Image segmentation is a crucial task in artificial intelligence fields such as computer vision and medical imaging. While convolutional neural networks (CNNs) have achieved notable success by learning representative features from large datasets, they often lack geometric priors and global object information, limiting their accuracy in complex scenarios. Variational methods like active contours provide geometric priors and theoretical interpretability but require manual initialization and are sensitive to hyper-parameters. To overcome these challenges, we propose a novel segmentation approach, named PolarVoting, which combines the minimal path encoding rich geometric features and CNNs which can provide efficient initialization. The introduced model involves two main steps: firstly, we leverage the PolarMask model to extract multiple source points for initialization, and secondly, we construct a voting score map which implicitly contains the segmentation mask via a modified circular geometric voting (CGV) scheme. This map embeds global geometric information for finding accurate segmentation. By integrating neural network representation with geometric priors, the PolarVoting model enhances segmentation accuracy and robustness. Extensive experiments on various datasets demonstrate that the proposed PolarVoting method outperforms both PolarMask and traditional single-source CGV models. It excels in challenging imaging scenarios characterized by intensity inhomogeneity, noise, and complex backgrounds, accurately delineating object boundaries and advancing the state of image segmentation.