# K2S Challenge: From Undersampled K-Space to Automatic Segmentation
## 4 Discussion  
In this work, we describe the K2S challenge, which aims to reframe image reconstruction and image analysis as end-to-end rather than serial tasks, opening room for optimization. We curated the K2S dataset of 300 patients that had undergone 3D fat-suppressed knee MRI acquisitions, each with 3D raw k-space and bone and cartilage segmentations, challenging participants to segment the tissues directly from 8\(\times\) undersampled k-space. A variety of solutions were submitted for the challenge. Some, like NYU-Knee AI and UglyBarnacle, spent considerable time optimizing reconstruction networks, leveraging VN and CS frameworks to attain high-quality reconstructions that served as inputs for standard segmentation networks. Interestingly, FastMRI-AI did not pursue a reconstruction network at all, choosing exclusively to optimize the segmentation network and develop unique postprocessing techniques, attaining very competitive results. K-nirsh, on the other hand, pretrained separate reconstruction and segmentation networks, performing end-to-end optimization of both for weighted DSC. The end-to-end optimization made this the only approach that implicitly optimized reconstruction outputs for segmentation inputs, possibly playing a role in their top finish within the challenge. All told, however, all top submissions produced high-quality segmentations in knee cartilage and bone, maintaining accuracy with respect to ground truth despite working originally from 8\(\times\) undersampled multicoil k-space. Beyond strong DSC metrics, predicted segmentations from all top submissions produced cartilage thickness maps that either maintained minimal bias or strong correlation to ground truth cartilage thicknesses. Statistical shape modeling generated five features that captured the most variance in bone shape for each of the patella, tibia, and femur. Each of the top submissions was most correlated to ground truth along at least one of the features, with moderate to good correlations seen in many, while K-nirsh and NYU-Knee AI generally showed the best performance in retaining bone shape. As such, for both bone and cartilage, all top submissions yielded cartilage and bone segmentations that to varying degrees were suitable for subsequent biomarker analysis. An added observation was that downstream biomarker performance did not always correspond with segmentation metrics: for instance, NYU-Knee AI delivered among the best correlations between predicted and  
Figure 12: Correlations along femoral, tibial, and patellar bone shape features between submissions and ground truth. For many of the bone shape features, correlations were moderate to strong, indicating another means in which submitted segmentations from 8\(\times\) undersampled images at times were suitable for downstream biomarker analysis. K-nirsh and NYU-Knee AI appeared to have strong correlations most consistently between predicted and ground truth bone shapes among the top 4 submissions. ground truth bone shape features despite obtaining the poorest weighted DSC among the top 4 submissions, with segmentations that often appeared slightly dilated compared to ground truth but preserved shape. Likewise, UglyBarnacle slightly outperformed K-nirsh in correlations between tiboifemoral cartilage thicknesses and ground truth despite slightly poorer weighted DSCs, but its slightly reduced bias was not statistically significant. This accentuates the complexity of segmentation as an image analysis task: there is no all-encompassing, perfect metric to quantify segmentation quality. A noteworthy finding from this challenge was that strong reconstruction performance was not a prerequisite for strong segmentation performance. K-nirsh had by far the poorest metrics of the submitted pipeline reconstruction intermediates, poorer even than the root sum-of-squares coil-combined 8\(\times\) undersampled images that FastMRI-AI used as pipeline inputs.