On the roots of the 3x3, 5+, 5x, 13-pt and 5x5 2D median filters
SIP '07 Proceedings of the Ninth IASTED International Conference on Signal and Image Processing
LULU operators and discrete pulse transform for multidimensional arrays
IEEE Transactions on Image Processing
| Hi-index | 35.68 |
Locally monotonic regression is the optimal counterpart of iterated median filtering. In a previous paper, Restrepo and Bovik (see ibid., vol.41, no.9, p.2796-2810, 1993) developed an elegant mathematical framework in which they studied locally monotonic regressions in RN. The drawback is that the complexity of their algorithms is exponential in N. We consider digital locally monotonic regressions, in which the output symbols are drawn from a finite alphabet and, by making a connection to Viterbi decoding, provide a fast O(|A|2αN) algorithm that computes any such regression, where |A| is the size of the digital output alphabet, a stands for lomo degree, and N is the sample size. This is linear in N, and it renders the technique applicable in practice