This paper presents a new method for light field applications such as content replacement and fusion in the gradient domain. This approach is inspired by successful gradient domain based image and video editing techniques. A necessary and important part of gradient‐based solutions is recovering the signal of interest from artificially generated, and typically non‐integrable, gradient data. As such, a new algorithm is developed to reconstruct a light field from a given gradient data set. In the algorithm, first, the 4D Haar wavelet decomposition of the light field is obtained from the given gradient data. Then, the light field is obtained from a wavelet synthesis step. This algorithm is intended as a building block for gradient‐based light field editing methods, and as such, its performance is analysed on a set of benchmark light field data sets. The proposed reconstruction algorithm is an essential part in developing solutions for two light field problems: light field editing and light field fusion. Results show that processing light fields in the gradient domain offers significant advantages over processing in the intensity domain.

An efficient wavelet-based algorithm to reconstruct non-square/non-cubic signals from gradient data is proposed. This algorithm is motivated by applications such as image or video processing in the gradient domain. In some earlier approaches, the non-square/non-cubic gradients were extended to enable a square/cubic Haar wavelet decomposition and the coarsest resolution subband was derived from the mean value of the signal. In this paper, a non-square/non-cubic wavelet decomposition is obtained directly without extending the gradient data. The challenge comes from finding the coarsest resolution subband of the wavelet decomposition and an algorithm to compute this is proposed. The performance of the algorithm is evaluated in terms of accuracy and computation time, and is shown to outperform the considered earlier approaches in a number of cases. Further, a closer look on the role of the coarsest resolution subband coefficients reveals a trade-off between errors in reconstruction and visual quality which has interesting implications in image and video processing applications.