On piecewise-planar representation of images

It is customary to represent an analog image in digital form by dividing its support to pixels, and within each pixel to represent the brightness by a quantized scalar i.e., to approximate the 2-D image function by a horizontal planar patch. This paper studies a representation scheme in which the image function is represented within each pixel by an inclined planar patch. If the image function is to be represented by b bits per pixel, a bit allocation trade-off arises, and the optimal allocation of bits to the representation of the average value and of the two slope coefficients within each pixel needs to be determined. Analysis shows that allocating all the bits to represent the average brightness is not always optimal, and bits should be allocated to the representation of the slope coefficients. Similar results were obtained for the 1-D case