Enhancing dermatological segmented images using the Sakaguchi kind function coefficient with balancing polynomial

his MATLAB code estimates image segmentation quality metrics without performing actual segmentation, using a novel Geometric Function Theory (GFT) based approach. Coefficient bounds derived from a Sakaguchi-kind bi-univalent function class subordinate to balancing polynomials are used to construct a mathematically justified 3×3 Gaussian filter mask. The code loads a dermoscopic skin lesion image, converts it to a binary ground truth mask using Otsu's thresholding, and applies the Gaussian kernel via 2D convolution to simulate segmentation boundary smoothness. Salt-and-pepper noise is then added to simulate prediction errors, and the noisy image is re-binarized to produce the final predicted mask. The predicted mask is compared pixel-by-pixel with the ground truth to compute TP, TN, FP, and FN, from which eleven quality metrics — Accuracy, Specificity, Precision, Recall, IoU, F1-Score, FPR, FNR, NPV, FDR, and MCC — are derived and reported.本MATLAB代码无需执行实际分割操作，即可估算图像分割质量指标，其采用了一种基于几何函数理论（Geometric Function Theory，GFT）的创新方法。研究借助从属于均衡多项式的坂口型双单叶函数族推导得到的系数界，构建了具备数学严谨合理性的3×3高斯滤波掩码。该代码加载皮肤镜皮肤病变图像，通过大津（Otsu）阈值法将其转换为二值化基准掩码（ground truth mask），并通过二维卷积应用高斯核以模拟分割边界的平滑性。随后添加椒盐噪声以模拟预测误差，并对含噪图像再次进行二值化处理，得到最终的预测掩码。将预测掩码与基准掩码逐像素对比，计算真阳性（TP）、真阴性（TN）、假阳性（FP）以及假阴性（FN），并基于上述指标推导并报告共计11项分割质量指标：准确率（Accuracy）、特异度（Specificity）、精确率（Precision）、召回率（Recall）、交并比（IoU）、F1分数（F1-Score）、假阳性率（FPR）、假阴性率（FNR）、阴性预测值（NPV）、错误发现率（FDR）以及马修斯相关系数（MCC）。