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A new rotation invariant texture descriptor based on the difference of offset Gaussian (DooG) and a sub-micro pattern encoding are proposed. We first apply the Gabor wavelet to texture images. We then utilize the DooG to measure the difference between the center positive Gaussian and the neighbor rotated negative one. We encode the local micro texture using our proposed method, a sub-micro pattern analysis. In classification step, we convert the rotation problem to the circular shift one by applying the Trace transform on the encoding image to get another 2D image and then compute the circular shift invariant features in the Trace transform. A {\it k}-nearest neighbor classifier is employed to classify the shift invariant features. The proposed method is local rotation invariant texture descriptor and is robust to the additive Gaussian noise as a result of adapting the DooG. We evaluate the proposed method on the Brodatz album with respect to rotation and Gaussian noise. Experimental results have shown that our proposed method outperforms the recent texture analysis methods.