A path between specified start and end voxels along a biological object with a lumen, such as a vessel, within a patient image three-dimensional volume data set comprising an array of voxels of varying value is identified using an algorithm that works outwards from the start voxel to identify paths of low cost via intermediate voxels. The intermediate voxels are queued for further expansion of the path using a priority function comprising the sum of the cost of the path already found from the start voxel to the intermediate voxel and the Euclidean distance from the intermediate voxel to the end voxel. A cost function that depends on the voxel density is used to bias the algorithm towards paths inside the object. The number of iterations of the voxel required to find a path from the start to the end voxel, and hence the time taken, can be significantly reduced by scaling the Euclidean distance by a constant. Usefully, the constant is greater than 1, such as between 1.5 and 2.