Splitting-integrating method for inverse transformation ofn-dimensional digital images and patterns

Abstract

The splitting-integrating method is proposed to normalize digital images and patterns inn dimensions under inverse transformation. This method is much simpler than other approaches because no solutions of nonlinear algebraic equations are required. Also, the splitting-integrating method produces images free from superfluous holes and blanks, which often occur in transforming digitized images by other methods.

The splitting-integrating method has been applied successfully to pattern recognition and image processing; but no error analysis has been provided so far. Because the image greyness is represented as an integral value, we can derive by numerical analysis error bounds of approximate greyness solutions, to show that when piecewise constant and multi-linear interpolations are used, convergence ratesO(1/N) andO(1/N ²) can be obtained respectively, whereN is a division number such that a pixel in then-dimensional images is split intoN ⁿ subpixels. Moreover, numerical and graphical experiments are carried out for a sample of binary images in two dimensions, to confirm the convergence rates derived.