Accurate segmentation of organoids in bright-field microscopy is essential for high-content screening in drug discovery and disease modeling, yet separating touching instances remains challenging. We present a training-free framework that combines Phase Congruency, an illumination-invariant image feature detector, with Persistent Homology, a topological method that extracts stable topological features such as \({H}_{1}\) cycles that correspond to organoid boundaries. Representative cycles derived from Phase Congruency responses provide interpretable separation contours that align close with true edge pixels, enabling robust separation of touching organoids without shape priors or supervised learning. Evaluated on a recent public dataset (OrgaSegment), our method achieves higher overlap which outperforms both deep-learning baselines and a previously proposed Phase Congruency-based segmentation method. Our results demonstrate that Phase Congruency combined with topological data analysis offers a highly accurate, interpretable, and generalizable strategy for organoid segmentation that does not require expensive data generation for training.