“…To begin, we will start developing our theory for spatiotemporal scale selection with respect to the problem of detecting sparse spatio-temporal interest points [6,9,11,14,18,20,21,30,49,88,94,97,99,100,107,122,124,126,127], which may be regarded as a conceptually simplest problem domain because of the sparsity of spatio-temporal interest points and the close connection between this problem domain and the detection of spatial interest points for which there exists a theoretically well-founded and empirically tested framework regarding scale selection over the spatial domain [1,4,5,15,17,25,42,65,72,74,84,89,90,112]. Specifically, using a non-causal Gaussian spatio-temporal scale-space model, we will perform a theoretical analysis of the spatio-temporal scale selection properties of eight different types of spatiotemporal interest point detectors and show that seven of them: (i) the spatial Laplacian of the first-order temporal derivative, (ii) the spatial Laplacian of the second-order temporal derivative, (iii) the determinant of the spatial Hessian of the first-order temporal derivative, (iv) the determinant of the spatial Hessian of the second-order temporal derivative, (v) the determinant of the spatio-temporal Hessian matrix, (vi) the first-order temporal derivative of the determinant of the spatial Hessian matrix and (vii) the second-order temporal derivative of the determinant of the spatial Hessian matrix, do all lead to fully scale-covariant spatio-temporal scale estimates and scale-invariant feature responses under independent scaling transformations of the spatial and the temporal domains.…”