Diffusion inside axons is restricted and thus non-Gaussian, with diffusion MRI (dMRI) signal strongly sensitive to the shape of the confining axon. This sensitivity is confounded by the coarse-graining of the diameter/shape variation along the fiber during the diffusion time. Here, we analytically relate dMRI metrics to the axonal shape, and validate our theory using 3d Monte-Carlo simulations in beaded cylinders and realistic axons reconstructed from electron microscopy images of the mouse brain white matter. Our simulation results show that the intra-axonal space has a non-trivial kurtosis transverse to axons. Its value is different from that in a perfectly straight cylinder, and needs to be considered in axonal diameter measurements (e.g., spinal cord, strong gradients, intra-axonal metabolites).