Abstract: The observed images are usually degraded by non-ideal imaging systems or imaging conditions,for example,images are likely to contain blur due to being out of focus or relative motion between the camera and the scene,geometric degradations are often present in images due to different viewpoints.To solve this problem,a kind of combined moment invariants to affine transformation and Gaussian convolution degradation is proposed.First,blur and geometric degradation by Gussian convolution and affine transformation are modeled.Then,the property of the Fourier spectrum after combined affine and Gaussian transforms are analysed,and a kind of combined affine and convolution invariants in explicit forms are proposed.Through retrieval and recognition experiments to images under supervised transformations by computer and those shot in real scenes,the effectiveness of these combined invariants in the degraded scene is validated.