Precise segmentation of objects with highly similar shapes remains a challenging problem in dense prediction, especially in scenarios with ambiguous boundaries, overlapping instances, and weak inter-instance visual differences. While conventional segmentation models are effective at localizing object regions, they often lack the discriminative capacity required to reliably distinguish a target object from morphologically similar distractors. In this work, we study fine-grained object segmentation from an identity-aware perspective and propose Identity-Aware U-Net (IAU-Net), a unified framework that jointly models spatial localization and instance discrimination. Built upon a U-Net-style encoder-decoder architecture, our method augments the segmentation backbone with an auxiliary embedding branch that learns discriminative identity representations from high-level features, while the main branch predicts pixel-accurate masks. To enhance robustness in distinguishing objects with near-identical contours or textures, we further incorporate triplet-based metric learning, which pulls target-consistent embeddings together and separates them from hard negatives with similar morphology. This design enables the model to move beyond category-level segmentation and acquire a stronger capability for precise discrimination among visually similar objects. Experiments on benchmarks including cell segmentation demonstrate promising results, particularly in challenging cases involving similar contours, dense layouts, and ambiguous boundaries.