Coding for fast access to image regions defined by pixel range

Many technical imaging applications, like coding "images" of digital elevation maps, require extracting regions of compressed images in which the pixel values are within a predefined range, and there is a need for coding methods that allow finding these regions efficiently, without having to decompress the whole image. A series of techniques to solve this problem is presented. First, it shows that many of the linear transforms commonly used for image compression can be used for that purpose by proving that the inclusion of nonlinear factors (like minimum or maximum pixel value in a block) does not render the transformation irreversible, and can be made to have very limited impact on the compression efficiency. For example, it shows how the "DC" coefficient of an 8×8 discrete cosine transform (DCT) can be replaced by the minimum or maximum in the 8×8 block. This result is valid for a large set of transforms, including the DCT, Walsh-Hadamard, and dyadic Haar transforms, and valid for any type of order-statistic filter output. Next, it shows the results also apply to the quantized transform coefficient cases as well as integer-to-integer transforms. The choices for coding the minimum and maximum values simultaneously, while providing quick access to pixel range and efficient compression were finally studied.