This paper proposes a fully automatic method to segment wood knots from images obtained by an X-ray Computed Tomography scanner. Wood knot segmentation is known to be a difficult problem in the presence of sapwood because of the quite similar density of knots and wet sapwood. Classical segmentation techniques produce unsatisfactory results due to the very weak distinction between these two intensities. To overcome this limitation caused by physical characteristics, we propose to exploit the geometric properties of both the knot shapes and knot-sapwood interface. Based on previous work related to automatic knot detection, a new segmentation algorithm is proposed that uses a robust curvature estimation of 2D digital contours. The segmentation process is fast, easily parallelizable and produces better segmentation results than other state-of-the-art algorithms. It may be reproduced from the precise description given here or from source code available online.