There has been increasing interest in the analysis of corneal nerve fibers to support examination and diagnosis of many diseases, and for this purpose, automated nerve fiber segmentation is a fundamental step. Existing methods of automated corneal nerve fiber detection continue to pose difficulties due to multiple factors, such as poor contrast and fragmented fibers caused by inaccurate focus. To address these problems, in this paper we propose a novel weighted local phase tensor-based curvilinear structure filtering method. This method not only takes into account local phase features using a quadrature filter to enhance edges and lines, but also utilizes the weighted geometric mean of the blurred and shifted responses to allow better tolerance of curvilinear structures with irregular appearances. To demonstrate its effectiveness, we apply this framework to 1578 corneal confocal microscopy images. The experimental results show that the proposed method outperforms existing state-of-the-art methods in applicability, effectiveness, and accuracy.