Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions

Gabor schemes of multiscale image representation are useful in many computer vision applications. However, the classic Gabor expansion is computationally expensive due to the lack of orthogonality of Gabor functions. Some alternative schemes, based on the application of a bank of Gabor filters, have important advantages such as computational efficiency and robustness, at the cost of redundancy and lack of completeness. In a previous work we proposed a quasicomplete Gabor transform, suitable for fast implementations in either space or frequency domains. Reconstruction was achieved by simply adding together the even Gabor channels. In this work, we develop an optimized spatial-domain implementation, using one-dimensional, 11-tap filter masks, that is faster and more flexible than Fourier implementations. The reconstruction method is improved by applying fixed and independent weights to the Gabor channels before adding them. Finally, we analyze and implement, in the spatial domain, two ways to incorporate a high-pass residual, which permits a visually complete representation of the image.