv.org/abs/2003.07311)
+
+Represents an topology-preserving overlap score. Can be used as loss. Uses skeletonize and calculates the Dice coefficient on the skeletonized version of prediction and reference.
+
+## Average Symmetric Surface Distance
+
+$$
+\text{ASSD}(X,Y) = \frac{\text{asd}(A,B) + \text{asd}(B,A)}{ |X| + |Y|} \in [0,\infty]
+$$
+with $\text{asd}(A, B)$ being the average surface distance from the border of $A$ to $B$.
+
+ASSD is a typically good metric to report, as it shows whether errors are local or if the prediction has widespread noise voxels not even close to the reference.
+
+
+## Relative (Voxel-)Volume Difference
+
+$$
+\text{RVD}(X,Y) = \frac{|X| - |Y|}{|Y|} \in [-\infty,\infty]
+$$
+
+The relative volume difference is the predicted volume of an instance in relation to the reference volume. For a journal, this might not be the most important metric. However, when the RVD is consistently positive, the predictions are oversegmenting. If negative, it is underpredicting (overall).
+
+## Recognition Quality
+
+$$
+\text{RQ}(\text{tp},\text{fp}, \text{fn}) = \frac{\text{tp}}{\text{tp} + \frac{1}{2} \cdot (\text{fp} + \text{fn})} \in [0,1]
+$$
+
+It is the F1-score basically. Represents how well your instances match the references well (well = determined by threshold).
+
+## Segmentation Quality
+
+The segmentation quality is the average of all true positive metrics. So for sq_dsc, this is the average of all dice scores among the true positives in this prediction/reference pair.
+
+As this metric is linked to another metric, we support all combinations of it. You can calculate the segmentation quality with IoU, DSC, clDSC, ASSD, and even RVD.
+
+## Panoptic Quality
+
+$$
+\text{PQ}(X,Y) = \text{SQ} \cdot \text{RQ} \in [0,1]
+$$
+
+Combines the F1-score of instances with the Segmentation Quality.