Multi-Scale Surface Reconstruction from Images

Many surface reconstruction algorithms have been developed to process point data originating from laser scans. Because laser scanning is a very expensive technique and not available to everyone, 3D reconstruction from images (using, e.g., multi-view stereo) is a promising alternative. In recent years a lot of progress has been made in the computer vision domain and nowadays algorithms are capable of reconstructing large 3D scenes from consumer photographs. Whereas laser scans are very controlled and typically only a few scans are taken, images may be subject to more uncontrolled variations. Standard multi-view stereo algorithms give rise to multi-scale data points due to different camera resolutions, focal lengths, or various distances to the object. When reconstructing a surface from this data, the multi-scale property has to be taken into account because the assumption that the points are samples from the true surface might be violated. This thesis presents two surface reconstruction algorithms that take resolution and scale differences into account. In the first approach we model the uncertainty of each sample point according to its footprint, the surface area that was taken into account during multi-view stereo. With an adaptive volumetric resolution, also steered by the footprints of the sample points, we achieve detailed reconstructions even for large-scale scenes. Then, a general wavelet-based surface reconstruction framework is presented. The multi-scale sample points are characterized by a convolution kernel and the points are fused in frequency space while preserving locality. We suggest a specific implementation for 2.5D surfaces that incorporates our theoretic findings about sample points originating from multi-view stereo and shows promising results on real-world data sets. The other part of the thesis analyzes the scale characteristics of patch-based depth reconstruction as used in many (multi-view) stereo techniques. It is driven by the question how the reconstruction preserves surface details or high frequencies. We introduce an intuitive model for the reconstruction process, prove that it yields a linear system and determine the modulation transfer function. This allows us to predict the amplitude loss of high frequencies in connection with the used patch-size and the internal and external camera parameters. Experiments on synthetic and real-world data demonstrate the accuracy of our model but also show the limitations. Finally, we propose a generalization of the model allowing for weighted patch fitting. The reconstructed points can then be described by a convolution of the original surface and we show how weighting the pixels during photo-consistency optimization affects the smoothing kernel. In this way we are able to connect a standard notion of smoothing to multi-view stereo reconstruction. In summary, this thesis provides a profound analysis of patch-based (multi-view) stereo reconstruction and introduces new concepts for surface reconstruction from the resulting multi-scale sample points

Modulation transfer function of patch-based stereo systems

A widely used technique to recover a 3D surface from photographs is patch-based (multi-view) stereo reconstruction. Current methods are able to reproduce fine surface details, they are however limited by the sampling density and the patch size used for reconstruction. We show that there is a systematic error in the reconstruction depending on the details in the unknown surface (frequencies) and the reconstruction resolution. For this purpose we present a theoretical analysis of patch-based depth reconstruction. We prove that our model of the reconstruction process yields a linear system, allowing us to apply the transfer (or system) function concept. We derive the modulation transfer function theoretically and validate it experimentally on synthetic examples using rendered images as well as on photographs of a 3D test target. Our analysis proves that there is a significant but predictable amplitude loss in reconstructions of fine scale details. In a first experiment on real-world data we show how this can be compensated for within the limits of noise and reconstruction accuracy by an inverse transfer function in frequency space