Many biomedical applications require detection of curvilinear structures in images and would benefit from automatic or semiautomatic segmentation to allow high-throughput measurements. Here, we propose a contrast-independent approach to identify curvilinear structures based on oriented phase congruency, i.e., the phase congruency tensor (PCT). We show that the proposed method is largely insensitive to intensity variations along the curve and provides successful detection within noisy regions. The performance of the PCT is evaluated by comparing it with state-of-the-art intensity-based approaches on both synthetic and real biological images.