In this paper, we propose a novel technique to segment handwritten document images into text lines by shredding their surface with local minima tracers. Our approach is based on the topological assumption that for each text line, there exists a path from one side of the image to the other that traverses only one text line. We first blur the image and then use tracers to follow the white-most and black-most paths from left to right as well as from right to left in order to shred the image into text line areas. We experimentally tested the proposed methodology and got promising results comparable to state of the art text line segmentation techniques.