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We present a method of introducing rotation invariance in texture features based on a local Fourier histogram (LFH) computed using a 1-D discrete Fourier transform (DFT). To compensate for image rotation, a local image-gradient angle at each image pixel is found from within one of the 1-D DFT coefficients. The rotation invariance is established theoretically, analytically as well as empirically. The rotation-compensated features extracted from the same texture image oriented at different angles exhibit very high cross correlation. Therefore, the proposed texture features are expected to yield very high accuracies for a variety of image data and applications. The improved LFH-based features outperform the earlier version of the features and the features based on Gabor filters in texture recognition on 8560 images from the Brodatz album.