Watermarking is a data authentication technique which embeds the watermark data within the original image in order to claim for copyright protection. Watermark techniques must be design to be robust against the various attacks. In this paper an invisible robust watermarking method is designed using edge detection in stationary wavelet transform domain. Proposed method initially decomposes the input image in to wavelet sub-band coefficients using L level SWT. The edge coefficients are calculated using the standard Sobel edge detection mask. The watermark is embedded around the edges of the high frequency sub-band SWT coefficients which lead to better invisibility. The advantage of using the SWT is its robustness against shift variations. In addition scaled morphological dilation of the low frequency sub-band is used as key along with the SWT coefficients. This in turns improves the robustness and invisibility of the watermark embedding. Performance of proposed method is tested on the four distinct categories of medical image data sets including CT scan, MRI, X ray and Fingerprints. The parametric performance is evaluated by calculating the MSE and PSNR. It is observed that proposed method not only improves the invisibility of the watermark but is robust to various attacks like cropping, compression, and interpolation. Therefore method is useful to authenticate the patients imaging data using robust watermarking.