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In this work, a robust and oblivious image watermarking scheme based on discrete wavelet transform (DWT) for copyright protection is presented. The original unmarked image is not required for watermark extraction. Third-level DWT is applied to the original cover image. Third- and second-level horizontal detail sub-band (LH2 and LH3) coefficients are grouped into different blocks. Grouping of the coefficients is done in such a way that each block should contain one coefficient from LH3 sub-band and four coefficients from LH2 sub-band. In each block, the first minimum and the second minimum are identified and modified according to the watermark bit. After watermark insertion, inverse DWT is applied to the sub-bands with modified coefficients to obtain the watermarked image. For watermark extraction, a threshold-based decoder is designed. Embedding and extraction process are characterised with parameters and genetic algorithm is used for parameter optimisation. Optimisation is to maximise the values of peak signal-to-noise ratio of the watermarked image and normalised cross correlation of the extracted watermark. The performance of the proposed scheme is compared with the existing schemes and significant improvement is observed. Experimental results show that, this algorithm is highly robust for many image attacks on the watermarked image.