If the noise component of image data is nonisotropic, i.e., if it has nonconstant smoothness or effective point spread function, then theoretical results for the P value of local maxima and the size of suprathreshold clusters of a statistical parametric map (SPM) based on random field theory are not valid. This assumption is reasonable for PET or smoothed fMRI data, but not if these data are projected onto an unfolded, inflated, or flattened 2D cortical surface. Anatomical data such as structure masks, surface displacements, and deformation vectors are also highly nonisotropic. The solution offered here is to suppose that the image can be warped or flattened (in a statistical sense) into a space where the data are isotropic. The subsequent corrected P values do not depend on finding this warping; it is sufficient only to know that such a warping exists.