Many proposed image watermarking techniques are sensitive to geometric distortions such as rotation, scaling, and translation. Geometric distortion, even by a slight amount, can disable a watermark decoder. In this study, a geometric distortion-invariant watermarking technique is designed by utilizing Tschebycheff moments of the original image to estimate the geometric distortion parameters of corrupted watermarked images. The Tschebycheff moments of an original image can be used as a private key for watermark extraction. The embedding process is a closed-loop system that modifies the embedding intensity according to the results of the performance analysis. The convergence of the closed-loop system is proved. Different from early heuristic methods, the optimal blind watermark detector is designed with the introduction of dual-channel detection utilizing high-order spectra detection and likelihood detection. Even with a small signal-to-noise ratio (SNR), the detector can still get a satisfying detection probability if there is enough high-order spectra information. When the high-order spectra are small, this dual-channel detection system will become a likelihood detection system. The watermark decoder extracts a watermark by blindly utilizing independent component analysis (ICA). The computational aspects of the proposed watermarking technique are also discussed in detail. Experimental results demonstrate that the proposed watermarking technique is robust with respect to attacks performed by the popular watermark benchmark, StirMark.