Mitigating discontinuities in segmented Karhunen-Loeve Transforms

The Karhunen-Loeve Transform (KLT) is a popular transform used in multiple image processing scenarios. Sometimes, the application of the KLT is not carried out as a single transform over an entire image. Rather, the image is divided into smaller spatial regions (segments), each of which is transformed by a smaller dimensional KLT. Such a situation may penalize the transform efficiency. An improvement for the segmented KLT, aiming at mitigating discontinuities arising on the edge of adjacent regions, is proposed in this paper. In the case of moderately varying image regions, discontinuities occur as the consequence of disregarded similarity between transform domains, as the order and sign of eigenvectors in the transform matrices are mismatched. In the proposed method, the KLT is adjusted to guarantee the best achievable similarity via the optimal assignment and sign correspondence for eigenvectors. Experimental results indicate that the proposed transform improves the similarity between transform domains, and reduces RMSE on the edge of adjacent regions. In consequence, images processed by the adjusted KLT present better cohesion and continuity between independently transformed regions.