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This paper describes a method for scene reconstruction of complex, detailed environments from 3D light fields. Densely sampled light fields in the order of 109 light rays allow us to capture the real world in unparalleled detail, but efficiently processing this amount of data to generate an equally detailed reconstruction represents a significant challenge to existing algorithms. We propose an algorithm that leverages coherence in massive light fields by breaking with a number of established practices in image-based reconstruction. Our algorithm first computes reliable depth estimates specifically around object boundaries instead of interior regions, by operating on individual light rays instead of image patches. More homogeneous interior regions are then processed in a fine-to-coarse procedure rather than the standard coarse-to-fine approaches. At no point in our method is any form of global optimization performed. This allows our algorithm to retain precise object contours while still ensuring smooth reconstructions in less detailed areas. While the core reconstruction method handles general unstructured input, we also introduce a sparse representation and a propagation scheme for reliable depth estimates which make our algorithm particularly effective for 3D input, enabling fast and memory efficient processing of "Gigaray light fields" on a standard GPU. We show dense 3D reconstructions of highly detailed scenes, enabling applications such as automatic segmentation and image-based rendering, and provide an extensive evaluation and comparison to existing image-based reconstruction techniques.