1. An image processing apparatus, comprising: a filtering unit that performs filtering on each pixel position in an image using a second order partial differential of a function representing a solid sphere and calculates a Hessian matrix; and an evaluation unit that discriminates a structure included in the image using eigenvalues and eigenvectors obtained by performing eigenvalue analysis on the calculated Hessian matrix, wherein the filtering unit includes a correction unit that performs filtering on each pixel position in the image using a first order partial differential of a function representing a hollow sphere having the same radius as the radius of the solid sphere and obtains first order partial differential vectors, and carries out correction to cancel out one of response waveforms of the second order partial differential of the function representing the solid sphere in each direction, the response waveforms appearing at two positions symmetrically separated with respect to the center of the solid sphere, using values obtained by projecting the obtained first order partial differential vectors onto directions of the eigenvectors.