Efficient Gradient-Domain Compositing Using an Approximate Curl-free Wavelet Projection

Abstract

Gradient-domain compositing has been widely used to create a seamless composite with gradient close to a composite gradient field generated from one or more registered images. The key to this problem is to solve a Poisson equation, whose unknown variables can reach the size of the composite if no region of interest is drawn explicitly, thus making both the time and memory cost expensive in processing multi-megapixel images. In this paper, we propose an approximate projection method based on biorthogonal Multiresolution Analyses (MRA) to solve the Poisson equation. Unlike previous Poisson equation solvers which try to converge to the accurate solution with iterative algorithms, we use biorthogonal compactly supported curl-free wavelets as the fundamental bases to approximately project the composite gradient field onto a curl-free vector space. Then, the composite can be efficiently recovered by applying a fast inverse wavelet transform. Considering an n-pixel composite, our method only requires 2n of memory for all vector fields and is more efficient than state-of-the-art methods while achieving almost identical results. Specifically, experiments show that our method gains a 5x speedup over the streaming multigrid in certain cases.