Length distributions can be estimated using a class of morphological sieves constructed with a so-called Rotation-Invariant, Anisotropic (RIA) morphology. The RIA morphology can only be computed from an (intermediate) morphological orientation space, which is produced by a morphological operation with rotated versions of an anisotropic structuring element. This structuring element is defined as an isotropic region in a subspace of the image space (i.e. it has fewer dimensions than the image). A closing or opening in this framework discriminates on various object lengths, such as the longest or shortest internal diameter. Applied in a sieve, they produce a length distribution. This distribution is obtained from grey-value images, avoiding the need for segmentation. We apply it to images of rice kernels. The distributions thus obtained are compared with measurements on binarized objects in the same images.