This paper introduces single-image 3D scene reconstruction from water reflection photography, i.e., images capturing direct and water-reflected real-world scenes. Water reflection offers an additional viewpoint to the direct sight, collectively forming a stereo pair. The water-reflected scene, however, includes internally scattered and reflected environmental illumination in addition to the scene radiance, which precludes direct stereo matching. We derive a principled iterative method that disentangles this scene radiometry and geometry for reconstructing 3D scene structure as well as its high-dynamic range appearance. In the presence of waves, we simultaneously recover the wave geometry as surface normal perturbations of the water surface. Most important, we show that the water reflection enables calibration of the camera. In other words, we show that capturing a direct and water-reflected scene in a single exposure forms a self-calibrating catadioptric stereo camera. We demonstrate our method on a number of images taken in the wild. The results demonstrate a new means for leveraging this accidental catadioptric camera.
Stereo matching with translucency , @cite_20 @cite_3 or image-based reflection separation , @cite_14 @cite_22 @cite_32 @cite_16 explicitly model transmission through semi-translucent surfaces. They utilize either 3D recovery or models in the Fourier domain for blind separation of reflected and transmitted images. They cannot, however, be applied to non-planar surfaces such as wavy water surfaces.
@cite_14 @cite_22 @cite_32 @cite_3 @cite_16 @cite_20
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In this paper, we address the stereo matching problem in the presence of reflections and translucency, where image formation can be modeled as the additive superposition of layers at different depth. The presence of such effects violates the Lambertian assumption underlying traditional stereo vision algorithms, making it impossible to recover component depths using direct color matching based methods. We develop several techniques to estimate both depths and colors of the component layers. Depth hypotheses are enumerated in pairs, one from each layer, in a nested plane sweep. For each pair of depth hypotheses, we compute a component-color-independent matching error per pixel, using a spatial-temporal differencing technique. We then use graph cut optimization to solve for the depths of both layers. This is followed by an iterative color update algorithm whose convergence is proven in our paper. We show convincing results of depth and color estimates for both synthetic and real image sequences. Convolutive mixtures of images are common in photography of semi-reflections. They also occur in microscopy and tomography. Their formation process involves focusing on an object layer, over which defocused layers are superimposed. We seek blind source separation (BSS) of such mixtures. However, achieving this by direct optimization of mutual information is very complex and suffers from local minima. Thus, we devise an efficient approach to solve these problems. While achieving high quality image separation, we take steps that make the problem significantly simpler than a direct formulation of convolutive image mixtures. These steps make the problem practically convex, yielding a unique global solution to which convergence can be fast. The convolutive BSS problem is converted into a set of instantaneous (pointwise) problems, using a short time Fourier transform (STFT). Standard BSS solutions for instantaneous problems suffer, however, from scale and permutation ambiguities. We overcome these ambiguities by exploiting a parametric model of the defocus point spread function. Moreover, we enhance the efficiency of the approach by exploiting the sparsity of the STFT representation as a prior. We apply our algorithm to semi-reflections, and demonstrate it in experiments. This paper provides an introduction to photometric methods for image-based 3D shape reconstruction and a survey of photometric stereo techniques. We begin with taxonomy of active and passive shape acquisition techniques. Then we describe the methodical background of photometric 3D reconstruction, define the canonical setting of photometric stereo (Lambertian surface reflectance, parallel incident light, known illumination direction, known surface albedo, absence of cast shadows), discuss the 3D reconstruction of surfaces from local gradients, summarize the concept of the bidirectional reflectance distribution function (BRDF), and outline several important empirically and physically motivated reflectance models. We provide a detailed treatment of several generalizations of the canonical setting of photometric stereo, namely non-distant light sources, unknown illumination directions, and, in some detail, non-Lambertian surface reflectance functions. An important special case is purely specular reflections, where an extended light source allows capturing a surface that consists of perfectly specular surface patches. Linear combinations of purely Lambertian and purely specular reflectance components are favorably used for reconstructing smooth surfaces and also human skin. Nonuniform surface reflectance properties are estimated based on a simultaneous 3D reconstruction and determination of the locally variable parameters of the reflectance function based on a multitude of images. Assuming faceted surfaces, the effective resolution of the 3D reconstruction result can be increased to some extent beyond that of the underlying images. Other approaches separate specular and diffuse reflectance components based on polarization data or color information. The specular reflections can be used additionally to estimate the direction from which the surface is illuminated. Finally, we describe methods to combine photometric 3D reconstruction techniques with active and passive triangulation-based approaches. Translucency introduces great challenges to 3-D acquisition because of complicated light behaviors such as refraction and transmittance. In this paper, we describe the development of a unified 3-D data acquisition framework that reconstructs translucent objects using a single commercial time-of-flight (ToF) camera. In our capture scenario, we record a depth map and intensity image of the scene twice using a static ToF camera; first, we capture the depth map and intensity image of an arbitrary background, and then we position the translucent foreground object and record a second depth map and intensity image with both the foreground and the background. As a result of material characteristics, the translucent object yields systematic distortions in the depth map. We developed a new distance representation that interprets the depth distortion induced as a result of translucency. By analyzing ToF depth sensing principles, we constructed a distance model governed by the level of translucency, foreground depth, and background depth. Using an analysis-by-synthesis approach, we can recover the 3-D geometry of a translucent object from a pair of depth maps and their intensity images. Extensive evaluation and case studies demonstrate that our method is effective for modeling the nonlinear depth distortion due to translucency and for reconstruction of a 3-D translucent object.