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The new High Efficiency Video Coding (HEVC) standard achieves higher encoding efficiency when compared to its predecessors such as H.264/AVC. One of the factors responsible for this improvement is the new intra prediction method, which introduces a larger number of prediction directions resulting in an enhanced rate-distortion (RD) performance obtained at the cost of higher computational complexity. This paper proposes an algorithm to accelerate the intra mode decision, reducing the complexity of intra coding. The acceleration procedure takes into account the texture local directionality information and explores the correlation of intra modes across levels of the hierarchical tree structure used in HEVC. Experimental results show that the proposed algorithm provides a decrease of 39.22 and 43.88% in the HEVC intra prediction processing time on average, for all-intra high efficiency (AI-HE) and low complexity (AI-LC) configurations, respectively, with a small degradation in encoding efficiency (BD-PSNR loss of 0.1 dB for AI-HE and 0.8 dB for AI-LC on average).