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The visibility of an image depends a lot on its contrast. Improving contrast by various techniques can enhance the color image quality. However, most of them often get poor results if the images are high contrast and have wide dynamic range. This paper proposes a method for enhancing contrast in images by combining bilateral filtering and exact histogram equalization using wavelet coefficients. This method enhances contrast while preserving details in the Intensity component of the Hue, Saturation and Intensity color space of the color image.