# AdaptiveConv2d: A Novel Convolutional Module for Medical Image Segmentation
## 2 Materials and Methods
### Validation Metrics  
To verify the robustness of AdaptiveConv2d, six validation metrics were employed: Dice Similarity Coefficient (DSC), Intersection over Union (IoU), accuracy, Specificity, Sensitivity, and Precision.  
1. Dice Similarity Coefficient (DSC) The Dice Similarity Coefficient (DSC), also known as the F1 score, is a widely used metric for binary classification tasks, such as image segmentation, that evaluates the overlap between the predicted results and the true labels. It is particularly effective for imbalanced datasets and can accurately reflect the segmentation performance for small target regions. The Dice coefficient ranges from 0 to 1, where 1 indicates complete overlap and 0 indicates no overlap. \[\text{DSC}=\frac{2\times|A\cap B|}{|A|+|B|}\] (8) Among them, \(A\) represents the predicted binary segmentation result, and \(B\) represents the actual binary annotation. \(|A\cap B|\) is the number of pixels at the intersection of the prediction result and the actual annotation, and \(|A|\) and \(|B|\) are the total numbers of pixels in the prediction result and the actual annotation, respectively.
2. Intersection over Union (IoU) Intersection over Union (IoU) is a metric commonly used to evaluate the performance of segmentation models. IoU is calculated as the ratio of the intersection of the union of the predicted segmentation area and the true annotated area, effectively measuring the spatial overlap of the model's predictions. The value of IoU ranges from 0 to 1, where 1 indicates complete overlap and 0 indicates no overlap. \[\text{IoU}=\frac{|A\cap B|}{|A\cup B|}\] (9)where \(|A\cap B|\) is the number of pixels at the intersection of the predicted result and the ground truth label, and \(|A\cup B|\) is the number of pixels in the union of the predicted result and the ground truth label.
3. Accuracy In image segmentation tasks, accuracy measures the proportion of correctly classified pixels to the total number of pixels. For binary segmentation problems (e.g., foreground and background), accuracy reflects the model's ability to classify pixels correctly across the entire image. \[\text{Accuracy}\;=\frac{TP+TN}{TP+TN+FP+FN}\] (10) \(TP\): number of pixels correctly segmented as foreground. \(TN\): number of pixels correctly segmented as background. \(FP\): number of background pixels incorrectly segmented as foreground. \(TP\): number of foreground pixels incorrectly segmented as background. While accuracy reflects overall performance, it can be biased when there is a significant imbalance between foreground and background pixels.
4. Specificity Specificity refers to the proportion of pixels that are correctly segmented as background (negative class) among all pixels that are actually background. Specificity evaluates the model's ability to recognize background regions. \[\text{Specificity}\;=\frac{TN}{TN+FP}\] (11) Specificity is crucial in segmentation tasks where the background area is large compared to the foreground, as it helps assess the model's performance in correctly identifying background pixels.
5. Sensitivity Sensitivity, also known as recall, measures the proportion of actual foreground (positive class) pixels that are correctly segmented as foreground. Sensitivity indicates the model's ability to detect foreground regions. \[\text{Sensitivity}\;=\frac{TP}{TP+FN}\] (12) Sensitivity is especially important in scenarios where it is necessary to ensure complete detection of foreground objects, such as lesion detection in medical image segmentation.
6. Precision Precision measures the proportion of pixels predicted by the model as foreground that are actually foreground. Precision assesses the model's accuracy in predicting foreground regions. \[\text{Precision}\;=\frac{TP}{TP+FP}\] (13) Precision is vital for evaluating the accuracy of the model's predictions, especially when false positives need to be minimized.