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42
A Theory of Specular Surface Geometry
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1995
"... A theoretical framework is introduced for the perception of specular surface geometry. When an observer moves in threedimensional space, real scene features, such as surface markings, remain stationary with respect to the surfaces they belong to. In contrast, a virtual feature, which is the specula ..."
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Cited by 74 (2 self)
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A theoretical framework is introduced for the perception of specular surface geometry. When an observer moves in threedimensional space, real scene features, such as surface markings, remain stationary with respect to the surfaces they belong to. In contrast, a virtual feature, which is the specular reflection of a real feature, travels on the surface. Based on the notion of caustics, a novel feature classification algorithm is developed that distinguishes real and virtual features from their image trajectories that result from observer motion. Next, using support functions of curves, a closedform relation is derived between the image trajectory of a virtual feature and the geometry of the specular surface it travels on. It is shown that in the 2D case where camera motion and the surface profile are coplanar, the profile is uniquely recovered by tracking just two unknown virtual features. Finally, these results are generalized to the case of arbitrary 3D surface profiles that are trav...
A Theory of Refractive and Specular 3D Shape by Lightpath Triangulation
"... We investigate the feasibility of reconstructing an arbitrarilyshaped specular scene (refractive or mirrorlike) from one or more viewpoints. By reducing shape recovery to the problem of reconstructing individual 3D light paths that cross the image plane, we obtain three key results. First, we show ..."
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Cited by 51 (5 self)
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We investigate the feasibility of reconstructing an arbitrarilyshaped specular scene (refractive or mirrorlike) from one or more viewpoints. By reducing shape recovery to the problem of reconstructing individual 3D light paths that cross the image plane, we obtain three key results. First, we show how to compute the depth map of a specular scene from a single viewpoint, when the scene redirects incoming light just once. Second, for scenes where incoming light undergoes two refractions or reflections, we show that three viewpoints are sufficient to enable reconstruction in the general case. Third, we show that it is impossible to reconstruct individual light paths when light is redirected more than twice. Our analysis assumes that, for every point on the image plane, we know at least one 3D point on its light path. This leads to reconstruction algorithms that rely on an “environment matting” procedure to establish pixeltopoint correspondences along a light path. Preliminary results for a variety of scenes (mirror, glass, etc) are also presented.
Multiview Stereo Beyond Lambert
 In International Conference on Computer Vision and Pattern Recognition
, 2002
"... We consider the problem of estimating the shape and radiance of an object from a calibrated set of views under the assumption that the reflectance of the object is nonLambertian. Unlike traditional stereo, we do not solve the correspondence problem by comparing imagetoimage. Instead, we exploit a ..."
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Cited by 51 (8 self)
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We consider the problem of estimating the shape and radiance of an object from a calibrated set of views under the assumption that the reflectance of the object is nonLambertian. Unlike traditional stereo, we do not solve the correspondence problem by comparing imagetoimage. Instead, we exploit a rank constraint on the radiance tensor field of the surface in space, and use it to define a discrepancy measure between each image and the underlying model. Our approach automatically returns an estimate of the radiance of the scene, along with its shape, represented by a dense surface. The former can be used to generate novel views that capture the nonLambertian appearance of the scene.
Multiview stereo reconstruction of dense shape and complex appearance
 The International Journal of Computer Vision
, 2005
"... appearance models. ..."
Dynamic Refraction Stereo
, 2005
"... In this paper we consider the problem of reconstructing the 3D position and surface normal of points on an unknown, arbitrarilyshaped refractive surface. We show that two viewpoints are sufficient to solve this problem in the general case, even if the refractive index is unknown. The key requiremen ..."
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Cited by 36 (6 self)
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In this paper we consider the problem of reconstructing the 3D position and surface normal of points on an unknown, arbitrarilyshaped refractive surface. We show that two viewpoints are sufficient to solve this problem in the general case, even if the refractive index is unknown. The key requirements are (1) knowledge of a function that maps each point on the two image planes to a known 3D point that refracts to it, and (2) light is refracted only once. We apply this result to the problem of reconstructing the timevarying surface of a liquid from patterns placed below it. To do this, we introduce a novel "stereo matching" criterion called refractive disparity, appropriate for refractive scenes, and develop an optimizationbased algorithm for individually reconstructing the position and normal of each point projecting to a pixel in the input views. Results on reconstructing a variety of complex, deforming liquid surfaces suggest that our technique can yield detailed reconstructions that capture the dynamic behavior of freeflowing liquids.
Local Analysis for 3D Reconstruction of Specular Surfaces
 IEEE Conf. on Computer Vision and Pattern Recognition, II 738–745
, 2001
"... Abstract. We analyze the problem of recovering the shape of a mirror surface. We generalize the results of [1], where the special case of planar and spherical mirror surfaces was considered, extending that analysis to any smooth surface. A calibrated scene composed of lines passing through a point i ..."
