Smooth local sinusoidal bases on two-dimensional L-shaped regions

In this article, we construct two-dimensional continuous/smooth local sinusoidal bases (also called Malvar wavelets) defined onL-shaped regions. With this construction, one is able to construct local sinusoidal bases and lapped orthogonal transforms (LOT) on arbitrarily shaped regions. This work is motivated from and useful in object-based video coding, where a segmented moving object may have arbitrary shape and block transform coding of this object is needed. Acknowledgements and Notes. His work was partially supported by an initiative grant from the Department of Electrical and Computer Engineering, University of Delaware, the Air Force Office of Scientific Research (AFOSR) under Grant No. F49620-97-1-0253, and the National Science Foundation CAREER Program under Grant MIP-9703377.