This paper proposes a new image watermarking scheme which is robust to RST attacks with cropping by improving Fourier-Mellin transform based watermarking (FMW). The proposed scheme reorders and modifies function blocks of FMW for improvement of realization and performance. Unlike FMW, our method uses log-polar map (LPM) in the spatial domain for scaling invariance, while translation invariance is provided by the use of an invariant centroid (IC) as the origin of LPM. IC is a gravity center of a central area on gray scale image that is invariant although an image is attacked by RST. For this, its calculation method is proposed. Also since LPM includes the property which transforms rotation of Cartesian coordinates system into a cyclic shift, 2-D DFT is performed on the LPM image and the magnitude spectrum extracted to provide a domain that is rotation invariant. The resulting domain, which is invariant to RST, is then used as the watermark-embedding domain. Furthermore, to prevent the watermarked image from degrading due to the coordinate system conversion, only LPM image of watermark signal is inverse mapped to Cartesian coordinates and add to the original image. Experimental results demonstrate that the proposed scheme is robust to RST attacks.