Methods and apparatus for binarizing images represented by sets of multivalent pixel values in a computationally efficient manner are described In a grayscale image to be binarized, one group of pixel values represents “foreground”, e.g., text to be converted to black, while another group represents a shaded “background” region to be converted, e.g., to white. The difference between foreground and background is often a function of the scale of the image components, e.g., text and/or other images. Filters in the form of morphological operators, computationally efficient quick-open and quick-close morphological operators are employed to binarize images, e.g., grayscale images. The methods and apparatus effectively handle both smooth and sharp image background structures in a computationally efficient manner.