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Cited by 35 (3 self)
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Abstract. We analyze the problem of recovering the shape of a mirror surface. We generalize the results of [1], where the special case of planar and spherical mirror surfaces was considered, extending that analysis to any smooth surface. A calibrated scene composed of lines passing through a point is assumed. The lines are reflected by the mirror surface onto the image plane of a calibrated camera, where the intersection and orientation of such reflections are measured. The relationship between the local geometry of the surface around the point of reflection and the measurements is analyzed. We give necessary and sufficient conditions, as well as a practical algorithm, for recovering first order local information (positions and normals) when three intersecting lines are visible. A small number of ‘ghost solutions ’ may arise. Second order surface geometry may also be obtained up to one unknown parameter. Experimental results with real mirror surfaces are presented.
Stereo in the Presence of Specular Reflection
 IN ICCV
, 1995
"... The problem of accurate depth estimation using stereo in the presence of specular reflection is addressed. Specular reflection is viewpoint dependent and can cause large intensity differences at corresponding points. Hence, mismatches can result causing significant depth errors. Current stereo algor ..."
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Cited by 27 (1 self)
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The problem of accurate depth estimation using stereo in the presence of specular reflection is addressed. Specular reflection is viewpoint dependent and can cause large intensity differences at corresponding points. Hence, mismatches can result causing significant depth errors. Current stereo algorithms largely ignore specular reflection which is a fundamental reflection phenomenon from surfaces, both smooth and rough. We analyzed the physics of specular reflection and the geometry of stereopsis which led us to an interesting relationship between stereo vergence, surface roughness, and the likelihood of a correct match. Given the lower bound on surface roughness, an optimal binocular stereo configuration can be determined which maximizes precision in depth estimation despite specular reflection. However, surface roughness is difficult to estimate in unstructured environments. Therefore, multiple view configurations independent of surface roughness are determined such that at each scen...
Towards a Theory of Shape from Specular Flow
 IN PROCEEDINGS OF IEEE INTERNATIONAL CONFERENCE ON COMPUTER VISION (ICCV) (2007
, 2007
"... The image of a curved, specular (mirrorlike) surface is a distorted reflection of the environment. The goal of our work is to develop a framework for recovering general shape from such distortions when the environment is neither calibrated nor known. To achieve this goal we consider farfield illum ..."
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Cited by 24 (6 self)
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The image of a curved, specular (mirrorlike) surface is a distorted reflection of the environment. The goal of our work is to develop a framework for recovering general shape from such distortions when the environment is neither calibrated nor known. To achieve this goal we consider farfield illumination, where the objectenvironment distance is relatively large, and we examine the dense specular flow that is induced on the image plane through relative objectenvironment motion. We show that under these very practical conditions the observed specular flow can be related to surface shape through a pair of coupled nonlinear partial differential equations. Importantly, this relationship depends only on the environment’s relative motion and not its content. We examine the qualitative properties of these equations, present analytic methods for recovery of the shape in several special cases, and empirically validate our results using captured data. We also discuss the relevance to both computer vision and human perception.
Specular Flow and the Recovery of Surface Structure
 In Proc. of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2006
, 2006
"... In scenes containing specular objects, the image motion observed by a moving camera may be an intermixed combination of optical flow resulting from diffuse reflectance (diffuse flow) and specular reflection (specular flow). Here, with few assumptions, we formalize the notion of specular flow, show h ..."
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Cited by 23 (1 self)
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In scenes containing specular objects, the image motion observed by a moving camera may be an intermixed combination of optical flow resulting from diffuse reflectance (diffuse flow) and specular reflection (specular flow). Here, with few assumptions, we formalize the notion of specular flow, show how it relates to the 3D structure of the world, and develop an algorithm for estimating scene structure from 2D image motion. Unlike previous work on isolated specular highlights we use two image frames and estimate the semidense flow arising from the specular reflections of textured scenes. We parametrically model the image motion of a quadratic surface patch viewed from a moving camera. The flow is modeled as a probabilistic mixture of diffuse and specular components and the 3D shape is recovered using an ExpectationMaximization algorithm. Rather than treating specular reflections as noise to be removed or ignored, we show that the specular flow provides additional constraints on scene geometry that improve estimation of 3D structure when compared with reconstruction from diffuse flow alone. We demonstrate this for a set of synthetic and real sequences of mixed speculardiffuse objects.
Stereo and Specular Reflection
 IJCV
, 1998
"... . The problem of accurate depth estimation using stereo in the presence of specular reflection is addressed. Specular reflection, a fundamental and ubiquitous reflection mechanism, is viewpoint dependent and can cause large intensity differences at corresponding points, resulting in significant dept ..."
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Cited by 21 (2 self)
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. The problem of accurate depth estimation using stereo in the presence of specular reflection is addressed. Specular reflection, a fundamental and ubiquitous reflection mechanism, is viewpoint dependent and can cause large intensity differences at corresponding points, resulting in significant depth errors. We analyze the physics of specular reflection and the geometry of stereopsis which lead to a relationship between stereo vergence, surface roughness, and the likelihood of a correct match. Given a lower bound on surface roughness, an optimal binocular stereo configuration can be determined which maximizes precision in depth estimation despite specular reflection. However, surface roughness is difficult to estimate in unstructured environments. Therefore, trinocular configurations, independent of surface roughness, are determined such that at each scene point visible to all sensors, at least one stereo pair can produce correct depth. We have developed a simple algorithm to reconstru...