Algorithm 1: Hybrid Panoptic-Style Segmentation of Dense Breast Tumors

Input: Mammogram image $I(x,y)$ Output: Panoptic segmentation map $P(x,y)$ Step 1: Preprocessing Normalize the input image to obtain $I_n(x,y)$; Step 2: Bias Correction Perform intensity inhomogeneity correction using the MICO_2D model to obtain $I_c(x,y)=I_n(x,y)/b(x,y)$; Step 3: Global Segmentation Apply distance-regularized multiphase Chan–Vese segmentation to obtain a coarse semantic mask $S_g(x,y)$; Step 4: Localized Refinement Refine object boundaries using localized active contours with LIF energy to obtain $S_r(x,y)$; Step 5: Instance Extraction Extract tumor instances $\left\{T_k\right\}$ from $S_r(x,y)$ using distance transform and watershed segmentation; Step 6: Panoptic Assignment Assign semantic and instance labels to construct the panoptic output $P(x,y)$;