Real-Time Image Analysis Using MIMD Parallel à trous Wavelet Algorithms

Abstract

The à trous algorithm represents a discrete approach to the classical continuous wavelet transform. Similar to the fast or pyramidal wavelet transform, the input signal is analysed by using the coefficients of a properly chosen low-pass filter, but in contrast to the latter, all frequency sub bands are retained with full resolution. Therefore, this algorithm is much more demanding in terms of computational complexity compared to the fast wavelet transform and requires some sort of acceleration in order to satisfy real-time constraints. In this paper we develop parallel algorithms for different MIMD architectures for the two-dimensional à trous decomposition. In particular, classical border treatment strategies are discussed and compared in the context of data partitioning. It turns out that in contrast to the fast wavelet transform, the proper choice of a border treatment strategy does not depend on the underlying hardware. Additionally, only low scalability is achieved on multi-computers and multi-processors when employing the message passing paradigm, whereas much better behaviour is observed on multi-processors using the shared memory programming model.