In sawmills, it is essential to accurately measure the raw material, i.e. wooden logs, to optimise the sawing process. Earlier studies have shown that accurate predictions of the inner structure of the logs can be obtained using just surface point clouds produced by a laser scanner. This provides a cost-efficient and fast alternative to the X-ray CT-based measurement devices. The essential steps in analysing log point clouds is segmentation, as it forms the basis for finding the fine surface details that provide the cues about the inner structure of the log. We propose a novel Point Transformer-based point cloud segmentation technique that learns to find the points belonging to the log surface in unsupervised manner. This is obtained using a loss function that utilises the geometrical properties of a cylinder while taking into account the shape variation common in timber logs. We demonstrate the accuracy of the method on wooden logs, but the approach could be utilised also on other cylindrical objects.