We present a new discrete transform, the Gould transform (DGT). The transform has many interesting mathematical properties. For example, the forward and inverse transform matrices are both lower triangular, with constant diagonals and sub-diagonals and both can be factored into the product of binary matrices. The forward transform can be used to detect edges in digital images. If G is the forward transform matrix and y is the image, then the two dimensional DGT, GyGT can be used directly to detect edges. Ways to improve the edge detection technique is to use the "combination of forward and backward difference", GT(Gy) to better identify the edges. For images that tend to have vertical and horizontal edges, we can further improve the technique by shifting rows (or columns), and then use the technique to detect edges, essentially applying the transform in the diagonal directions.
Proc. SPIE. 5685, Image and Video Communications and Processing 2005
KEYWORDS: Image processing, Video, Control systems, Computer programming, Telecommunications, Signal processing, Video processing, Algorithm development, Parallel computing, Computer programming languages
The discrete cosine transform (DCT) is commonly used in signal processing, image processing, communication systems and control systems. We use two methods based on the algorithms of Clenshaw and Forsyth to compute the recursive DCT in parallel. The symmetrical discrete cosine transform (SCT) is computed first and then it can be used as an intermediate tool to compute other forms of the DCT. The advantage of the SCT is that both the forward SCT and its inverse can be computed by the same method and hardware implementation. Although Clenshaw’s algorithm is the more efficient in computational complexity, it is not necessarily the more accurate one. The computational accuracy of these algorithms is discussed. In addition, the front-to-back forms of Clenshaw and Forsyth’s algorithms are implemented in aCe C, a parallel programming language.